Notes on "Abstraction"

I wanted to revisit the notion of abstract and abstraction. 

For example, abstraction may refer to something purely formal in character, as when one abstracts from the content, such as when Marx refers to 'the population' in the Grundrisse:

"It seems to be correct to begin with the real and the concrete, with the real precondition, thus to begin, in economics, with e.g. the population, which is the foundation and the subject of the entire social act of production. However, on closer examination this proves false. The population is an abstraction if I leave out, for example, the classes of which it is composed. ... if I were to begin with the population, this would be a chaotic conception of the whole, and I would then, by means of further determination, move analytically towards ever more simple concepts, from the imagined concrete towards ever thinner abstractions until I had arrived at the simplest determinations. From there the journey would have to be retraced until I had finally arrived at the population again, but this time not as the chaotic conception of a whole, but as a rich totality of many determinations and relations."

"In the analysis of economic forms, moreover, neither microscopes nor chemical reagents are of use. The force of abstraction must replace both." 

1867 Preface to the First German Edition.  Here abstraction is required because the forms are not simply material nor are they isolatable in the same manner.

"My standpoint, from which the evolution of the economic formation of society is viewed as a process of natural history, can less than any other make the individual responsible for relations whose creature he socially remains, however much he may subjectively raise himself above them." 

What is of interest in this presentation is that if individuals are abstracted from, starting with individuals as "concrete" would also be an abstraction.  Taken in tandem with the quote from the Grundrisse we have the meaning of Marx's comment in the Afterword to the Second German Edition:

"Of course the method of presentation must differ in form from that of inquiry. The latter has to appropriate the material in detail, to analyse its different forms of development, to trace out their inner connexion. Only after this work is done, can the actual movement be adequately described. If this is done successfully, if the life of the subject-matter is ideally reflected as in a mirror, then it may appear as if we had before us a mere a priori construction."

Marx however refers to practices and relationships which may be abstract but also actual:  

"The mediating process between men engaged in exchange is not a social or human process, not human relationship; it is the abstract relationship of private property to private property.... Since men engaged in exchange do not relate to each other as men, things lose the significance of human personal property."

or

"The value form of the product of labour is not only the most abstract, but is also the most universal form, taken by the product in bourgeois production and stamps that production as a particular species of social production, and thereby gives it its special historical character." (Capital, vol. 1, fn. 33 Marxists.org)

That is, the value form of the product of labor really is universal and abstract in practice.

In these latter we have a social process of abstraction, not merely a conceptual process of abstraction.

A universal power opposed to individuals is also an abstract power: The state as the illusory community, for example or Marx's contraposition of societies based on "direct relations of dominance and servitude" with capitalist society, in which the social form is not determined by direct relations of dominance, but by indirect relations of dominance.  Capital, money, the market, etc. compel us to work.  No individual capitalist or even individual capital can compel us to sell our labor power, though having sold it they can compel us to use it in whatever manner suit them.  We can go from employer to employer at will.  We can go to the state and the state can even take over the management of production and wipe out the class of capitalists in any meaningful sense.  However, if we want to live we must sell a commodity, which for most of humanity at this point is their capacity to labor, their labor power.  This compulsion is abstract not because it is an abstraction from, a merely formal gesture separate from a content, but because it is a universal existing in and through particular social practices, while those social practices only exist in relation to their universal social form.

Richard Gunn (and following him, Werner Bonefeld, John Holloway, et al) distinguish between kinds of abstraction (cf. http://www.riff-raff.se/en/furtherreading/gunn_metatheory.php, but also the more detailed essays "Marxism and Philosophy" in Capital & Class #37, and "Against Historical Materialism: Marxism as First-Order Discourse", Open Marxism, Vol. 2).  The normal mode of abstraction is that of empiricist abstraction, abstraction from or that abstracting from the concrete into the universal that is the mode of all genus-species type abstraction.  The mode of determinate abstraction obtains in practice and in theory, that is, there is no genus-species distinction, no separation of universal from particular.  Abstract labor as universal form is also particular, in a double sense because all particular labors only count if they are counted as abstract labor, and in the sense that abstract labor is a historically specific, bounded notion of labor.  Abstract labor is not something one does, but the form of all particular labors in generalized commodity production.  Labor in general, labor as a generic abstraction, is thus not what Marx is on about.

As Gunn notes, 

To construe labour as a generally applicable category for all societies is to abstract from particular social conditions; to construe labour as a peculiarly capitalist abstraction, both in theory and in practice, is to approach it as an abstraction in and of the specific social world of the ‘doubly free’ labour whose historical preconditions the final section of Capital Volume I reports.

"When I state that coats or boots stand in a relation to linen, because it is the universal incarnation of abstract human labour, the absurdity of the statement is self-evident. Nevertheless, when the producers of coats and boots compare those articles with linen, or, what is the same thing, with gold or silver, as the universal equivalent, they express the relation between their own private labour and the collective labour of society in the same absurd form."  Capital, Vol. 1, Ch. 1

This statement captures quite clearly what I think you have in mind about Marx's irony, but the issue with Marx is that this absurd (perverse/inverse) state of affairs obtains in practice, that abstract human labor is a practical or determinate abstraction (the particular labors only count or have validity insofar as they are moments of abstract labor, of universal labor.)

Also, I will poach Werner Bonefeld here: 

"In the English translation, the German verruckte Form is translated as 'absurd form' (Marx, 1983, p. 80). The translation is 'absurd'. In German, 'verruckt' has two meanings: verruckt (mad) and ver-ruckt (displaced). Thus, the notion of 'perverted forms' means that these forms are both mad and displaced. In other words, they are the modes of existence of social practice, in which 'subject and object do not statically oppose each other, but rather are caught up in an "ongoing process" of the "inversion of subjectivity into objectivity, and vice versa"' (Backhaus, 1992, p. 60, quoting Kofler)."

I take Hegel in a similar vein in his discussion of utility and absolute freedom in the Phenomenology of Spirit, paragraphs 580-83, because in that moment of utility, where everything is turned into an object of utility, at that same moment objectivity is emptied because things are only objectively what I will them to be in my use of them.  A hammer is not objectively "an implement for pounding nails into some material, such as wood or concrete".  A hammer is whatever I use it for: for pounding nails, for beating someone to death, for breaking walnuts, for breaking a window to rob a house.  The objectivity of the hammer dissipates into my use of it.  So too does the labor of the laborer cease to be a particular kind of labor.  I don't hire a bricklayer; I hire a laborer to lay bricks for me.  Tomorrow I might have her dig ditches or wash clothes.  In the absolute freedom of Enlightenment utility, what the universal subject wills determines the object and its use.  Thus use is emptied of reference to an object in absolute freedom.  Utility is abstracted from the object in practice.  (Knowledge is also connected with this transformation, and I cannot help but think of both Faust and de Sade as the knowing self here.)