The publication of Reading Capital in 1965 initiated a theoretical intervention that would both culminate in and be extinguished by the events of May ’68. In this and the following chapter, I wish to argue that the thought of Alain Badiou, beyond the historical and epistemological break that was 1968, though never explicitly engaging Marx’s magnum opus, provides crucial theoretical resources that carry forward the apodictic, anti-empiricist and anti-historicist reading of Capital initiated by Althusser that I have analysed to this point. In this sense, I wish to pursue Althusser’s original assertion that in Capital, Marx ‘really did invent a new form of order for axiomatic analysis, … a new order in the theoretical, a new form of apodicticity or scientificity’.1 Badiou does so not by considering Capital directly, but by theorising 1) the general imperative of an axiomatic orientation of thought and 2) reconceptualising logic as the science of the appearance of things in a given world. These imperatives, fundamental to Badiou’s entire philosophical project, can be brought to bear on the reading of Capital itself, to further specify and develop Marx’s tendency, discussed above, to develop an additive synthetic demonstration of the structure of the capitalist social form. In other words, Badiou’s elaboration of a logical materialism (in his early texts ‘Mark and Lack’ and Concept of Model) and an ontological materialism (in Being and Event and related texts such as Number and Numbers) constitutes a direct development of the Althusserian critique of empiricism and idealism, one that further specifies the tendency of Marx’s revisions to Capital toward formalisation and schematisation as a materialist critique determined by the axiomatic starting point Marx chooses for his argument.
That said, Badiou’s relation to Capital is nonetheless an uncanny mixture of manifest disinterest to the point of disavowal and censorship (is it not odd for such a committed philosopher of Marxist communism never to have discussed Capital at some point in over two hundred monographs?), and the corresponding recurrent, unacknowledged reinscription of the order of Marx’s critique within the abstract terms Badiou’s universal logic. This insistent reinscription constitutes an objective process of displacement [Verschiebung] within the greater topography of theory, passing from a latent order (the critique of political economy) to a manifest one (Badiou’s reconstruction of abstract logic).2
The insistent recurrence of this process gives the objective and obscure impression (uncanny on the part of a Marxist) that the structure of the capitalist social form can, for Badiou, only be addressed indirectly; in short, that the various discursive iterations of Badiou’s logics (not at the level of a spurious psychology but through the analysis of real discursive objects) rewrite Marx’s Capital, but with its charge censored and diminished via its displaced reinscription within the more abstract terms of post-Cantorean logic.
In these two concluding chapters, I will argue that if 1968 marks the end of the Althusserian initiative to construct a Marxian, anti-humanist ‘philosophy of the concept’ (to redeploy Jean Cavaillès’s famous imperative), the Althusserian theoreticist position ended by ’68 nonetheless takes on its purest form as Badiou’s logical materialism of the mark (in ‘Mark and Lack’ and Concept of Model), lectures whose oral presentation was itself short-circuited by the event of May itself. The appearance of Being and Event two decades later in 1988, in turn, dismisses the materiality of the logical mark to sound the call for an axiomatic reorientation of philosophy as an ontological materialism of generic multiplicity, against both empiricism and logicist idealism, including that of the early Badiou himself.
While this tendency, I will argue in the following chapter, will culminate in Logics of Worlds, it is already decipherable in Badiou’s 1967 contribution to Cahiers pour l’Analyse, ‘Mark and Lack: On Zero’. Here, as if in a logician’s dream of Capital, is that essay’s dense opening paragraph:
Epistemology breaks away from ideological recapture [reprise], in which every science comes to mime its own reflection, insofar as it excludes that recapture’s institutional operator, the notion of Truth, and proceeds instead according to the concept of a mechanism of production, whose effects, by contrast, one seeks to explain through the theory of its structure.3
Here we find Badiou already moving in silent parallel with Marx: not with the political Marx of the Communist Manifesto, but with the theorist of the scientific critique of capitalism.
Badiou’s 1967 statement should be read, I am suggesting, as the objective, formal reduction of the methodological programme Marx sketches out in the ‘1857 Introduction’ to the Grundrisse.4 In his 1857 text, Marx set himself the project, in what would become Capital, of breaking away from the recapture of political economy as the mere articulation of the ideology of bourgeois capitalism, a theoretical recapture typical of classical economics, the consummate example of which is Adam Smith. For Smith, the theoretical articulation of a true image of capitalism was an empiricism based on the mere representation of the concrete. This entailed an analytic process that sought to articulate abstract conceptual generalisations drawn from the phenomenological manifestations of capitalism, an abstraction based on the observed regularities of its universal features. The classic example of this procedure is Smith’s famous assertion of a universal and transhistorical ‘human propensity to barter and truck’.
