1All scientific thought—that is, all thought that focuses on natural phenomena rather than its own processes—proceeds from some ontological intuition. For Galileo, it was that all bodies have a weight; for Lavoisier, that their mass is conserved; for Pasteur, that life is a break in symmetry; and, for Newton, that there are central forces that hold the world together, guarantee its unity, and realize the One in actuality. Marx’s ontological intuition is that everything is transformation, Verwandlung. While still a student, he wrote to his father: “The triangle allows the mathematician to construct and to demonstrate, yet it remains a mere idea in space and doesn’t develop any further. One must put it next to other things, and then it takes on other positions, and when this difference is added to what is already there, it acquires different relations and truths. By contrast, in the concrete expression of a living concept world, as in law, the state, nature, and all of philosophy, the object must be studied in its development, arbitrary divisions may not be brought in, and the reason of the thing itself must be disclosed as something imbued with contradictions and must find in itself its unity.” [1]

2I argue here that (1) the three volumes of Capital are a series of connected transformations; (2) Marx relied on Hegelian syllogistics to conceptualize transformation; and (3) we find an explanation for Capital’s incompleteness in one of these transformations, that of values into costs of production, which is itself incomplete and therefore faulty—something that offers a theoretical reason for the failure of socialist economies.

Transformations in Capital

3The first transformation, already described in Volume I, Part 1, is the transformation of the product of labor into money through the mediation of exchange. This mediation is in turn mediated by the distinction between the utility of the product of labor for meeting needs, and its utility for exchange. The distinction is overcome by a commodity, money, whose utility is precisely to enable exchange, and whose use value is simply its exchange value. As a result of this transformation, money becomes a universal commodity, the embodiment of all human labor of any sort. As a consequence, the transformation of the value of a commodity into a price—i.e. into its monetary equivalent—transforms the quantity of labor incorporated in the production of this commodity into socially necessary labor. The process of exchange is therefore the transformation of commodities into money and money into commodities, such that the quantity of labor embodied in each commodity is the quantity of labor that is socially necessary, and the nature of the labor embodied in the one is equivalent to the nature of the labor embodied in the other. The two poles of commodities are mediated by money, which is universal and serves as a middle term.

4Next comes the transformation of money into capital, in Volume I, Part 2. While Marx schematizes the first transformation in the model C-M-C (commodity-money-commodity, or “selling in order to buy”), the model of the second transformation is M-C-M (money-commodity-money, or “buying in order to sell”). The two extremes in the first transformation—i.e. the particular commodities—are mediated by money as a universal commodity. In the second transformation, money (the universal commodity) is itself positioned at the extremes, and must be mediated by a particular or individual commodity. In the first transformation, the two extremes are different in quality but equal in quantity (price). In the second, they are identical in quality (both are money), but are quantitatively different—otherwise there would be no need for a transformation. Marx calls this quantitative difference “surplus value” (Mehrwert), and this is what turns money into capital. However, this transformation is no longer mediated by exchange. Instead, it is mediated by labor. Money is only transformed into capital by buying and selling labor power, which has the property of creating more value than it consumes and of being able to exert itself for longer than was necessary to produce it. In other words, the extremes that constitute universal money, which represent social labor, must be mediated by an individual commodity, labor power.

5This mediation is itself mediated in the third, fourth, and fifth parts of Capital. This takes place initially through a distinction between variable capital, which is used to purchase labor power, and constant capital, which is used to purchase those things labor power is applied to—such as machines, tools, buildings, and raw materials—and which gives entitlement to the purchase of labor power. Because workers are deprived of the means of production, they must sell their labor power and give up the surplus value to the owners of these means of production. Evidently, labor power must be for sale if it is to be purchased—i.e. those offering it must lack the means to use it for themselves. This mediation is in turn mediated by the transformation of small independent producers—who own their means of production and enjoy all the value of their product—into proletarians who have only their labor power to sell.

6The realization of this surplus value completes the transformation of money into capital in Volume I, Parts 6 and 7. The accumulation of capital is the transformation of surplus value into capital. Another mediation is needed to accumulate capital: manufacturing must be transformed into mechanized industry, which constantly reduces the labor necessary to reproduce labor power. The surplus labor that produces surplus value thus increases, because an increase in labor productivity reduces the cost of labor power and thus the cost of reproducing it, and consequently the time it takes. In addition to absolute surplus value, there is also therefore relative surplus value.

