The problem of the value-form
Within the framework of the analysis of the value form, Marx is not concerned with analyzing the exchange relations of commodities, whether they are conceptually founded as historical or logical or as historical-logical forms of exchange, since capitalist exchange relations with their quantified units and relations are already assumed in the analysis of the simple value form through the unfolded to the general value form, the corresponding determinations and measures of quantity and, first and foremost, the incorporeal measure of money, symbolic capitalist money, with whose existence commodities can only really enter into quantifiable relations. According to Peter Ruben, within the framework of Marx’s illustration of capitalist wealth as an “immense collection of commodities”, this can be defined purely logically as an intensional quantity (an intensional quantity is characterized by the fact that its elements are determined by a single property common to them). And the individual commodity – neither empirically nor ideally definable – represents an element of this set, which means that Marx’s definitions – collection of commodities and “elementary form” commodity – are initially not essentially different from the set-theoretical definitions of “set and element”, except for the fact that Marx always has a very specific set in mind with “set”, namely an empirically given set of products as potential commodities. (Cf. Ruben 1998: 17) Collections of commodities in capitalism, which Marx finds in their historical-singular reality, namely as the results of capitalist production processes, represent a given precondition for the conceptual explication of capital and its forms. A currently given quantity of products in capitalism can thus simultaneously be described as a (potential) realization of (capitalist) commodity wealth. (Ibid.) (It should be added, however, that in capitalism there are also a large number of materializations of wealth as non-commodities, e.g. institutions such as schools, hospitals, prisons, etc., as described in detail by Foucault). With Marx, we are therefore dealing with an objective theory of value, insofar as objects – which are initially only potentially commodities, because they must be realized by money in circulation in order to attain commodity status (“commodities are not”) – are first and foremost addressed in the context of objective relations/structures of capitalist exploitation – and thus not subjects, for example as executors of a rational choice theory, whose unit of reference is the actor rationally calculating his utility in the course of affirming strategies of optimization. At this point, Marx’s objective theory of value decouples itself not only from the subjectivist or neoclassically oriented theories of value, but also from the classical labor theories of value of Ricardo and Smith. Similarly, a radical cut must be made against the positions that still argue in terms of the logic of reflection and want to tie Marx to Hegel’s discourse, as was partly forced by the so-called capital-logical reading of Marx, not to mention the numerous attempts to bring Hegel’s absolute spirit and Marx’s problematic procedure into some kind of correspondence.
One of Marx’s first important theses is that the concepts of value and use-value imply opposing determinations of a thing – commodity – whereby in the same breath the peculiar relationship between at least two commodities is addressed, peculiar insofar as the second commodity in particular plays a very specific role in this relationship. We will see this later. For if we consider a commodity in complete isolation, it initially distinguishes nothing at all from a mere object of use, from which a different, an invisible value could possibly be expressed. An object cannot be valuable in itself, it needs to be related to another object. Nevertheless, those opposing determinations of use-value and value are not initially distributed over two commodities, but concentrated in a single commodity; they represent two structural moments (forms) concentrated in one object, which as opposing determinations cannot, of course, enter into a relationship of interaction in one commodity. Commodity as an elementary form of social wealth means that something existing (commodity) represents it directly, but wealth must be separated into a form and determined as a relationship between two commodities. Marx writes with regard to commodities: “They are, however, only commodities, because they are doubles, objects of use and at the same time bearers of value. They therefore appear only as commodities or possess only the form of commodities, insofar as they possess a double form, natural form and value form.” (MEW 23: 62) Here, the designation of the commodity as an object of use (in addition to the designation of the property “value”) proves to be correct compared to the term “use value”, which Marx often used synonymously, because after all, the term “use value” first and foremost designates the usefulness of an object, while what Marx calls a “commodity”, insofar as it is the material carrier of value, is conformed to by the use of the term “object of use”. (Cf. Ruben 1998: 18f.) The usefulness of an object thus generates the use value and therefore the commodity has a use value because it permits some kind of satisfaction of need, while the commodity as an object of use is the bearer of value. In this way it could also be understood that the commodity as a unity of commodity and value contains a strange synthesis of the sensual and the supersensual, the finite and the infinite – it is precisely this synthesis that the commodity itself cannot represent. And this is precisely where Marx saw an antinomy. (Marx’s analysis of the value form is based on a historically contingent social situation, otherwise we would not be dealing with the analysis of a singular mode of production, but with the initial determination of Hegel’s process, for example. And what we describe as hyper-objects of the critique of political economy or of non-economy are not things in themselves, but always only very specific “phenomena”, so to speak, which are constituted by the capitalist economy and which could perhaps be described as spectral objects; the thing in itself, however, does not simply elude us, but can be described through an antinomic experience of reality).
