No subject

thread of my scientific/intellectual life -- a process which has continued 
ever  since.  
 
Central to that pursuit of Marxian theory has been the question of the  
clarification and further development of the Marxian dialectic.
 
Thus, I have been on the lookout for developments regarding the Marxian  
dialectic for many years.
 
However, apart from contributions by Bertell Ollman, Tony Smith, and others  
regarding Dialectics and the Philosophy of Internal Relations, and regarding  
Systematic Dialectics vs. Historical Dialectics, respectively, plus some of 
the  work in the Value-Form Dialectic tradition, the pickings have been slim,  
especially with regard to "Historical Dialectics", "the Dialectic of Nature",  
and the relation of the Marxian Dialectic to the critique of the ideology in  
Modern Science [including in the "natural sciences", not just in the 
ideological  science(s) of classical political economy, or of modern "economics"].
 
Thus I was quite excited when, some time ago, I ran a search on a phrase --  
the phrase: historical dialectical algebra -- whose "returns" pointed  to the 
following site:
 
_http://www.dialectics.org/current.htm_ 
(http://www.dialectics.org/current.htm)   
 
The remainder of this post is a review of what, to my knowledge, is  new and 
unprecedented about the large number of texts posted to that site.
 
______________________________________________________________________________
______________________________________________________________________________
___________ 
 
The texts posted to the dialectics.org site contain a large number of  
"dialectical mathematical models", for both "systematic dialectics" and  "historical 
dialectics", including for the "historical dialectic of human social  
meta-evolution", and for "the dialectic of nature" as "the historical dialectic  of 
cosmological natural history".  
 
"Dialectical-mathematical models" for "systematic dialectics"  include models 
that generate "category-progressions", including a model  that -- sketchily 
-- reproduces much of the "categorial progression" of the  table of contents of 
Hegel's "Science of Logic", starting with a category-value  that is assigned 
to the category of "Being-in-General", and a model that  reproduces major 
portions of the chapter and sub-chapter progression of Marx's  "Capital:  A 
Critique of Political Economy", starting from a category-value  that is assigned to 
the category of Chapter I of "Capital", Section A -- the  category called by 
Marx "The Elementary or Accidental Form of Value".
 
For a graphical rendition of the historical "dialectic of nature" model,  see 
slides #s 12-14 at:
 
_http://www.dialectics.org/archives/pdf/F.E.D.,Dialectical%20Pictography,Part%
20II.,Historical%20Dialectics,04MAR2008.pdf_ 
(http://www.dialectics.org/archives/pdf/F.E.D.,Dialectical%20Pictography,Part%20II.,Historical%20Dialectics,04M
AR2008.pdf)  
(http://www.dialectics.org/archives/pdf/F.E.D.,Dialectical%20Pictography,Part%20I.,Systematic%20Dialectics,05MAR2008.pdf) 
 
For a graphical rendition of the "historical dialectic" of "the  
meta-evolution of the social relations of production" model, see slides #s  8-11 via the 
same URL.
 
For a graphical rendition of the "systematic-dialectical model" of Hegel's  
"Logik", see slide #27at:
 
_http://www.dialectics.org/archives/pdf/F.E.D.,Dialectical%20Pictography,Part%
20I.,Systematic%20Dialectics,05MAR2008.pdf_ 
(http://www.dialectics.org/archives/pdf/F.E.D.,Dialectical%20Pictography,Part%20I.,Systematic%20Dialectics,05MAR
2008.pdf) 
 
For a graphical rendition of the "systematic-dialectical model" of Marx's  
"Capital", see slide #38  via the same URL.
 
However, the crux of all of these models appears to be a new "mathematics  of 
dialectics", though this "new" mathematics apparently also harks back, as  a 
"psycho-historical materialist" DE-inversion, to the mysterious,  idealistic 
"dialectical arithmetic" of "unaddible, qualitative numbers" of  Plato's 
"arithmoi eidetikoi", his "arithmetic of ideas".
 
This new "arithmetic of dialectics", that "undergirds" the "algebra of  
dialectics" used in most of this website's plethora of  "dialectical-mathematical 
models", is billed as a  "Contra-Boolean Arithmetic and Algebra", and as a 
"Non-Standard Model"  of "Natural Arithmetic", i.e., of the arithmetic of the 
"set" of  numbers that "Standard" mathematicians often symbolize by N, which 
stands  for the "infinite" set of numbers { 1, 2, 3, ... }.
 