7Volume II looks at three transformations. The first returns in greater depth to the transformation of money into capital through the buying and selling of labor power. Marx now analyzes it as a transformation of money capital into productive capital. The reverse transformation—from productive capital to money capital—allows the process to perpetuate itself, but it is not the mirror image of the direct transformation. Instead, it is constituted by the purchase of the “daily value of labor power” (Tageswert der Arbeitskraft). But during the production process this value is transformed into the “value of a working day” (Wert der Tagesarbeit). The second of these is greater than the first, and the difference between them is the surplus value. The reverse transformation thus provides a quantity of money capital greater than the amount invested in buying labor power. Marx summarizes the transformation concisely: “Let us now consider the total movement, M — C … P … C′ — M′, or, M — C<LMP … P … C′ (C + c) — M′ (M + m), its more expanded form [where M stands for money, C for commodities, and P for production]. Capital here appears as a value which goes through a series of interconnected, interdependent transformations, a series of metamorphoses which form just as many phases, or stages, of the process as a whole. Two of these phases belong in the sphere of circulation, one of them in that of production. In each one of these phases capital-value has a different form for which there is a correspondingly different, special function. Within this movement the advanced value does not only preserve itself but grows, increases in magnitude. Finally, in the concluding stage, it returns to the same form which it had at the beginning of the process as a whole. This process as a whole constitutes therefore the process of moving in circuits.” [2]

8The second transformation in Volume II is that of constant and variable capital into fixed and circulating capital. In the salaried form of alienated labor (slavery, serfdom, wage labor), workers can dispose freely of their labor power, and can alienate it for a set period of time. The value of labor power is transformed into time wages. This value is the result of an asymmetry in the sale and purchase of labor power: the worker sells a day of labor power, whereas the capitalist buys a day’s worth of labor power. Another transformation then follows: time wages become piece wages. The day’s worth of labor power bought by the capitalist becomes a working day. The result of this twofold transformation is that all the labor seems to be paid for, and so surplus value becomes disconnected from variable capital and instead associated with constant capital.

9The difference between paid and unpaid work is replaced by the difference between what it costs the capitalist, and what costs him nothing. Variable capital spent in wages, combined with other items of constant capital, such as raw materials, is transformed into circulating capital, which is consumed over a period of production and fully becomes part of the cost of production in the period. The other elements of constant capital, such as buildings and machinery, turn into fixed capital, and this is amortized over several production periods, consequently forming only part of the cost. Surplus value then appears as an excess of value relative to the cost of production. Because the cost of production only replaces the capital consumed, which is circulating and partly fixed, it cannot create surplus value. In fact, what matters to the capitalist is the whole sum of capital, both circulating and fixed, that he has to advance in order to appropriate the surplus value for himself. Once this surplus value has been added to the total capital advanced, it is transformed into profit. It is no longer labor that creates surplus value, but capital that creates profit. Capital no longer has any relationship to the other, to labor, but only to itself. In Hegelian terms, in this form it is “for itself.”

10The third transformation in Volume II returns in greater depth to that described at the end of the first volume, on the accumulation of capital. This involves simple reproduction, where the transformation of surplus value into profit consumed by the capitalist means that the entirety of the production is sold off. This is equivalent to the physiocrats’ tableau économique. In a two-sector economic model, the value of production in the production goods sector must be equal to the constant capital value of both sectors, and the value of production in the consumption goods sector must be equal to the sum of variable capital and surplus value in both sectors. The entirety of the production is thus consumed, and the economy is reproduced identically from one production cycle to the next. Production is transformed into the reproduction of capital.

11The expanded reproduction model still has two sectors. The value of production in the production goods sector must be equal to the constant capital value of both sectors, plus an aliquot part for the surplus value of the two sectors, which is thus reinvested. The value of production in the consumption goods sector must be equal to the variable capital value of the two sectors, plus the remainder of the surplus value of the two sectors. Because there is no mechanism to determine the aliquot part of reinvested surplus value, capitalist economies are always at risk of crises of overproduction and underconsumption.