With the concept of value, Marx is already referring to very specific concepts of relation. Relational terms are terms that cannot be determined by themselves, but only reciprocally by the other term. In contrast to the mathematical concept of relation, Engels defined the category “relation” from the outset on two levels: a) “The fact that it is a relation already means that it has two sides that relate to each other” (MEW 13: 475), (b) “But relations are always bound to things and appear as things”. (ibid.: 476) In Engels’ view, binary relations (which always contain an interaction of concepts with one another) differ from both actions and facts, and they also differ from mathematical relations insofar as relations do not exist without objects or things. One could then describe the process of commodification as the way in which differentiated, independent objects are reduced or homogenized to equivalent units (commodities), whereby objects with their different materials and different relations, which may open up a plural field, are translated into the infinite self-similarity of commodities, which can ultimately only be grasped by a non-representational third party. By means of the validity of money, objects that are potentially commodities are integrated into a social context, whereby their singularity and their nuances, the improbable about them is itself erased. This leads to the conclusion that commodities are first and foremost for money, in that they represent their values in it – as commodities they are thus in a certain sense not commodities, whereby they represent something like a dynamei, insofar as they must first be realized as such in exchange for money. Commodities therefore do not have an independent existence, which Marx also expressed in a concentrated way with the metaphor of the “sensual-supersensible thing”. There is no more depth or withdrawal here, and this distinguishes the commodity from intentional or material objects, which have an independent existence, even if they are not to be understood as vacuum-packed (Graham Harman) and (must) enter into relations. The science theorist Roy Bhaskar claims that some events are non-existent or some objects remain dark, even if they have a tendency to rise to the surface or become “hot”, because there may be forces that work extremely against these objects. On the other hand, one could also say that certain events or bright objects persist precisely because there are social forces and circumstances that seem to determine these kinds of objects as eternal positivities. Now commodification itself could be understood as such a process of structuring objects, and this due to the fact that here an abstraction of the objects to an un-property takes place, in that external relations that are external to the relations/objects are permanently transformed into internal relations, insofar as relations/goods have a single strange un-property in common, which apparently binds them to each other forever: Value – whereby primarily the relations of objects constituted by this un-property are considered socially relevant. At the same time, it must be assumed that the commodities entering into the relation do not precede their relationalization. The commodity is primarily relevant as a price. However, this specific formation of the social inevitably requires procedures that we want to describe here not only as actualization, but also as the immanent terrorism of capitalist commodification, which works by means of a tautological repetition that can be grasped with the (conceptual) figures of self-similarity and reflexivity of value forms. And this has absolutely nothing to do with the kind of repetition that the sociologist Gabriel Tarde, for example, described as invention in his construction of a microsociology, insofar as the latter is about the invention of something truly new through the combination of what exists in each case, repeating the difference. Paradoxically, however, it is precisely the immanent terrorism of commodification that accentuates a strong moment of activity even in relation to invention, insofar as it manages to either homogenize the inventions, their conflicting creations, affects and impulses within the social hologram that we might call society (without imagining it as an all-quantifier, container or original objectivity), or, as we will see later, to permeate it with extraordinary dissonances (synthetic finance). Thus, today the commodity form is increasingly transformed into a cybernetic code in the processes of value formation, i.e. the commodity form is a sign form. Arthur Kroker speaks here of a recombinant commodity form, with which the speed of circulation becomes dependent on the transformation of use value into an economy of speed and the virtual (cf. Kroker 2004); and finally, Kroker, in agreement with Baudrillard, speaks of a “rational terrorism of the code” as a decisive form of capitalist axiomatics. On the other hand, the arbitrary reductionism inherent in commodification is also reflected in the inadequate conceptions of subject-oriented economic sciences: After all, a scientific discipline should never claim conclusively that it can lay claim to something like universal validity for all differentiations, nuances and facets of its (economic) object or subject matter, just as an epistemology (set of concepts, axioms, definitions) is never able to represent or delineate the totality of a field within a discipline (in this case, economics). Within this framework, the principle of every sufficient economic science, which claims to manage the sufficient reason for every single economic phenomenon, can be paraphrased with these words: Every economics has the same form, which is the template for every kind of empirical economic science.
