Explanandum and Explanans

An explanandum (L.) is a sentence describing a phenomenon that is to be explained, and the explanans is the sentences adduced as explanations of that phenomenon. For example, one person may pose an explanandum by asking 'why is there smoke?', and another may provide an explanans by responding 'because there is a fire'. In this example, 'smoke' is the explanandum, and 'fire' is the explanans.

As a siderbar, consider similar latinate terminology:

  • Explicandum — that which gets explicated vs. Explicans — that which gives the explication
  • Constitutum — that which gets made up, constituted vs. Constituens — that which makes it up, e.g. the constituents
  • Definiendum — that which is being defined vs. Definiens — that which constitutes a definition

In accounting for the differences between artworks it is not enough to produce an explanation which merely restates difference, as this would simply echo the explanandum. e.g. It is no use saying that the difference between Gentile de Fabriano's Madonna and Child with Angels (1425) and Masaccio's Virgin and Child (1426) 'lies in' the stylistic differences between late Gothic and early Renaissance modes of figuration. That would merely present us with a restated difference to be explained (an explanandum), and not an explanation (explanans).

"Explanandum

Nor, according to the Marxist art historian Frederick Antal[1] does a difference in influence (regional, generational) upon the respective artists account for the essential differences: 'influences do not explain essentials'.[2]

For Antal there must be a fundamental cause of the differences, and as an 'orthodox' Marxist art historian, this fundamental explanation can only be given through an understanding of the economic basis of class society: a fundamental social antagonism expresses itself in the differences between Gentile and Masaccio's stylistic approaches; the rational, natural, frugal, sober and realistic style of the latter expresses the values of a newly prosperous and briefly powerful bourgeoisie asserting itself, while Gentile's more courtly, geometricised and ritualistic style expresses a conservative outlook more befitting the aristocracy.[2]

[1] Hatt, M. & Klonk, C., 2006, Art History: A Critical Introduction to its Methods, p. 132
[2] Antal, F., 1948, Florentine Painting and its Social Background, 9.3.

Real Abstraction

The Marxian conception of Real Abstraction can be found all over the place; for example, in Simmel[1], Sohn-Rethel[2], Adorno[3], Toscano[4] and more generally, scattered throughout critical theory.

Marx wrote:

Within the value-relation and the value expression included in it, the abstractly general accounts not as a property of the concrete, sensibly real; but on the contrary the sensibly-concrete counts as the mere form of appearance or definite form of realisation of the abstractly general … This inversion, by which the sensibly-concrete counts only as the form of appearance of the abstractly general and not, on the contrary, the abstractly general as property of the concrete, characterises the expression of value. At the same time, it makes understanding it difficult.[5]

.

It is as if together with and besides lions, tigers, hares and all the other real animals, which as a group form the various genuses, species, subspecies, families etc of the animal kingdom, there also existed the Animal, the individual incarnation of the whole animal kingdom.[6]

In the second edition of Capital, we find the famous phrase: '[t]he equalisation of the most different kinds of labour can be the result only of an abstraction from their inequalities, or of reducing them to their common denominator viz. expenditure of human labour power or human labour in the abstract', while in the French edition Marx added a comma, continuing '… and only exchange produces this reduction, by bringing the products of the most diverse kinds of labour into relation with each other on an equal footing'. [7]

For Marx the mystery of real abstraction lies in how the production process (labour) is concealed in the exchange between commodities through the medium of their universal equivalency in exchange value, this latter (materially performed, practiced) abstraction being at the centre of capitalist life. Far from being an idea that floats free of daily practice, abstraction here is concrete and real, having determinate effects in social relations. Abstraction here is not something thought; it is something done.

[1] The Philosophy of Money, p. 78
[2] Intellectual and Manual Labor, p. 69
[3] Introduction to Sociology, pp. 31-32
[4] Fanaticism, pp. 186-190
[5] 'The Value Form', Das Kapital, pp.39-140
[6] Das Kapital 1st ed. p.234
[7] Le Capital I p.70