The site's texts note that the "CO-necessity" of "NON-Standard Models of  
Natural Arithmetic", given that of the Standard Model, was "predicted" by the  
joint implications of the "Godel Completeness and Incompleteness Theorems", and  
also by something called the "Lowenheim-Skolem Theorem", but that official  
"Standard" mathematics has failed to explore these "NON-Standard  Arithmetics". 
 That is at least one of the reasons why these texts describe  their content 
as "A Contribution to the Immanent Critique of  Arithmetic".
 
The site's texts characterize the system of "Natural Numbers Arithmetic" as  
an arithmetic of "pure, unqualified quantifiers", i.e., not of, e.g.,  "3 
cats", or of "3 anythings", but just of "3 [period]".  
 
Those texts then characterize the initial "dialectical arithmetic" as a  
diametrical opposite to that "Standard Natural Arithmetic"; as  a "contra-thesis" 
to that "arche' thesis" of "Natural Arithmetic", that is,  as an arithmetic of 
"pure, UNquantifiable qualifiers", which stand  for "ontological qualifiers"! 
 Yes!, as an "arithmetic" of "numbers"  and "numerals" that are 
"purely-qualitative".  
 
These "qualitative numbers" they call "meta-numbers".
 
These texts even use a "non-standard" symbol to stand for "non-quantitative  
inequality", or "qualitative inequality", which is a greater-than  sign, ">", 
stacked on top of an equals sign, "_", stacked on top of  a less-than sign, 
"<", with a vertical slash through all three signs to  indicate their joint 
negation, meaning "neither greater than or equal to, nor  less than or equal to".  
 
They describe how the system of arithmetic of the "purely-quantitative"  
"Natural" numbers gives rise, "systematic-dialectically", to the  second system of 
"dialectical arithmetic", of purely-qualitative "meta-numbers",  forming the 
"non-amalgamative", "non-reductionist", or "irreducible" sum,  or 
"antithesis-sum", of the first two systems in a "CO-presence" or  "CO-positing".
 
They then describe how that very "CO-positing" also  
"systematically-dialectically" gives rise to a third system of arithmetic, as  the "first uni-thesis" 
of the "first thesis" system and the "first  contra-thesis" system, a 
"quanto-qualitative" language of arithmetic, involving  even-more-meta "meta-numbers", 
each of which stands for a  different "QUANTIFIABLE ontological qualifier".
 
This step therefore yields a "CO-presence" of all three systems of  
arithmetic, forming a "non-amalgamative", "non-reductionist", or "irreducible"  "sum", 
the first "synthesis-sum" of systems of arithmetic.  
 
That "CO-positing" of the three system then  generates, 
"systematically-dialectically", a new, fourth system of  arithmetic, as a new, second 
"contra-thesis" to the totality formed by the  previous three. 
 
The "systematic-dialectical" derivation of increasingly "rich in  descriptive 
power", "increasingly complex/concrete" dialectical-mathematical  languages 
-- systems of "arithmetic" -- builds ever onwards from there.
 
These texts even model this "categorial progression" of higher and higher  
dialectical languages, of higher and higher systems of dialectical  arithmetic, 
using the first "dialectical arithmetic", by assigning, to  the first 
"meta-number" of that "dialectical arithmetic",  the "connotations", or "intuition", 
or "intension" of the category of  the "first-order", "purely-Quantitative" 
Natural Arithmetic,  N, so that the "self-reflexion'", or "immanent critique", of 
that  system of arithmetic, "N confronting N itself", or NN, or  N "of" N, or 
N-"squared", yields [N +  delta-N] as [N + Q], where Q represents that  first 
"dialectical arithmetic", the "pure-Qualitative arithmetic" of  dialectical 
categories.
 
This means "N of N" -- N "times" N, or N  "operating on itself" -- which is 
described as modeling the "aufheben  self-negation" of N, which "conserves" N 
in the product, N  + Q, but also "elevates" and "annuls" N, in the  opposite, 
delta-N or Q component of that  product-sum, N + Q.
 
The "self-reflexion", or "self-critique", of the  "antithesis-sum", [N + Q], 
namely [N + Q] "of"  [N + Q], or the "[inner] self-confrontation", [N +  Q][N 
+ Q], or [N + Q]-"squared", in turn,  yields  [N + Q + U + M], where U stands  
for the "uni-thesis" system/category, reconciling the antithesis of the  
systems/categories N and Q -- with the category U  thus connoting the first 
"Quanto-Qualitative Arithmetic" -- and where M  connotationally stands for the 
category/system of "pure, UNquantifiable  Metrical Qualifiers", or "the 
[rudimentary] Arithmetic of Dimensional  Analysis".  And so on, to the "self-squaring" of 
[N + Q  + U + M], and beyond.
 