2. simple and unfolded value form
We assume, on the one hand, with the so-called capital-logical reading (which, starting from Hans-Georg Backhaus, has been widely discussed as value form analysis since the 1968 student movement, especially in Germany, cf. Backhaus 1997/ Elbe 2008) and, on the other hand, following the semio-economic reading of the problem by Harald Strauß, that the representation of value forms from the simple to the unfolded to the general value form contains a formal explication of the conceptual figures of “self-similarity and reflexive form” (Strauß 2013: 159ff) (of commodities) and thus does not refer to the representation of certain historical phases of development before or in capitalism (simple commodity production). We are therefore dealing with the problem of representing the “contemporaneous history” of capital, in and with which capital sets itself, a history for which Marx himself provided a catchy definition with regard to the aspect of the “contemporaneous”: “These preconditions, which originally appeared as conditions of its becoming – and therefore could not yet spring from its action as capital – now appear as results of its own realization, reality, as set by it – not as the result of its coming into being, but as the results of its existence.” (Marx 1974: 364) The expropriation of the immediate producers from their means of labor is presupposed for capital and thus it is in turn a set form, but also remains the permanently setting form of this expropriation. In a certain sense, the process of separating the producers from the means of production continues throughout the internal history of capitalism. If we follow Althusser’s position, the auto-logic of capital, as Marx attempts to categorize it in Capital, is preceded by the necessity of an initially singular encounter between deterritorialized labour flows and capital flows, which emerged from the side of the labour flows in and with the processes of original accumulation and was described by Marx in the concluding chapter of Capital vol. 1 primarily as the separation of producers from their means of production, a process that Marx describes as the prehistory of capital. This must be understood as a singular, non-linear history, within which the relationship between workers and capital only most likely became necessary, for ultimately the incorporation of actors into the wage-labor relation did not necessarily result from the transformation of serfs into doubly free laborers, but when this happened historically, Marx could speak of the mass expropriation of the producers of the means of production as an abolition in the necessity of capitalist accumulation, as its secret premise, insofar as capitalist reproduction perpetuates the doubly free worker by subsuming him to a form process based on the appropriation of surplus value. Thus, capitalist accumulation implies the perpetual reproduction of the fundamental process of separation. This is the dynamic of an immanent static (Adorno), a becoming of social relations in and with which all fixations tend to be dissolved and the “law” of capitalist development nevertheless remains unchanged. Only from the perspective of fully developed, self-setting capital can the meaning of original accumulation, which itself has no inherent teleology, be explained. At the same time, with regard to the development of deterritorialized capitalist money flows, both the emergence of urban commercial capital in northern Italy and the absolutist state and its industrial-military complex must be taken into account, because the financing of wars in Europe in the 16th century was only possible through an economy that tended to prosper, which ultimately led to mercantilism and the development of manufactories.
Let us now finally turn to the various forms of value. Marx wants to read the equation x commodity A = y commodity B as an expression of value “x commodity A is worth y commodity B”, as an expression that indicates that commodities a) are certain quantities of different commodities (the parameters x and y denote quantities, while A and B symbolize specific types of commodities), b) are equated in a very specific form, insofar as the identity set by the sign “=” conceals a difference. At the same time, one could also say that in the expression of value, analogous to the meaning of the philosophical term “expression”, the expression envelops what is expressed, as long as it does not exist outside the expression. However, it is important to note here that Marx always analyzes economic expressions in terms of their possibility, indicating that they shift in the course of the representation of the self-similarity of value forms until they are finally exposed to the break (in the “transition” from the general value form and money), in order to finally abandon the expressions completely to decay, which as a process of critique already points beyond the representation of the various concepts. In the expression itself, the rupture by which it is characterized is thus itself traced.
First of all, the problem at this point is that the expression of value, if it is written as an equation, requires a kind of dimensional equality, without which we are immediately faced with a logical contradiction, because 20 cubits of canvas are no more equal to 1 skirt than 5 apples are equal to 3 pears. The linguistic formulation explicating the equation “20 cubits of canvas are worth 1 skirt” can also be formulated as follows: “The value of 20 cubits of canvas = the value of 1 skirt”, a formula which, however, again expresses nothing but a tautology, because what Marx wants to explain, namely the value, he already presupposes by fixing the equation. (Cf. Ruben 1998: 21f.) To put it another way, it would have to be shown through the analysis of the simple form of value that commodities realize something like an ideal identity in a quantitative way. Putting equation and value expression into one another really does seem to pose a problem here, as long as one does not bring the differential (symbolic) determination of the value expression into play. And finally, one would have to show that this equation can only be read against the background of a third party, because the “value of the commodity” cannot be conceptually extracted purely from the factors of objecthood and relation. Hans-Joachim Lenger has pointed out that the proposition of the identity A=A already points to a third, to a difference that precedes the equation, insofar as A has already doubled itself in A=A and is therefore, as the first A, at the same time a third, so that the identity emerges from the repetition of difference. A is not simply identical with itself, but will have been identical with itself via a detour, whereby A as origin or as first is already deleted. (Cf. Lenger 2004: 68f.) Here again we are dealing with an “there is” that is to be understood as a difference to positivity, but which takes place in positivity itself. And this difference already touches on the non-representational and thus on value.
