Monday, April 29, 2019

‘The Marxian Singularity’.

The Marxian Singularity.

Dear Readers,

In the Grundrisse manuscripts, as well as elsewhere, Karl Marx wrote about the way in which fixed capital is the ‘epitomeous’ form of capital, coming to dominate capital-mass in the epoch of the ‘“real domination”’ or “real subsumption” of the labor process by capital, the epoch that begins with a prevalence of the “relative surplus-value” form of surplus-value production, and which Seldon also identifies as the “descendence phase” of the capitalist system.  Marx also wrote there about how fixed capital lawfully tends to develop into an automatic system of machinery, as the incarnation and objectification of the very essence of “the capital-relation” itself in the shape of the physical embodiment of capital as fixed capital.

In the third volume of «Das Kapital», Marx wrote of what Seldon calls The Marxian Singularity, and which others have termed The Automation Crisis, in these words --

A development of the productive forces [M.D.:  E.g., a penultimate level of growth of industrial productivity via automation] which would diminish the absolute number of laborers, i.e., enable the entire nation to accomplish its total production in a shorter time-span would cause a revolution [and would thus also constitute an historical boundary, a productive force upper bound and limit, of the capitals-system; an end of the very possibility of the continuing the capitals-system; of the capital social-relation-of-production as predominating social relation of social reproduction -- M.D.] because it would put the bulk of the population out of the running.

[Karl Marx, Capital, volume III, The Process of Capitalist Production as a Whole, International Publishers Co., Inc. [NY:  1967], p. 263, bold italic shadowed emphasis added by M.D.].

It might be instructive, as a “thought-experiment”, to note what happens in the ‘Marxian ratios’ -- the “dimensionless” value proportions central to the Marxian “law of value”, and to the Marxian theory of the capitalist system as a whole -- in a scenario characterized by an extremity of automation.  Such a scenario would be modeled “in the limit” as “Variable capital-value”, V -- the aggregate of the values of wages or of living human labor-power commodities purchased to form part of “productive capital” -- goes to 0.

A.  Let us first apply this limit-process to the Marxian value-profit-rate ratio -- the ratio that resides at the very heart of Marx’s theory of the historical dynamics and ‘meta-dynamics’ [Seldon] of “the capital relation”, and of its lawful fate -- in its “purely”-quantitative, classical form:

lim    .      S    .       =   .  0  .       =   0
V --> 0    
          (C + V)           C

-- wherein S goes to zero together with V, because no “necessary labor” also means no “surplus-labor”, hence no “surplus-value”, S, hence no net “surplus-value”, S.  And no net “surplus-value” means no profit, hence, before long, no capitalism.

It is also interesting to see what happens in this V --> 0 limit to that form of the Marxian value-profit-rate ratio which arises by multiplying both the denominator and the numerator of the ratio as given above by 1 in the form of ((1/V)/(1/V)) -- the form in which both the “organic composition of capital” ratio, C/V, and the (net) “rate of surplus-value” ratio, (S/V), figure explicitly, as ‘sub-ratios’ --

lim    .      (S/V)     .       =   .      oo      .       =  . oo .
V --> 0    
           ((C/V) + 1)            (oo + 1)              oo

 =  ‘“indeterminate”’.

We might visualize this scenario-idealization, of ‘automation extremity’, as one in which --

*     All agental production work, which no longer figures as “living [human] labor”, is performed by AI ‘‘‘Android Robots’’’, whose costs of reproduction do not figure as V, but might, rather, be assimilated to C, or;

*     All such production work, which, again, no longer figures as “living [human] labor”, is performed by genomically re-engineered ‘meta-humans’, whose costs of reproduction therefore also no longer figure as V, or;

*      All such production work, which, again, no longer figures as “living [human] labor”, is performed by ‘hybrid meta-humans’, that combine genomically re-engineered genotypes with implants/artificial body-parts [i.e., ‘‘‘prosthetics’’’] originally developed for Android Robots, i.e., by ‘‘‘Cyborgs’’’, whose costs of reproduction thus also no longer figure as V.

-- or by combinations of the three cases described above.

The above, “infinity over infinity”, “indeterminate” result arises from the outcome that both the (C/V) ‘sub-ratio’, in the denominator, and the (S/V) ‘sub-ratio’, in the numerator, “become infinite” in the limit as V goes to 0, due to divisions by zero, in terms of such calculations as are available in standard, “purely”-quantitative “Real” arithmetic, as augmented by the “limit” operation and by the non-standard "infinity" symbol ‘oo’ --

lim    . C .       =   . C .      =  oo
V --> 0    
            V           0

-- and --

lim    . S.       =   . S.      =  oo .
V --> 0    
            V            0

B.  Let us next apply this limit-process to the Marxian value-profit-rate in its Seldonian, ‘qualo-quantitative’ or ‘quanto-qualitative” form, as that form arises through ontological and metrical ‘re-qualification’ of ‘‘‘quantifiers’’’, by ontological and metrical ‘arithmetical qualifier’ factors or coefficients, in the seventh ‘arithmetic for dialectic’ in the “slow version” of the Seldonian ‘‘‘systematic-dialectical’’’ method of presentation of the axioms-systems of the Seldonian ‘arithmetics for dialectic’, as a dialectical categorial progression of axioms-systems’ categories:  [forthcoming].

For more information regarding, and for [further] instantiations of, these Seldonian insights, please see --


For ‘poster-izations’ of many of these insights -- as specimens of dialectical art -- see:



Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Participant, F.E.D. Special Council for Public Liaison,
Officer, F.E.D. Office of Public Liaison.

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