"Meristem" and "Tail" ["Evolute-ness"] in Systematic-Dialectical Categories-Progressions as Marxian "Method of Presentation" -- Continuation of Immediately Preceding Blog-Entry
Dear Reader,
There are two key passages from Hegel's writings on dialectic -- passages that are, for the most part, not compromised by those elements of Idealism and subject/object inversion that form the focus of Marx's critique of Hegel's ideology -- which give Hegel's description of the "evolute" structure of his gigantic Systematic-Dialectical categorial progressions, e.g., in his works on <<Logik>>, <<Natur>>, and <<Geist>> [i.e., on "Spirit", on "Mind" -- on humanity, or human-<<Natur>> ["objective spirit"] ].
These two passages imply Hegel's justifications for his "evolute" mode of categories-presentation.
These passages also show that, despite his opposition to mathematics as a philosophical <<organon>>, or instrument of knowledge, and despite the fact that he could not have possessed an axiomatically-developed dialectical algebra, such as that of the F.E.D. NQ dialectical arithmetic, that Hegel did have an algorithm of a sort in mind for his Dialectic.
The first passage is from the concluding section of Hegel's <<Logik>>, where he addresses "The Absolute Method", i.e., the method of presentation of philosophical-scientific content that, per Hegel, satisfies all criticism, from all sides --
"... 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[ '«speci»-ficity' -- M.D.] which was a result is itself, by virtue of the form of simplicity into which it has withdrawn, a fresh beginning; as this beginning is distinguished from its predecessor precisely by that determinateness, cognition rolls onward from content to content.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 [ '«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. [This last is an assertion by Hegel of what we have termed above, and in the immediately-previous previous blog-entry, the '«aufheben» evoluteness' of dialectic -- M.D.]."
Source:
[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 and square-bracketed commentary added]].
Thus, the content of Hegel's <<Logik>> is not a mere "convolute" succession of individual categories --
pure, immediate Being ---> Nothing ---> Becoming ---> . . .
-- but, on the contrary, is the ["self-"]advancing ['''evolute'''] "cumulum" --
Being ---> Being + Nothing ---> Being + Nothing + Becoming ---> . . .
-- or, per F.E.D.'s Systematic-Dialectics model, is --
)-|-(stage = s = (Being)^(2^s):
)-|-(stage = 0 = Being
)-|-(stage = 1 = Being + Nothing
.
.
.
-- etc.
The second passage from Hegel, below, reveals -- more clearly than does any other that I have ever read -- the generic "mental, qualitative algorithm" that Hegel had in mind for dialectic -- an algorithm that is, in my opinion, aptly captured by the F.E.D. axioms for their NQ dialectical arithmetic, which were posited in this blog in an earlier blog entry --
"The first determination [ '«speci»-fication' ] 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 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 dialectic -- M.D.}
Whereas, in what preceded, each [momentarily immediate] determination … passed as ultimate { i.e., when it was the vanguard determination; the "meristem" -- M.D.}, it is now demoted into being only a moment { i.e., as it has become "just another" -- the latest -- part of the "Tail" -- M.D.}. . ."
Dear Reader,
There are two key passages from Hegel's writings on dialectic -- passages that are, for the most part, not compromised by those elements of Idealism and subject/object inversion that form the focus of Marx's critique of Hegel's ideology -- which give Hegel's description of the "evolute" structure of his gigantic Systematic-Dialectical categorial progressions, e.g., in his works on <<Logik>>, <<Natur>>, and <<Geist>> [i.e., on "Spirit", on "Mind" -- on humanity, or human-<<Natur>> ["objective spirit"] ].
These two passages imply Hegel's justifications for his "evolute" mode of categories-presentation.
These passages also show that, despite his opposition to mathematics as a philosophical <<organon>>, or instrument of knowledge, and despite the fact that he could not have possessed an axiomatically-developed dialectical algebra, such as that of the F.E.D. NQ dialectical arithmetic, that Hegel did have an algorithm of a sort in mind for his Dialectic.
The first passage is from the concluding section of Hegel's <<Logik>>, where he addresses "The Absolute Method", i.e., the method of presentation of philosophical-scientific content that, per Hegel, satisfies all criticism, from all sides --
"... 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 [ '«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. [This last is an assertion by Hegel of what we have termed above, and in the immediately-previous previous blog-entry, the '«aufheben» evoluteness' of dialectic -- M.D.]."
Source:
[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 and square-bracketed commentary added]].
Thus, the content of Hegel's <<Logik>> is not a mere "convolute" succession of individual categories --
pure, immediate Being ---> Nothing ---> Becoming ---> . . .
-- but, on the contrary, is the ["self-"]advancing ['''evolute'''] "cumulum" --
Being ---> Being + Nothing ---> Being + Nothing + Becoming ---> . . .
-- or, per F.E.D.'s Systematic-Dialectics model, is --
)-|-(stage = s = (Being)^(2^s):
)-|-(stage = 0 = Being
)-|-(stage = 1 = Being + Nothing
)-|-(stage = 2 = Being + Nothing + Becoming +
Determinate Being.
.
.
-- etc.
The second passage from Hegel, below, reveals -- more clearly than does any other that I have ever read -- the generic "mental, qualitative algorithm" that Hegel had in mind for dialectic -- an algorithm that is, in my opinion, aptly captured by the F.E.D. axioms for their NQ dialectical arithmetic, which were posited in this blog in an earlier blog entry --
"The first determination [ '«speci»-fication' ] 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 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 dialectic -- M.D.}
Whereas, in what preceded, each [momentarily immediate] determination … passed as ultimate { i.e., when it was the vanguard determination; the "meristem" -- M.D.}, it is now demoted into being only a moment { i.e., as it has become "just another" -- the latest -- part of the "Tail" -- M.D.}. . ."
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