Within the “equation”, commodities A and B (in a relationship purely as such, i.e. independent of the exchange of commodities) stand opposite each other in a polar relationship, i.e. they occupy different positions: While commodity A is in relative value form (active), commodity B occupies the position of equivalent form (passive), whereby it is impossible for a commodity to be actualized in one of the two positions at the same time, although the positions can be virtually exchanged. With the possibility of changing places, commodity A possesses a weak passivity, because it must already have been assigned that it is active, while commodity B cannot be separated from a weak activity as a form of immediate exchangeability, so that, as Lenger has shown, différance is already integrated into the game here, in that it both gives and withdraws the moments of activity/passivity from the expression of value, whereby the object of Marx’s theory at this point simply proves to be an impossible one. (ibid.) Virtualization at this level thus implies that changes of position take place (changes of position are virtual and at the same time positions are given), but no commodity can actualize itself simultaneously in both forms (value form and equivalent form). (Cf. Strauß 2013: 159f.) The statement “20 cubits of canvas are worth 1 skirt” can therefore be supplemented by the statement “1 skirt is worth 20 cubits of canvas”, which establishes a relation back or equivalence. With the concepts of relative value form and equivalence form, Marx brought into play from the outset concepts of relation that are initially polar and at the same time mutually determined, insofar as one concept does not “function” without the other concept. And it should be pointed out that the two commodities A and B, with their positioning as “relative value form” and “equivalent form”, are in an asymmetrical relation, which also means that the equation is characterized by a non-simultaneity of places at the moment of equation (currently the commodities can only be in one place), so that even with the simple value form one must assume an underdetermination of the expression or the fiction of a conclusion.
What does value expression mean at this point? Commodity A actively makes commodity B its expression of value and at the same time it expresses its value in itself via commodity B, and in this way it distinguishes itself from itself as an object of use. Marx writes: “By equating the other commodity with itself as value, it refers to itself as value. By referring to itself as value, it simultaneously distinguishes itself from itself as use-value.” (MEGA II/5: 30) This equation of commodity A with commodity B (by means of the production of self-similarity) suggests that commodity A would reflect its value in commodity B (whereby the natural form of commodity B would be transferred into a reflexive form), whereby Marx, with the formulation “expression of commodity A in the body of commodity B”, actually refers to the fact that commodity A expresses something in the expression of value or expresses its value, so that commodity B with its secondary use value is regarded as something, namely as a “mirror” of the value of commodity A. (MEGA II/6: 89) However, this mirroring includes an as-if, because commodity A does not, of course, appear before a mirror with its value, but this type of mirroring is solely the result of a formal determination that arises from the juxtaposition of the two commodities. (Cf. Strauß 2013: 160) As commodity A is related to commodity B as an equivalent, commodity B is regarded as an expression of the value of commodity A, whereby the validity in the semiotic dimension is to be understood as a symbol. Commodity B thus becomes the interpretant of the value of commodity A, but not of object A. Depending on which position commodities occupy within the expression of value, Marx ascribes to them either an active or a passive mode; he wants to show that commodity A, which is in the relative value form, effects something on the second commodity B that could never take place outside this relation, whereby commodity B in the reflexive form is initially the passive element, but as an object of use, which is regarded as an expression of the value of commodity A, it acquires the form of immediate exchangeability (and thus an active status). “The expression of the canvas value in the skirt imprints a new form on the skirt itself. In fact, what does the form of value of the canvas say? That the skirt is interchangeable with it. As it walks or lies, with skin and hair, in its natural form of skirt it now possesses the form of immediate interchangeability with other commodities, the form of an interchangeable use-value or equivalent.” (MEGA II/5: 29) (Through the potential reversal of its position, commodity B can also express its own value in itself via the detour of commodity A).
Hans-Joachim Lenger writes the following on this Marxian conceptual figure: “Rather, both places mark a difference that initially reveals itself as one of ‘activity’ and ‘passivity’.” (Lenger 2007) The fact that commodity A as an active moment passes through its other (commodity B as a passive moment) in order to return to itself is both indicated and concealed in the equal sign. At this point, Lenger adds Derrida’s famous figure of différance to Marx’s expression of value. (Lenger 2004: 75) Because commodity B is not actually expressed in the equation in the first place, but only helps commodity A to express value, a kind of “inexpressible postponement” is present in the expression itself at this point and with it a difference that remains as withdrawn as it is indicated, and thus this kind of equation is always already torn by the postponement. Lenger emphasizes here the aspect of the (real) impossibility of the formula or the concept of the “value form”. He refers to Derrida, who writes here: “Every concept is inscribed by law in a chain or in a system in which it refers to the other, to the other concepts, through the systematic play of differences. Such a play, the différance, is not simply a concept, but the possibility of conceptuality, of the conceptual process and system in general.” (Derrida 1976: 16) For