12Volume III of Capital is devoted exclusively to the transformation of values into costs of production. This follows on from the transformation of surplus value into profit described in the previous volume. [3] The rate of surplus value—the ratio of a business’s surplus value to its variable capital—is transformed into a rate of profit—the ratio of surplus value to total capital, i.e. constant plus variable capital. Since surplus value is equal to profit in the numerator, and variable capital is smaller than total capital in the denominator, it follows that the rate of profit is always lower than the rate of surplus value. But it remains proportional to it. On the other hand, it is inversely proportional to the ratio between constant and variable capital—to what Marx calls “the organic composition of capital.” The organic composition of capital is what differentiates the various branches of industry. Some, due to their production techniques, use more machinery (more constant capital) and fewer workers (less variable capital) than others. The organic composition of capital is higher in the former and lower in the latter. It follows that the rate of profit is lower in branches of industry with a higher organic composition of capital. But competition means that there is a single rate of profit for all the different branches. If this were not the case, those branches in which it is lower would be abandoned in favor of those in which it was higher. Supply in the former would fall, and prices and profits would rise until the rate of profit became the same in this branch as in all the others. On the other hand, if a branch with low organic composition of capital—and therefore a higher rate of profit than the general rate—manages to escape competition, as agriculture did in Marx’s day, the difference between the rate of profit and the general rate takes the form of a rent that goes to the landowner. Surplus value is thus transformed into profit and rent.

13This transformation of values into production prices raises a number of issues that have been fiercely debated ever since Capital was published. Here I will mention only four. The first is the formation of a general rate of profit, which shows clearly that Marx conceived his transformations within a framework of Hegelian syllogistics. The second is that Marx made a mistake—one that he suspected, but was unsure how to correct, especially because correcting it would render the law of value useless. The third is the explanation of the incomplete nature of Capital. The fourth and final problem is the failure of socialist economies.

Transformation and Hegelian syllogistics

14Marx uses the average rate of profit as the general rate for the transformation of values into costs of production. But why this rate rather than another? Marx’s choice can only be understood in terms of Hegelian syllogistics. The general rate of profit is formed according to a syllogism, which takes the form PUG: the particular capitals (P) belonging to each of the branches of industry are viewed as forming a unique capital (U), which thus becomes a general capital (G) with each particular capital making up an aliquot part. The constant part of the individual capital is the sum of the constant capital in all of the branches, and the variable part is the sum of their variable capital. The organic composition of capital of this individual capital, as well as its rate of profit, are therefore an average composition and an average rate in an average branch. Within this, surplus value is also an average that, when multiplied by the proportion of total capital invested in each branch, is added to each branch’s cost of production (the part of the fixed capital consumed, plus the circulating capital) to form their cost of production.

15For Hegel, a totality—i.e. an organized whole, as for instance an economy in the present case—is a system of syllogisms forming a loop. This is what he says in the third-to-last paragraph of The Science of Logic, [4] and even more explicitly in his remark in §198 of his Encyclopedia of the Philosophical Sciences in Basic Outline: “It is only through the nature of this concluding, or through this triad of syllogisms with the same terms, that a whole is thoroughly understood in its organisation.” [5]

16Hegelian syllogistics distinguishes itself from classical syllogistics in relation to this point because it quantifies not just its propositions, but also its terms. These quantifiers—individual, particular, and general—are thought of as moments of the concept that is deployed by the syllogism through an equivalent number of determinations. Predicative propositions are interpreted through comprehension (the predicate is inherent in the subject) and extension (the subject is included in the predicate). For instance, mortality is inherent to man, and man is included among the mortals. But Hegel does not accept the rule of inverse variation, that the broader the extension of a concept, the more limited its content. Quantifiers are moments of a single concept, and may grant it a different extension, but certainly not a different content. The concept retains its content but does so differently with each of its quantifiers. In the general, it retains its in-itself, in an unreflective, immediate, potential manner. The movement from the general to the individual through the particular is the unfolding of this content, in which it becomes reflexively aware of itself and becomes for-itself. This is the movement that the syllogistic system describes.

17The figures are distinguished by the moment of the concept that acts as a middle term, and not—as in classical syllogistics—by its position. In Hegelian syllogistics, the middle term must always occupy the same position—as subject of the major premise and predicate of the minor premise— in order to function as a mediating term. Consequently, the point of departure for his syllogistics is the Barbara syllogism, which Hegel rewrites in IPG form: an individual being is placed in relation to a general determination through the mediation of a particular quality. The syllogism is incomplete: the two premises remain immediate and still need to be mediated. The major premise, PG, is mediated by I, which gives the second figure, PIG. The minor premise, IP, is mediated by G, which gives the third figure, IGP. Each moment of the concept acts successively as extreme and middle term, as mediated and mediating term. None of the premises remain immediate and simply given, as each has now been mediated and posited. At the same time, the two last figures pose a problem: the problem of the extension of the middle term when it is individual, since it cannot then include the particular in the second figure; or when it is general, as it can then never be subsumed under the particular in the third figure. Hegel resolves this problem by substituting the inductive syllogism for the second figure, and the disjunctive syllogism for the third.