For graphical renditions of the generic dialectical meaning of the  
succession of the Q "ontological qualifier meta-numerals" or  "dialectors", and of 
their "arithmetical operations", see slides #s 22  through 25,  at:  
 
_http://www.dialectics.org/archives/pdf/F.E.D.,Dialectical%20Pictography,Part%
20III.,Meta-Systematic%20Dialectics,05MAR2008.pdf_ 
(http://www.dialectics.org/archives/pdf/F.E.D.,Dialectical%20Pictography,Part%20III.,Meta-Systematic%20Di
alectics,05MAR2008.pdf) 
 
For a graphical rendering of the "Q dialectical model of the  dialectic of 
the systems of dialectical arithmetic, including Q", see  slide # 21, via the 
same URL.
 
The "dialectical-mathematical models" written, in these texts, in the  
algebra of the "interpreted" or "assigned" Q arithmetic, are  "connotative", 
"heuristic", and "intuitive" models, even though the calculations  of the 
"undergirding" arithmetic of the "uninterpreted" or "unassigned"  Q "meta-numerals" are 
purely "algorithmic" and "mechanical".
 
To me, this makes the Q models hard to pin down, kind of slippery,  hazy, and 
indefinite.
 
The site texts often acknowledge this defect, but assert that this  defect is 
progressively overcome in the "meta-system-atic" dialectical  progression of 
the higher categories/systems of dialectical mathematics, that  issue from N 
and Q, according to the Q model of that very  progression, with each successive 
system/category of dialectical mathematics  capable of modeling with greater 
clarity, greater "determinateness", greater  "complexity/concreteness", than 
any of its predecessor systems/categories.
 
They give a sample of these higher systems/categories of dialectical  
mathematics at the same URL, which they claim even overcomes some of the  chief 
defects of Standard "Nonlinear Dynamical Systems Theory", providing a  
"Meta-Dynamics" of "System Self-Revolution" which even makes sense of the  "infinitely 
erroneous infinite-values" of "Nonlinear Dynamical Systems Models"  which contain 
"zero-division conversion singularities". See slides #s 26-34 for  more on 
the higher/later arithmetic-systems/categories in the  
systems-progression/categories-progression that starts from the antithesis  of N and Q.
 
The fundamental concept of this site seems to be that every dialectical  
system is Janus-faced, with one face of its two-sided-ness being its outer face,  
or explicit face, the other face being its inner face, or implicit face  -- 
its suppressed, hidden, or occult face -- i.e., that every dialectical  
system/[sub-]totality contains an "intra-duality" or "self-duality" that is an  
inescapable feature of its very nature or essence, of its very "self", and that  
drives that systems self-development, "self-change", or  "auto-kinesis".
 
The "internal evolution", or "self-development" of that system/sub-totality  
gradually -- and then suddenly -- "outers" that inner face, in the form of an  
apparently separate, opposing system.  
 
This "outering" of the formerly suppressed face constitutes the first kind  
of "aufheben system self-revolution". 
 
The resulting opposing systems then eventually combine, or "hybridize",  into 
an apparently also separate, third system, with the second system  exercising 
a "real domination" or "real subsumption" of/over the first system,  in that 
"hybrid unity" or "complex unity".  However, an "uneven and  combined 
development", or "aufheben", "evolute" pattern, as opposed to a  "convolute", 
"erasive" pattern, is generally expected, where examples of  the first and second 
system may continue to be extant, even after the third  system has emerged.
 
This "hybridization" constitutes the second kind of "aufheben system  
self-revolution", or "meta-evolution".
 
So, this site's "algebra of dialectics" is, in the above-stated sense, an  
"algebra of revolution".
 
That algebra models historical dialectic as a many-system  
systems-progression, which its texts call a "diachronic meta-system", with each  "successor 
system" separated from its "predecessor system" in that  "systems-progression" by 
the gulf/rift created  by the immanent, "self-aufheben" self-revolutionization 
of that  predecessor system, the very revolution which gives rise to its 
successor system  in the first place.
 
Thoughts?
 
 
 
 



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