Derrida, what he calls différance appears neither as active nor as passive; rather, différance announces a medial form, the play of difference (medium) and unity, and it is precisely in this respect that, according to Lenger, in Marx’s conceptual games around the expression of value, the deferral actually remains present as well as withdrawn, which to a certain extent corresponds to a difference that differentiates itself, which Marx continues to shift through the medium of money without ever being able to master it. Nor does this mastery succeed through the operation of reversing the expression of value, through its “reading backwards and forwards”, with which Marx establishes equivalence – rather, according to Lenger, it is only with the concept of capital that the structure itself comes to light with all its aspects of spatialization and temporalization, so that one must always remember that “no term that differs from others can function as the genealogical principle of a structure from which it itself first emerges. “1
Peter Ruben makes an interesting attempt to formalize the simple value form when he resolves the tautology underlying the value equation – which immediately arises if the simple value form is read purely as an equation and not described as a differential expression – by using the linguistic statement value form “a/ = b”, which indicates the concrete equality – exactly comparability – of commodities. With regard to the value expression, Ruben writes: “In it, the subject ‘a’ denotes the object of value determination, the object ‘b’ the means of value determination and the predicate ‘= b’ the property of the object a to be valued.” (Ruben 2008:93) And Ruben comes to the conclusion that this statement is compatible with Marx’s definition of the expression of value or with the polar opposite categories of value form and equivalent form. Here, the grammatical structure “commodity A is equivalent to commodity B” must be observed, in which A and B are distinguished as subject and object, whereby commodity A (active) is in “relative value form” and commodity B (passive) is in “equivalent form”. A is designated as the subject/object and B as the object, whereby the object B serves as a means of expressing the value of the object A, which also requires a predicate (property) through which a relationship of equivalence is given or established. In Ruben’s statement, commodity B stands as a reflexive form for the unity of the property of equality (predicate/logical center) and the means of comparison, which is an object or an object of use. And thus the unity of property and object (which of course presupposes an analytical separation), which expresses equivalence, could be written down in a syntactically and logically flawless way. Paradoxically, commodity B as a reflexive form and thus as the actually passive element of the commodity relation simultaneously provides the active moment of differentiation in the course of the self-similarity of commodities A and B, in that it only puts commodity A into the form of accepting its own activity quasi like a reception. The reflexive form, which consists in the fact that commodity B, as the embodiment of the value of commodity A, simultaneously sets itself up as the body of its own value, contains the figure of a retroflexion here. Finally, it should be noted that the (logical) problem of the genesis of the value form is not precisely how value forms come about at all, but which transitions are necessary to get from the simple to the general value form. Subsequently, in the context of the problem of representation, one could now decide in favor of a “logic” of representation by means of the conceptual unfolding from the simple to the unfolded to the general form of value, whereby money would be quasi “caught up” in its first function as a general measure of value. (Cf. Engster 2010) Or, as we do in any case, for the necessity of constructing conceptual problems, whereby (previous) constellations, systematics and argumentative positions are deconstructed or even destroyed at the respective conceptual structural level produced. At the same time, it could be shown that specific problems do not necessarily have to be resolved in appropriate conceptual relations, but require a further generation, assembly and systematization of concepts, so that new objects of knowledge (Althusser) emerge without, however, arriving at a conclusive system. In the simple value form, the conceptual postponement as a break and as a necessary transition is suggested by the randomness of the value expression alone, because of course any commodity can take the place of the relative value or equivalent form, whereby the common feature that is supposed to be characteristic of commodities, namely being a product of labor, is only indicated as a cipher. (Cf. Lenger 2004: 112ff.)
The so-called unfolded form of value is a multi-digit relation or an extended elementary theorem, which contains the statement that the value of commodity A can be expressed in a potentially infinite number of other commodities: x commodity A= y commodity B = v commodity C etc., which immediately shows that a) in the context of this series, it does not matter in which commodity commodity A expresses its value, whether perhaps in skirt, canvas, wheat, computer chips or some other object, b) each new type of commodity offered increases the quantity of commodities that can take the place of the equivalent form, so that the equivalent form is potentially open. Commodity A is in the position of the relative value form, against which all other commodities are virtually in the position of special equivalents. Marx writes in this regard: “However, the individual form of value passes by itself into a more complete form. By means of it the value of a commodity A is expressed only in a commodity of another kind. But the nature of this second commodity […] is quite indifferent […] The number of its possible expressions of value is limited only by the number of different kinds of commodities.” (MEW 23: 76) It is immediately apparent that even with this configuration of commodities it is by no means possible to establish stable and fixed relations within a commodity-money-capital system.