18In §198 of the Encyclopedia he uses the example of the concept of the state, whose content is unfolded in three syllogisms. IPG: the individual, through his particular needs, is united with the state as a society of general law. PIG: the satisfaction of particular social needs through the activity of individuals realizes and accomplishes the state as a society of general law. IGP: the state as a society of general law is the “substantial middle term” (die substantielle Mitte)—i.e. the medium in which the individual is fulfilled and his particular needs are satisfied.

19This Hegelian syllogistics would appear to fully articulate Marx’s transformations, as it is able to express the full richness of a particular content—precisely what Marx was looking for in his search for the correct method.

Marx’s mistake

20The transformation of values into costs of production, as Marx conceived it, is incomplete. It is as though each branch of industry produced its own producer goods as well as its workers’ consumer goods. Marx accounts for them using their value. But if they bought them from other branches of production, Marx should account for them using their costs of production. His solution is only valid if there is just a single industry producing a single good that is both a productive good and a consumer good. This is the case with the production of wheat: as seed, it produces its constant capital; as flour, it produces its variable capital. But in this case the problem of forming a general rate of profit does not arise, as the rate would necessarily be that of this branch alone. In other words, either the problem arises and Marx’s solution is wrong, or his solution is right but the problem does not arise. Either way, the solution is inadequate.

21Marx realized this: “This statement [that the sum of production prices equals the sum of the values] seems to conflict with the fact that under capitalist production the elements of productive capital are, as a rule, bought on the market, and that for this reason their prices include profit which has already been realized, hence, include the price of production of the respective branch of industry together with the profit contained in it, so that the profit of one branch of industry goes into the cost-price of another.” [6]

22He did not correct his mistake, as he was satisfied with having established that the sum of surplus values was equal to the sum of profits (and rents). He was content with what we have come to call the fundamental theorem of Marxism: a positive rate of surplus value is necessary and sufficient for a positive rate of profit. Above all, he wanted to refute the “common” theory that each factor of production—labor, capital, and land—corresponded to a revenue: wages, profit, and rents.

23He modeled his economic categories on Hegel’s logical categories: use value corresponds to quality, exchange value to quantity, money to measure, surplus value to essence, and wages, profit, and rents to phenomena. Because the one he had chosen had proved a bad starting point, between Grundrisse and Zur Kritik Marx changed his approach. In accordance with the classical economics tradition, he began by excluding the category of use value from economics, retaining only the categories of exchange value and money value, which he conceived through a very Hegelian dialectic of the particular and the general. However, in broaching the transformation of money into capital, and in order to introduce the distinction between labor and labor power, he was forced to reintroduce the concept of use value. The category of quality provided a clearly marked place for it in Hegelian logic. Marx was able to write to Engels on January 14, 1858, that Hegel’s logic had been “of great service.”

24But Marx did not simply identify surplus value with the Hegelian category of essence, and wages, profit, and rents with that of phenomena. He also conceived the relationship between essence and phenomena in Hegelian terms, as one of inversion. Marx seems to have thought that this relationship of inversion was self-evident, and made no attempt to justify it anywhere in his writing. He assumed Hegel had established it once and for all in the Phenomenology of Spirit and the Science of Logic, [7] and that there was no need to reopen the question.

25According to Hegel, understanding denies the phenomenal reality of movement by explaining it in terms of its immutable essence, the interaction of forces. The movement of bodies can be reduced to the law of universal attraction. This is true for celestial and terrestrial bodies, for the trajectories of planets, and falling bodies. Whatever the nature of this movement, it must take place in accordance with the form of this law, which is proportional to the masses involved and inversely proportional to the square of the distances. As a matter of fact Coulomb’s law, which explains electrical attraction, accords with this form: electrically charged bodies attract each other proportionally to the product of their charges, and in inverse proportion to the square of the distance separating the charges. But in this case it is charges with opposite signs that attract each other, while charges with the same sign repulse each other. Hegel saw an inversion of the essence of mechanical movement in the fact that the similar is attracted to the dissimilar, and the dissimilar to the similar.

26This is not only true of the natural world, but also holds for the cultural world. In The Spirit of Christianity, Hegel discusses the Sermon on the Mount in the same terms, as an inverted world: “There are cries in which he enthusiastically deviates directly from the common estimate of virtue, enthusiastically proclaims a new law and light, a new region of life whose relation to the world could only be to be hated and persecuted by it.” [8] And, as he puts it in the Phenomenology of Spirit: “an action which in the world of appearance is a crime would, in the inner world, be capable of being really good (a bad action may be well-intentioned); punishment is punishment only in the world of appearance; in itself, or in another world, it may be a benefit for the criminal.” [9]

27Because this inverted world is the negation of the world of essences, which is itself the negation of phenomenal reality, the inverted world is the negation of the negation of phenomenal reality, and thus its restoration—no longer as mere movement, but as self-movement, a movement whose principle is contained in itself and not in an external force, such as life. The phenomenon is indeed therefore the inversion of essence. Whereas it is essence that wins out in Marx, for Hegel it is the phenomenon—but the phenomenon once restored by the inversion itself.

