Below is the opening exchange of a possible new internet dialogue.
Furthermore, there are instances in Capital itself where Marx does not at all “coquet” with Hegel’s distinct phraseology, but makes clear and emphatic statements regarding the general validity of the old philosopher’s insights. And without a hint of irony. Marx writes:
[T]he possessor of money or commodities actually turns into a capitalist only where the minimum sum advanced for production greatly exceeds the known medieval maximum. Here, as in natural science, is shown the correctness of the law discovered by Hegel, in his Logic, that at a certain point merely quantitative differences pass over by a dialectical inversion into qualitative distinctions. (Capital, pg. 423)
In the footnote attached to the end of this sentence, Marx adds: “The molecular theory of modem chemistry, first scientifically worked out by Laurent and Gerhardt, rests on no other law.”
As if this weren’t enough on its own, Marx further explains what he meant by this in a letter to Engels dated June 22 1867:
Incidentally, you will see from the conclusion to my Chapter III, where I outline the transformation of the master of a trade into a capitalist — as a result of purely quantitative changes — that in the text there I quote Hegel’s discovery of the law of the transformation of a merely quantitative change into a qualitative one as being attested by history and natural science alike. In the note to the text (I was as it happened attending Hofmann’s lectures at that time) I mention the molecular theory, but not Hofmann, who has discovered nothing in the matter except contributing general direction; instead I do mention Laurent, Gerhardt, and Wurtz, the latter being the real man.
What further proof is needed?”
Blog-entry URL: http://thecharnelhouse.org/2014/06/25/pour-hegel-marxs-lifelong-debt-to-hegelian-dialectics/
Since the lifetimes of Marx and Engels, their “followers” have generally done little to reconstruct the “dialectical method” that -- as you document so well in the blog entry above -- was of such central and crucial importance to revolutionary theory and practice in the views of both of them, and as Marx testified, again and again, e.g., in the passages from his books, letters, and manuscripts, many of which you cite.
That is changing.
There is a research collective which, at an accelerating rate, starting from 1999, has made publicly available a series of results, rooted in their extraction, in a Marxian, demystified manner, of the core mental operation, the ‘cognitive algorithm’, of Marx’s and Hegel’s dialectic -- the “fundamental law of dialectical process” -- and deployed that algorithm in the form of an intuitive, heuristic notation, capable of encoding both the Marxian, dialectical method of inquiry, and, in another interpretation, the Marxian, dialectical method of exposition, a veritable ‘dialectical ideography’, or ‘dialectical algebra’ -- indeed, a realization of viable aspects of Leibniz’s dream: a dialectical “characteristica universalis”.
Not surprisingly, the ‘dialectical arithmetic’ that undergirds this ‘mathematics of dialectics’ arises, via an immanent critique of the Boolean algebra of formal logic, as a ‘contra-Boolean arithmetic’, whose axioms imply a theorem that is a strong contrary of Boole’s “fundamental law of thought”.
This dialectical arithmetic co-arises as the fruition of an immanent critique of the foundational arithmetic of the so-called “Natural” Numbers, as a “Non-Standard Model” of the first order axioms of that “Standard Model”.
Such “Non-Standard” models of “Natural” arithmetic are implied by three of the deepest theorems of modern mathematics, but not constructively so.
This research collective -- Foundation Encyclopedia Dialectica -- has axiomatically constructed their ‘arithmetic of dialectics’ as a non-standard model of first-order “Natural” arithmetic.
Their ‘dialectical organon’ is, again, interpretable in the mode of the presentation of a present totality, i.e., as a categorial progression, with the symbols of the successive categories generated, by their dialectical model, in systematic order [‘‘‘systematic dialectic’’’].
It is also interpretable in the mode of a categorial recapitulation / ‘pre-capitulation’, or reconstruction / ‘pre-construction’ [prediction], of a chronological, causal progression, in chronological order [‘‘‘historical dialectic’’’].
They have recently applied this ‘dialectical ideography’ to reconstruct the high-level [tables of] contents of the 6+ treatises planned by Marx for his full “Critique of Political Economy”, of which only the first treatise, Capital, volumes I through IV, was even partly completed by Marx.
The main site for the free of charge distribution of these works is: www.dialectics.org.
Related sites include --
Applications of the whole dialectical progression of dialectical ideographies that grows out of their first dialectical ideography to the natural sciences are being explored here --
Applications to the critique of capital-based political-economics are being explored here --
Enjoy, and Profit [in a social-revolutionary sense!].