In contrast, Marx rejects both Hegelian Idealism and the methodology of classical political economy alike, as various modes of representation of the concrete. In their place, to deploy Badiou’s more abstract phrasing in ‘Mark and Lack’, Marx refuses the logic of conceptual representation for a novel ‘concept of a mechanism of production, whose effects, by contrast, one seeks to explain through the theory of its structure’.5 This, in a formulation analogous to Althusser’s reading of the same passage, albeit at a far higher degree of abstraction, is what Marx terms in the 1857 Introduction the ‘reproduction’ of a ‘thought-concrete [Gedankenkonkretum]’.6 Only here, in the manifest content of Badiou’s 1967 formulation (to pursue this Marxian chain of associations I am imposing on Badiou’s abstraction), ‘Truth’, as in Adam Smith’s ‘propensity to truck and barter’, or the image of the magic hand, constitutes the operator of ideological illusion, and is to be replaced by Marx’s categorial logic, a logic that Badiou, in essence furthering Marx’s tendency toward the abstraction of nonexistent idealities described in the previous chapter, pursues what Badiou calls the systematic production of formal marks.
Badiou’s fundamental assertion in his formalist essays of 1967–68 is that ‘The concept of identity holds only for marks. Logic never has recourse to any self-identical thing, even when thing is understood in the sense of the object of scientific discourse’.7 One way to read this statement is as a formalisation of the Spinozist distinction between actually existing and nonexistent things: the abstract schematisation process of logic does not indicate actually existing singular things, but purely atemporal relations.8 In this view, one could say that Adam Smith certainly produced a scientific, natural language discourse on political economy, but Marx’s critique reveals that Smith’s analysis is an ideological representation of the mere forms of appearance of capitalism in their superficial regularity (as the ‘tendency to truck and barter’).9 In other words, the putatively self-same concepts of classical political economy are revealed in Marx’s critique as fetishised forms of appearance of the true objects that only conceptual critique can produce: the substance of value, abstract labour power and the general social form of relation that he names the ‘value-form’, and the like. ‘Nothing here warrants the title of “object” ’, observes Badiou. ‘Here the thing is null: no inscription can objectify it. Within this space, one finds nothing but reversible functions from system to system, from mark to mark-nothing but the mechanical dependencies of mechanisms’.10 Badiou’s ultra-formalism thus radicalises in the mathematically grounded abstraction of nonexistent idealities, I am arguing, Althusser’s initial reading of Marx’s 1857 Introduction in Reading Capital, where Althusser famously asserted the fundamentally conceptual nature of Marx’s project, stressing Marx’s materialist rejection of empiricism and the destruction of all merely humanist Marxism.11 This reinscription of Althusser’s critique then becomes even more pressing in Badiou’s 1968 lectures, The Concept of Model.
1 1968: Logical Materialism
The Concept of Model consists of two brief lectures, along with a 2007 Preface by Badiou written for its reedition.12 These two lectures proceed in three moments: the first five sections rearticulate Althusser’s critique of Lévi-Strauss’s combinatory structuralism, rejected as an empiricist idealism, to which Badiou then appends a similar critique of logical formalism, followed in conclusion by Badiou’s presentation of his own materialist concept of logical structure.
Although the text itself is a punctual intervention, one that addresses the singular epistemological problem that Badiou calls the concept of ‘model’, it nonetheless allows us, when read in the broader historical perspective Badiou suggests in his 2007 introduction to the reprint of these lectures, to figure a broader, three-part typology of this period. Its first moment stretches from the initiation of the Althusserian philosophy of the concept, from the publication of For Marx and Reading Capital in 1965 to May ’68, including as well the journal, Cahier pour l’Analyse that emerged out of the Althusserian project to specifically develop this conceptual orientation and the articulation of a philosophy of the concept and the formalisation of conceptual categories.13 This is followed by a second period marked by the retreat from theory into political militancy (the ‘Red Years’, 1968–89). This is above all the moment of an in-formal politics, a politique de l’informel, a period in which Foucault and Deleuze famously invoked, against all universalism, a withdrawal into local, situated politics – a politics of local situations, problems, and interventions, refusing the overarching attempts to rearticulate the structural determinants of a given social configuration or order that arguably determine both Marx’s critique of capitalism and the dynamic of twentieth-century Marxism itself.14
This period of retreat into local politics is followed, according to Badiou’s chronology, by a third period: at the level of politics, universalism returns as tragic farce with the triumph of neoliberalism as a putative global destiny, while at the level of conceptual thought, Badiou bestows on this period (that extends into the present) a vital determination characterised by the axiomatic orientation initiated by Being and Event.15
Badiou begins The Concept of Model by reiterating term for term Althusser’s critique of Lévi-Strauss.16 He first defines empiricism as the (ideological) scientific discourse that articulates the distinction between empirical reality and theoretical form as a relation of representation, ‘the formal representation of a given [empirical] object’. Within this ideological figure, Lévi-Strauss’s structural anthropology is then said (in section 3) to constitute a specific form of this ideology, one in which