To illustrate the unfolded form of value, Ruben uses the propositional link “a /= b ∨ a/ = c ∨ a/ = d ∨ …” This is an open chain of (self-similar) signifiers, in mathematical terms a non-exclusive disjunction or a potentially infinite adjunction, within which it is possible to replace commodity B in its function as predicate/means of comparison with a potentially infinite number of commodities. (Ruben 2008: 94) This kind of syntax of the concatenation of commodities, which contains various reflexive forms within itself, leads, as is easy to see, to an infinite progress, or to put it another way, commodity A is now (virtually) opposed to all types of commodities, as Marx states in the first edition of Capital. The infinite nature of the value expression of any commodity A is shown by the fact that every other commodity can represent it, but does not come to an end through its representation in all the other commodities. At this point it already seems possible to imagine a patchwork of diverging expressions of value, whereby each commodity, insofar as it is in the relative value form, potentially expresses its value in an infinite number of other commodities, while with the realization of an expression of value each individual equivalent form excludes other equivalent forms. Commodity A is thus potentially confronted with all types of commodities, which means that a virtualization is present, but this cannot simultaneously be expressed as a realization. (Strauß 2013: 162) The number of all possible forms of value is ultimately equal to n (n = 1; 2; : : : ;N).2 With Marx’s definition of the unfolded form of value, commodity A, which is in the relative form of value, would now be confronted with n-1 other commodities, all of which are potentially capable of assuming the position of the equivalent form, although these commodities cannot be combined with each other at will, but are mutually exclusive as equivalents in each realization. On the basis of the frequency implication assumed in the unfolded value form alone, no stability and consistency can be ascribed to such an economic system (and only capitalism is an economic system), but also because the problem of mutual exclusions exists here. In the disjunctive series, which allows x possible substitutes for commodity B, the difference is simultaneously unfolded and postponed, insofar as it is supposed to express value without ever being able to eliminate the difference as which value is unwound. To put it another way, insofar as each commodity can be the general equivalent for the relation of all other commodities to one another, and thus each commodity can place all other commodities in relation to one another, the commodities are only decisive for themselves, but cannot form an economic system as such, because the measure and mathem of the economic system always fall into any given commodity, and this inevitably leads to an infinite regress.
- general form of value
In order to obtain the general form of value from the unfolded form of value, only the simple operation of inversion is required, which implies that we are virtually dealing with a simultaneous second and third form of value. The commodity A now no longer expresses its value in all possible commodities (as in the unfolded value form), but conversely all commodities express their value in a commodity X that is different from them. Marx writes: “The commodities now express their values 1. simply, because in a single commodity, and 2. uniformly, because in the same commodity.” (MEW 23: 79) This exclusion of a single commodity within a multitude of commodities means that any number of commodities such as noodles, skirts, books, computers or shirts express their value in a single commodity that is in the general equivalent form. Ruben writes: “By taking this circumstance into account, we reverse the position of the objects in the expression of value in such a way that a now becomes the only means of reflection, while the objects b, c, d, … become the many objects whose values are to be reflected by a. We thus gain ‘b/ = a’. We thus obtain ‘b/ = a ∧ c/ = a ∧ d/ = a ∧ … e’ as the linguistic expression of the universal or general form of value. The totality of the means of value is replaced by a specific universe of valued objects that are all related to exactly one means of value. This universe is an example of the meaning of the concept of quantity in mathematics. It is thus the second evolutionary step in the development of the value form, which provides the protomathematical precondition for the realization of descriptive thinking.” (Ruben 2008: 95) This universe could be understood in a broader sense with Günther Anders as an insufficient part of a cohesive, windowless, seamless and gapless system. (Anders 1980: 195) It can be read as a concatenation of conjunctions that can, but do not have to, transform into various disjunctions of actualization (products realize themselves as commodities in the sale that can, but does not have to, take place). (Cf. Strauß 2013: 162)
If a commodity occupies the position of general equivalent, then it is interchangeable with all other commodities, but all commodities can virtually occupy this position. And we immediately come across the fourth form of value, in which every commodity can take the form of the general equivalent, so that when this position is realized, all commodities exclude everyone from the general equivalent form. (Cf. the overview in Strauß 2013: 232f.) In order to demonstrate the lack of stability of economic form constitution, Marx resorts to the representation of a fourth form of value in the first edition of Capital: “The general form of equivalence always comes to only one commodity in contrast to all other commodities; but it comes to every commodity in contrast to all others. But if each commodity sets its own natural form against all other commodities as the general equivalent form, then all commodities exclude all others from the general equivalent form and therefore exclude themselves from the socially valid representation of their values.” (MEGA II/5: 43) The fourth form of value thus remains conceptually just as underdetermined (it does not “solve” any problems) as the simple, the unfolded and the general form of value, because with it it is ultimately possible that within this specific syntax of commodity concatenations every commodity in principle occupies the place of the general equivalent, whereby all commodities exclude all from the general equivalent form.
It can now be seen that the presentation of a (logical) genesis of the value forms, which should ultimately lead to the money form, whereby the money form is often misleadingly equated with the general equivalent form in the Marxist discussion, obviously does not achieve this goal. At this point, we also reach the limits of the logical-conceptual representation, as it is neither able to show the conditions of stability or the regulating “law” (cf. Strauß 2013: 164) for an economy, nor is it able to tame or shut down the deferral of the expressive, which must simply escape identifying thinking. At this point, the conclusion itself is postponed, it is called into question and in turn refers to the questionability of its own premises, thereby already giving itself a virtual evidence. The procedure of self-similar reflexivity, which guides the analysis of the value form, thus by no means leads to the money form or to a stringent concept of money due to the indeterminacy or contradictoriness of the fourth value form, which Marx then deletes from the second edition of Capital, not without consequences for the concept of money. Thus, the decisive argument in the context of the fourth form of value is that, from the perspective of a fully developed capital, the representation of the emergence of the money form from pre-monetary forms of value must fail. It turns out that there are potentially an infinite number of forms of the general equivalent, which, however, should not lead to the reverse conclusion that the existence of the general form of value should be treated exclusively as a question of historical contingencies, although there are indeed historical tendencies that form something like possible historical situations. Under the impulse of very specific tendencies, which at the same time require something that points beyond them, it is now necessary to show how these tendencies are integrated into a capitalist structure.
