The dialectics of the Abstract & the Concrete in Marx’s Capital
Chapter 5 – The Method of Ascent from the Abstract to the Concrete in Marx’s Capital

Contradiction as the Condition of Development of Science

Logical contradiction – the existence of mutually exclusive definitions in the theoretical expression of a thing – has long interested philosophy. There has never been one single philosophical or logical doctrine, that would not consider this question in one form or another and solve it in its own way. It always interested philosophy exactly because contradiction in definitions is first and foremost a fact independent from any philosophy, a fact that is continually and with fatal necessity reproduced in scientific development, in mankind’s thought, including philosophy itself. Moreover, contradiction most unambiguously reveals itself as a form in which thought about things moves, always and everywhere.

Ancient Greeks understood full well that truth was only born in the struggle of opinions. Critique of any theory was always directed at discovering contradictions in it. A new theory always asserted itself through demonstrating a method by which contradictions wore solved that had been insoluble within the framework of the principles of the old theory.

However, if this empirical fact is simply described as a fact, it will appear that a contradiction is something intolerable, something that thought always tries to get rid of in one way or another. At the same time, despite all attempts to get rid of it, thought reproduces it again and again.

Inasmuch as philosophy and logic study this fact, not content with simply stating and describing it, the question arises of the causes and sources of its origin in thought, of its real nature. In philosophy, this question arises in the following form: is contradiction admissible or inadmissible in the genuine expression of a thing? Is it something purely subjective, created only by the, subject of cognition, or does it necessarily emerge as the outcome of the nature of things expressed in thought?

That is the boundary between dialectics and metaphysics. In the final analysis, dialectics and metaphysics are two fundamentally opposed methods of solving contradictions which inevitably arise in scientific development, in the development of theoretical knowledge.

The difference between them, expressed in a most general form, is that metaphysics interprets contradiction as a mere subjective phantom which regrettably recurs in thought due to the imperfections of the latter, while dialectics considers it as the necessary logical form of the development of thought, of the transition, from ignorance to knowledge, from an abstract reflection of the object in thought to an ever more concrete reflection of it.

Dialectics regards contradiction as a necessary form of development of knowledge, as a universal logical form. That is the only way to consider contradiction from the point of view of cognition and thought as a natural historical process controlled by laws independent from man’s desires.

[It should be borne in mind that here and in the following we mean those contradictions in definitions which arise in the course of movement of thought that is correct from the standpoint of the logic of the object, that is, we mean dialectical contradictions in reasoning. As Lenin pointed out, in any enquiry there must be no logical contradictions in the narrow sense of the word, that is verbal, forced, or subjective contradictions. Rules barring these contradictions must be worked out by formal logic.]

The development of knowledge and science compels philosophy to recur to the problem of logical contradiction again and again. The question of contradiction, of its real significance, its source and the cause of its emergence in thought arises in those areas where science approaches the stage of systematic expression of its subject-matter in concepts, where reasoning has to construct a system of theoretical definitions. In cases of unsystematic recounting of phenomena, there is no question of contradiction. An elementary attempt to systematise knowledge immediately leads to the problem of contradiction.

We have already noted the points at which the development of the labour theory of value necessarily ran into this problem: in Ricardo, despite his wishes, a system of theoretical contradictions arises exactly because he attempts to develop all categories out of one principle – that of determining value by the quantity of labour time. He noticed some logical contradictions in his system himself, others were maliciously pointed out by the opponents of the labour theory of value.

The main type of logical contradiction that was the focal point of the struggle for and against the labour theory of value, proved to be the contradiction between universal law and the empirical universal forms of its own realisation.

Attempts to deduce from the universal law theoretical definitions of developed concrete phenomena that regularly recur on the surface of the capitalist production and distribution of commodities, resulted in paradoxical conclusions at every step.

A phenomenon (say, profit) is, on the one hand, included in the sphere of action of the law of value, its necessary theoretical definitions are deduced from the law of value; but, on the other band, its specific distinctive feature proves to be contained in a definition which directly contradicts the formula of the universal law.

This fatal contradiction manifested itself all the more clearly, the more efforts were made to get rid of it.

Contradictions are by no means a ‘privilege’ of political economy that studies the antagonistic reality of economic relations between classes.

Contradictions are inherent in any modern science. Suffice it to recall the circumstances of the birth of the theory of relativity. Attempts to explain certain phenomena established in the Michelson experiments in terms of the categories of classical mechanics resulted in the appearance, within the system of concepts of classical mechanics, of absurd, paradoxical contradictions in principle insoluble in these terms, and Einstein’s brilliant hypothesis was put forward as a means of solving these contradictions.

The theory of relativity did not, of course, eliminate contradictions from physics. For example, one may point out to the well-known paradox contained in the theoretical definitions of the rotating body. The theory of relativity, linking up the spatial characteristics of bodies with their motion, expressed this connection in a formula according to which the length of a body is reduced in the direction of motion proportionately with the speed of the body’s motion. This expression of the universal law of the motion of a body through space became a firmly established theoretical attainment of the mathematical arsenal of modern physics.

however, an attempt to apply it to a theoretical elaboration or assimilation of such an actual physical phenomenon as rotation of a hard disc round its axis results in a paradox: the circumference of a rotating disc diminishes with an increase of the speed of rotation, while the length of the radius, according to the same formula, remains unchanged.

Let us note that this paradox is no mere curiosity but an acute test of the physical reality of Einstein’s universal formulas. If the universal formula expresses an objective law of objective reality studied in physics, one should assume the existence in the reality itself of an objectively paradoxical relation between the radius and the circumference of a rotating body (even in the case of the spinning top), for the infinitely small decrease in the extent of the circumference changes nothing in the fundamental approach to the problem.

The conviction that physical reality itself cannot contain such a paradoxical correlation, is tantamount to a rejection of the physical reality of the universal law expressed in the Einstein formula. And that is a way to a purely instrumental justification of the universal law. If law serves theory and practice that is all to the good, and one should not bother about the vacuous problem whether it has anything to correspond to it in the ‘things in themselves or not.

One can cite quite a number of other examples showing that objective reality always reveals itself to theoretical thought as contradictory reality. The history of science from Zeno of Elea down to Albert Einstein, independently from any philosophy shows this circumstance to be an incontestable empirically stated fact.

Let us go back to the reality of capitalist economy and its theoretical expression in political economy. This is a good example because it is extremely typical: it shows graphically the cul-de-sacs in which metaphysical thought inevitably lands itself in trying to solve the prime task of science – that of unfolding a systematic expression of the object in concepts, in a system of theoretical definitions of the object, a system developed from one general theoretical principle. That is the first reason. And the second and probably most important reason is that in Marx’s Capital we find a rational way out of the difficulties and contradictions, a dialectical materialist solution of the antinomies which destroyed the labour theory of value in its classical Ricardian form.

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