The incomplete nature of Capital

28Marx remarked in 1877 that he had written the different parts of Capital in the inverse order of their publication, beginning with Volume IV. [10] In fact, things were rather more complicated. The Economic Manuscripts of 1861–1863 indicate the following order of composition: Volumes I, IV, III, I, III, II.

29Marx planned to publish three volumes: the first containing Volumes I and II, the second containing Volume III, and the third containing Volume IV, on the history of theories of surplus value. [11] But when Capital was issued in September 1867 it contained only the first volume. Marx continued to work on the second volume up to his death in 1883. Engels published this in 1885, and the third in 1894. He left the fourth in the hands of Karl Kautsky, who put out the initial part in 1905 and the remainder in 1910.

30Marx appears to have run into trouble with Volume II, and more precisely with the connection between Volumes II and III. The transformation of values into costs of production, which was conceived and drafted before the final version of Volume I, completed Capital, in a sense, before the theme of circulation had even been sketched out. On the one hand, Volume II has to come before Volume III, because differences in the time of circulation elide the distinction between constant and variable capital, substituting for it another, between fixed and circulating capital—a distinction that lays the groundwork for the concept of the cost of production. On the other hand, the transformation of values into costs of production should occur before circulation, as it is under the latter form, costs, that commodities circulate. In other words, circulation is both the final and the efficient cause of the transformation. Marx would have had to run together Volumes II and III. And, indeed, this is what he eventually settled on. [12] But the idea had always been that Volume III would unite the first two, and it could no longer do so if it was combined with Volume II. Marx clearly did not opt for this final change of plan, which would have required him to rewrite the whole of Volume III.

The economic failure of socialism

31Marx was all the less inclined to rewrite Volume III because the transformation of values into costs of production gave him a way of explaining the survival of feudal land rent in bourgeois capitalist society. Agriculture is supposed to be a branch of industry with low organic composition of capital, and its costs of production should consequently be lower than its values. But because there cannot be free circulation of land, agricultural products are sold for their actual value. And because farmers must settle for the general rate of profit, they can leave some rent to the landowner. In other words, capitalist competition requires the farmer to share the surplus value with the landowner.

32Marxists have generalized this explanation to include monopoly costs. A high organic composition of capital encourages the formation of monopolies, given the prohibitive cost of entry into the production sector. Monopoly holders are in a position to emphasize the divergence between costs and values to their own advantage, and to increase the transfer of surplus values from branches with low organic composition of capital. Similarly, underdeveloped countries that primarily export agricultural products, and have low organic composition of capital, transfer part of their surplus value to developed countries. Under the transformation model, as soon as there is a general rate of profit—that is, as soon as there is free circulation of capital—all exchange of products with different organic compositions is unequal.

33Similarly, socialist prices were monopoly costs of production manipulated by the state as part of its development plan. For instance, it was supposed that the early accumulation of socialist capital would not come about through violence—as ultimately happened—but through transformation. The state should require the agricultural branch of production to sell its products at their cost of production, and so below their value, in order to transfer the rent to the industrial branches of production. But there were necessarily arbitrary distortions that created shortages in some branches and waste in others, and consequently, over the course of successive price reforms, market prices returned—and that was the end of socialist economics.

34Our conclusion from all this is that the dialectic of essence does not raise the same problems as the dialectic of the concept. The dialectic of the concept is, in my view, incoherent: while concepts are quantifiable, they are not quantified. The state is not universal in itself. A state that is part of a federation is necessarily particular. In the same way, individuals are not by definition individual. Characters such as Tartuffe, Don Quixote, Don Juan, and Adrien Deume are all universal. By contrast, the dialectic of essence, in which negation functions as mediation, is crucial for the establishment of the truth. This is why a scientific law is only true ceteris paribus: the negation of the negation gives it its exceptional character, its conditions of validity. In the same way, in the social field, this dialectic of negation is the only possible way of doing justice to minorities. The negation of the negation is the law of the majority once the minority’s objections have been heeded. This is the condition that allows democracies to avoid degenerating into dictatorships of the majority.