In the first three chapters of Capital, Marx deals with the problem of money only as an auxiliary conceptual construction that ultimately allows him to develop the concept of the capitalist mode of production. After all, money, as the most general form of capital, only moves in its own self-valorization process, in which it is produced as a monetary credit to which all other forms of money, such as state-certified paper money, are subordinated. The circulation of money is therefore a dependent variable of capital accumulation, which is based on the typical money of capital, namely credit money. For this, however, capital needs economic math. And the conclusion in this respect should again be that there is a symbolic “force” that is responsible for the fact that in capitalism money occupies the place of a “homogeneous numéraire”, among other things.
Equivalence and Abstraction
The forms of value presented so far contain an asymmetrical or polar relation, whereby the property of symmetry and consequently the equivalence relation, which always includes back-reference, can already be established for the simple form of value by means of the operation of reversing the respective “equation”. The axiom of symmetry thus proves to be absolutely necessary for the representation of the equivalence relation of classical commodities. Hans-Dieter Bahr writes: “The logical form of an equation initially consists of an abstract mapping or projection that expresses the word. But without a further rule of operation, this mapping is indistinguishable from a metaphor: Canvas is like skirt, both like gold. It is only through the axiom of symmetry that this so – like gains the structure of an equivalence relation, an exactly so – like. 20 cubits of canvas are exactly equal to one skirt, if one skirt is equal to 20 cubits of canvas.” (Bahr 1983: 379) The value expression “commodity x A is worth commodity y B” (sentence: commodity A expresses its value in commodity B) is thus to be understood as equivalent to the value expression “commodity y B is worth commodity x A” (sentence: commodity B expresses its value in commodity A). If equivalence applies, then the two propositions can certainly differ with regard to the perspective of observation – which is always also an observation of difference inherent in all first-order observations – but their indifference and thus their symmetry remains guaranteed by the fact that the unity of difference can be established, insofar as the unity of difference here denotes a binary observation difference without one of the two sides of the observation difference being marked. The second-order observer, for example, who observes that a first-order observer describes a value expression, can describe the first-order observation as an observation that uses the unity of difference of value/object of use. From his point of view, this applies to both first-order observers, who can of course also take on the role of the second-order observer. The mode of equality of observation (the first-order observer), which is established by the second-order observer, reflects on the one hand the symmetry of the equivalence relation, which on the other hand is established by an assignment rule/axiom.
For Marx, the equivalence relation is supposed to indicate, among other things, that different commodities have a single common property (value), namely as a dimension for determining the elements belonging to a quantity, with which commodities can be compared as quantities in the first place. This property is quantity per se, which Sohn Rethel called “quantity in abstracto”, whereby for him the relational determination of this quantity always implies a practical realization. (Cf. Sohn Rethel 1970: 55f.) In this context, Sohn Rethel rightly said that the equivalence of the so-called exchange equation does not mean equality, but rather equivalence, although this statement should by no means be aimed at any kind of mediation between exchange and value expression (value form), as Sohn-Rethel himself believes. (Ibid: 57) Rather, this is an equivalence that is purely immanent to the value form, so that it must not be interpreted as a (capitalist) exchange relationship, because money is ultimately required for this. In the capitalist commodity economy, the relationship between relation and relata is a very special one, meaning that we are not dealing with a relation that remains external to the relata, but rather, as will be shown, value is usually understood by Marxist economists as one and the same common property of the relata in the relation of equality, more precisely the equivalence (internal relation) of classical commodities, i.e. of heterogeneous objects. i.e. of heterogeneous objects which, despite their qualitative difference in terms of value, are considered equal, with their property of symmetry representing quasi images of value in the value form by representing value in a homogeneous economic space, which is itself characterized by a rigid isometric movement of objects, i.e. the absolute non-variability of the properties of objects. And what tends to disappear with commodification/capitalization is what Deleuze calls the anti-sterile or clothed repetition, which only ever repeats the new or the variation and thus remains bound to a single case, to a singularity that always returns differently. (Deleuze 1992a: 43f.) This singularity is not only confirmed, but affirmed by difference thinking, in that it knows that with repetition one does not add a second and third time to the first, but raises the first time to the nth power. Deleuze writes in the introduction to Difference and Repetition: “As a mode of behavior and as a point of view, repetition concerns an irreplaceable, irreplaceable singularity.” (Deleuze 1992a: 15) It is precisely this non-identical kind of non-replaceability that gradually disappears with the contemporaneous internal history of capital (with whose comprehensive grasping (Althusser) the enormous tenacity, solidity and stability of capital is ensured to the point of fluid solidification) (although the problem of non-identical repetition emerges in a new form in synthetic financial instruments), whereby even the very last thought of the non-identical and the open is supposed to vanish into thin air, as if capitalism actually possessed the evolutionary tenacity and life expectancy of a crocodile. (Pohrt 2012: 69)
