Marx’s Capital – Philosophy and Political Economy. Geoff Pilling 1980
Chapter 2. Marx’s Critique of Classical Economics

Formal logic and the ‘exceptions’ to the law of value

Now with all respect to Hodgson, there is no doubt whatsoever that Ricardo’s confinement to a formal logic – that as its basic principle denied contradiction – led to the conclusion that there was, in fact, a series of exceptions to the law of value. Under pressure from Malthus and others, Ricardo accepted that changes in the rate of profit (rate of interest) as well as labour-time could affect relative commodity values. This would occur, Ricardo conceded, when the organic composition of capital (this was of course Marx’s category, in Ricardo it is the relationship of fixed and circulating capital) was not identical in every industry. For the rate of profit to remain uniform the rise or fall in wages – to which corresponds an inverse movement in profits – must have unequal effects on capital of different organic composition. If wages rise, then profits fall and so does the price of commodities in whose production a relatively large amount of fixed capital is used. Where the opposite is the case, the results will likewise be opposite. That is, the establishment of an equal rate of profit yielded by capital of different organic composition contradicts the law of value. And similarly, Ricardo admitted, with capitals having different rates of turnover and different degrees of durability. Summing up his discussion on the matter of fixed and circulating capital Ricardo says:

It appears that the division of capital into different proportions of fixed and circulating capital, employed in different trades, introduces a considerable modification into the rule, which is of universal application when labour is almost exclusively employed in production; namely, that commodities never vag in value unless a greater quantity of labour be bestowed on their production, it being shown in this section that without any variation in the quantity of labour, the rise of its value merely will occasion a fall in the exchange of goods, in the production of which fixed capital is employed; the larger the amount of fixed capital, the greater will be its fall. (Ricardo)

In short, the exchange of commodities could not be considered as ultimately independent of wages, that is of distribution. After setting out to show that Smith was mistaken on this matter, Ricardo actually yields the case to him.

On the problem of the durability of capital and its impact on the law of value, Ricardo, in a letter of 1818 to James Mill, stated:

I maintain that it is not because of this division into wages and profit- it is not because capital accumulates that exchangeable value varies, but it is in all stages of society due to only two causes: one the more or less quantity of labour required, the other the greater or lesser durability of capital: that the former is never superseded by the latter, but is only modified. (Ricardo, author’s italics)

Ricardo, as Sraffa (Introduction to Ricardo, 1951) has persuasively argued, was here trying to dispose of one of Adam Smith’s objections to the law of value. More germane to the argument here, however, is that Ricardo accedes to the proposition that value has two causes: labour-time (a social phenomenon) and the durability of capital (a natural-technical phenomenon). We shall return to this matter of the relationship of the ‘natural’ and the ‘social’ but this passage from Ricardo seems once more to underscore the fact that he had failed, in the last resort, in his major aim – to establish the entire science of political economy on the foundation of the law of value. As Marx comments:

Because Ricardo, instead of deriving the difference between cost price and value from the determination of value itself, admits that ‘values’ themselves . . . are determined by influences that are independent of labour-time and that the law of value is sporadically invalidated by these influences; this was used by his opponents, such as Malthus, in order to attack his whole theory of value. (Marx, Theories of Surplus Value, author’s italics)

This last reference to Malthus reminds us that there was one way out of the Ricardian antinomies. This lay in separating entirely the law determining value from that determining the rate of profit. Cost price and value could be identified completely: what in Ricardo was a sporadically occurring exception (which he could not in the first instance adequately explain) could now be elevated to the status of a law. Economics, in the period following Ricardo’s death, took precisely this turn. It came to the conclusion that profit originated not only in labour, but in a diversity of what were essentially discrete ‘factors’. It was necessary, so the argument now ran, to take into account the role of land, of machines, of supply and demand, etc. Thus was born the Trinity Formula: ‘capital-interest; land-rent, labour-wages’. All the contradictions left unresolved by Ricardo could now be disposed of. Rent, profit and wages no longer confronted each other as alienated forms having a common source, an inner unity, but now became in the conception of the ‘vulgar’ school, heterogeneous and independent of each other. Now they were considered merely different from one another, but in no sense fundamentally antagonistic. The problems which Ricardo’s genius had brought to the forefront of science disappeared; but so too had disappeared any theoretical approach to economic phenomena, in favour of the most shallow eclecticism. The notion that the durability of capital might play a role in the determination of value (for Ricardo an exceptional case) was now extended to the point where it was eventually alleged by the vulgar school that all social phenomena could be explained entirely in terms of a ‘given technology’.