Let us now turn to the concept of abstraction, which Peter Ruben wants to be understood in a genuinely Marxian sense as a logical operation that is directly linked to the establishment of the equivalence relation. In a completely different context, Dirk Baecker has referred to Korzybski’s “structural differential”, which comes close to Ruben’s argument and contains the following differentiations: “[…] between events, E, whose properties are infinitely many, objects, O, which select a few of these properties, and names, N, which consider even fewer properties to be essential […] Structures, S, are abstractions that can be written as follows in terms of set theory: S = N ⊂ O ⊂ E. ” (Baecker 2012) And similarly, the value form analysis involves the investigation of a structural differential relationship: If one wants to prove the equivalence relation R(x,y) with the structural properties R(xx) (reflexivity), R(x,y)→ R(y,x) (symmetry) and (R(x,y) & R(y,z)→R(x,z) (transitivity) for a basic set M, then one has to pick out an element a from the basic set M with which it is possible to form a class of equivalent objects with respect to a property. Ruben writes: “If it is possible to form a class of equivalent objects with respect to a characteristic for an element from a basic set, then an equivalence relation exists in the basic set with respect to this characteristic; if an equivalence relation exists, i.e. can be assumed in the basic set, then equivalence classes (abstraction classes) can be formed with respect to the characteristic in question (which is always expressed by a two-digit predictor). In this sense, abstracting means that equivalence classes are formed.” (Ruben 2007: 12) Ruben understands the logical operation of abstraction as the construction of the equivalence relation and the formation of equivalence classes and thus of course immediately denies that the concept of abstraction could be equated with the concept of generalization, for example, which is based on or appeals to a given insight, or that abstraction is even to be understood analogously to the peeling of an onion in order to penetrate step by step to the core.
With the equivalence relation, equivalence classes are defined at the same time, the elements of which are certain commodity quanta, whereby with Michael Heinrich it is also possible to speak of a quotient set with regard to the overarching or common features of these classes, in which in fact all commodities are integrated. With regard to commodities and their relation to a logical third party, no recourse is made at all to the concept of value substance, but rather only to the determination of commodities with regard to their belonging to a quotient set, whereby a product assumes commodity status in the first place. For Harald Strauß, in the case of commodities we must assume “actualizations of the virtuality of value in prices”, which is not a given, because not all products are sold on the markets and thus transformed into commodities; in other words, no matter how much labour is objectified in the products, only through their sale do they acquire commodity status in real terms and thus realize profit. (Strauß 2013: 232)
Let us summarize: If for any given commodity there is a value relation to two other commodities (which can be quantitatively specified as exchange values), then the axiom of transitivity is guaranteed for commodities A,B,C: W(A,B), W(B,C) and W(A,C) apply. The fact that Marx does not explicitly demonstrate this deduction in Capital, although it is already implicit in the unfolded value form, can probably be attributed to the fact that the axiom of transitivity is already included due to the justified assumption of the quantity of commodities as an intensional quantity and the logically flawless formation of equivalence classes that is thus possible, Otherwise, in capitalism we would never be dealing with any form of equivalent commodity-money transactions, but always with some singular form of profiteering, usury or overreaching, through the execution of which profits may be made. profits may be made. We will return to this problem later with the question of equivalent exchange and/or mercantilism. If the conditions of symmetry/equivalence, which according to Marx must be fulfilled for it to be even approximately possible to speak of an economic structural connection in capitalism, are now fulfilled within the framework of the concatenation of commodity-money transactions, then in principle any commodity can occupy the initial or final position in a series, whereby there are always several shifting series that ensure the syntax of commodity concatenations in relation to money. Accordingly, if a conjunctive value relation is written as follows: Wn (A,B,C, …)= W (A,B) and W(B,C) and W (C, …) and so on, the following relation can also be written due to the transitivity of W: Wn (A,B,C, …) = W(A,B) and W(A,C) and W (A, …) and so on; so here already the specific functionalization of the conjunction “and” makes it clear that exactly this syntax is equivalent to a system of relations that is open in genetic terms. Insofar as all commodities, if the axioms of reflexivity and symmetry apply, are in a relationship of equivalence to one another, something like a purely logical – systemic connection is constituted, but ultimately only insofar as objects are placed in relation to one another, which are realized as commodities in their reference to money. (Cf. Kirchhoff/Reutlinger 2006: 210)
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