As distinct from Ricardo’s opponents, Marx resolved the problems of classical political economy theoretically. To do this involved him, above all, in a rejection of the empiricism of political economy, along with its concomitant adherence to formal logic. Marx’s dialectical method allowed him to trace the entire chain of connecting links between the law of value and the determination of the rate of profit. This he did in his prices of production theory in which the contradictions of the lower economic forms (the analysis of value) are overcome not in a formal manner (through the redefinition of terms, etc.) but are sublated in a richer, more diverse and concrete theoretical conception.

Dialectics and formal logic

We have stressed that for Marx one of the limits of political economy lay in its implicit confinement to a purely formal logic, a logic which prevented it from grasping the laws of capitalist development. Now this should in no way be taken to mean, as Hodgson implies, that Marxism rejects formal logic completely. In point of fact it draws a sharp distinction between Aristotelean logic and its later degeneration at the hands of the scholastics (‘Clericalism killed what was living in Aristotle and perpetuated what was dead’, LCW, vol. 38). Aristotle’s logic, by virtue of its close connection with the scientific developments of his age, and the entire process of knowledge, cannot strictly speaking be called ‘formal’ logic in the sense in which this word is used in the logic of modern times. Aristotle did not place the logical forms of investigation in any rigid opposition to their concrete content. He tried to elicit the logical forms and connections from the basic characteristics of existence. It is this which explains the depth and richness of his thought. In the hands of the scholastics, logic degenerated into a mere proof-producing instrument, having no connection with the real content of the world, whereas in fact ‘even formal logic is primarily a method of arriving at new results, of advancing from the known to the unknown – and dialectics is the same, only much more eminently so’ (Engels).

Engels is here in effect drawing attention to the fact that materialist dialectics does not reject formal logic but rather determines its limits. The three principles of formal logic (non-contradiction; excluded middle; identity) are not false. They are however limited and all they can do is to prevent fallacies, without, however, rendering or reproducing the movement of ideas which reflect the movement of the material world.

Let us take these three principles of formal logic:

1 The principle of contradiction. Here the principle of a purely formal contradiction is formulated as follows: a proposition cannot be true and false at the same time. In other words, the opposition between two contradictory statements is placed on the same level. For dialectical materialism, contradiction reflects the development of reality (‘Nature is not, but it becomes’, Engels, Dialectics of Nature). That is why concepts, if they are to grasp adequately the movement of the material and social world, must be fluid. This was Lenin’s point, when, drawing attention to the limits of a purely formal logic, he wrote (LCW, vol. 38), ‘Ordinary imagination grasps difference and contradiction, but not the transition from one to the other, this however is the most important.’

2 The principle of excluded middle. This states that something is either A or not A. For materialist dialectics, the principle of the excluded middle is considered to be valid only on the purely formal level of abstract determinations. In concrete reality – which is intrinsically contradictory because of the interpenetration of opposites in all phenomena – it is impossible to situate anything in the rigid ‘either A or non-A’ dichotomy. This was Lenin’s point when, commenting with approval on Hegel, he says (LCW, vol. 38), ‘Every concrete thing, every concrete something, stands in multifarious and often contradictory relations to everything else, ergo it is itself and some other.’

3 The principle of identity. This states that A=A (and negatively, A cannot be simultaneously equal and unequal to A). What is missed here by a purely formal logic is the fact that everything is in continual change and therefore at every moment is both identical with itself and becoming distinct from itself. Of course, within limits this principle is perfectly acceptable, ‘like all metaphysical categories it suffices for everyday use, where small dimensions or brief periods of time are in question; the limits within which it is usable differ in almost every case and are determined by the nature of the object’ (Engels, Dialectics of Nature). Trotsky, in attacking those who thought that the nature of the USSR could be determined with a series of fixed abstractions, makes essentially the same point about the objective limits of the principle of identity when he writes:

Our scientific thinking is only part of our general practice including techniques. For concepts there also exists ‘tolerance’ which is established not by formal logic issuing from the axiom ‘A’ is equal to ‘A’, but by the dialectical logic issuing from the axiom that everything is always changing. ‘Common sense’ is characterised by the fact that it systematically exceeds dialectical ‘tolerance’.

The real objection to formal logic which Engels, Lenin and Trotsky here express is that format logic, being concerned with the classification of thought-forms and with their description as forms independent of any content, remains essentially subjective; this in opposition to dialectical logic which studies these forms in their connection as thought-forms having a definite content. The unity between the laws of thinking and the laws of being postulated by Marxism implies a close connection among the logical forms, forms which in their unity and interconnection reflect the entire concrete content of the world in its self-movement. (We shall return to the nature of concepts and their place in Capital in the next chapter.)

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