The pair empiricism/formalism takes the form of an opposition between the neutral observation of facts and the active production of a model. In other words, science is thought [by Lévi-Strauss] as the confrontation [vis-à-vis] between a real object, which one examines (ethnography), and an artificial object destined to reproduce and imitate the real object (ethnology) via the law of its effects.17
Lévi-Strauss implements precisely the empiricist procedure Althusser had condemned in the abstract in Reading Capital, extracting, in other words, the essential kernel from the observed object, to fashion it into a faithful representation of the real.18
The principal fault of Lévi-Strauss’s empiricist combinatory, for Badiou as it was for Althusser, is the incomprehensible, aleatory nature of any observable case or situation, the impossibility of determining, from mere observation of the case at hand, the necessity that has determined this phenomenon. Instead, the truth of scientific empiricism amounts to no more than the mere measure of the ‘fit’ between fact and model:
If the model represents the truth of scientific work [for Lévi-Strauss], this truth is never anything more than that of the best model. This is to restore the dominance of empiricism: theoretical activity cannot choose between necessarily multiple models, since its activity is precisely the fabrication of such models. It is then the ‘fact’ that decides, designating the best model as the best approximation of itself.19
The model, in this empiricist procedure, is no more than the constructed object that best accounts for, in the sense of representing, the observed facts. ‘To the question, what is the criterion of this “accounting for” ’, the empiricist observer has no other response than the circular reasoning of Lévi-Strauss, i.e., ‘the one that accounts for all the facts’.20
To this critique of Lévi-Strauss, which takes up the first half of Badiou’s lecture without adding anything substantial to Althusser’s previous critique, Badiou appends, in his fifth section, a similar critique of logical positivism. In Badiou’s presentation, the scientific doctrine of logical positivism is not at all gratuitous, but similarly depends upon a strict correlation between a formal system and its empirical objects. A formal system, as a system of necessary deductions, constitutes the accurate expression or representation of its objects, as ‘the correspondence between the statements of the formal system and the domain of scientific objects under consideration’. The formal system adheres to a syntactic regime of constraint at the level of its chain of deductions, without, however, deriving the materialist necessity that would determine the necessity of any specific axiomatic orientation.
When Badiou then turns to his own ‘construction of the concept of model’ in the final sections of his talk, it is conspicuous that this rigorous demonstration of ‘logical materialism’, as he will appropriately name this orientation in his 2007 Preface, no more attends to its axiomatic starting point then do the empiricisms of Lévi-Strauss and logical positivism he has just rejected. Badiou’s 2007 auto-critique is spot-on:
What is striking [in the talks comprising Concept of Model] is that of the two general determinations of the paradigmatic function of mathematics (the axiomatic decision and the logical constraint of its consequences), it is the second that receives attention. [In these lectures] the recourse to the normative script of formal logic is the principal focus, in so far as it imposes, through the materiality of marks and symbols, a mechanism of inscription opposed to all empiricist and idealist interpretations.21
Badiou’s definition of his earlier position as a logical materialism is revealing: rather than a (Spinozist) science of causes in which the axiomatic starting point (for example causa sui for Spinoza or Marx’s initial true idea of capitalism as general commodification) determines the materialist basis of a critique, here it is instead the mere materiality of the logical mark that produces a materialism, in which matter again stands as the emanant source, not of being qua being as in ontological, monist materialisms, but merely as a materialist guarantee of what Badiou terms the ‘mechanism of inscription’.
Indeed, Badiou’s exposition of the ‘construction of the concept of model’ consists of little more than a virtuosic manipulation of basic set theory materials. Despite his recognition that ‘the choice of axioms makes all the difference in a demonstration’, he simply begins immediately with the problem of syntax, admitting that his only concern is ‘to convey the articulation of the construction of the concept [of a model]’.22 The only difference from the rigor of logical positivism is that Badiou has detached the model he constructs from any and all reference to empirical objects to which it would correspond; neither determined at the front end by the sensuous given, nor idealistically via the rigor of proof which would determine being, Badiou’s 1968 concept of model amounts to little more than a free-floating formal system that finds its adequacy in the mere ‘material sequence of the proof’.23 The closing invocation of Dialectical Materialism is in this sense telling, clearly indicating this as an ultra-formalist version of traditional matter-based materialism, the destiny of which, Badiou claims, would be to find ‘its efficacious integration within proletarian ideology’.24
In retrospect, Badiou coherently qualifies his subsequent rejection of this ‘logical materialism’ (‘my materialism of the sixties is a logical materialism’) via the decisive turn in his thought formulated by the publication of Being and Event in 1988, as the initiation of a quite different problematic, one that he names in turn an ‘ontological materialism’:
I moved from a positive reading of mathematics [in The Concept of Model] as the site of regulated inscriptions to one according to which the mathematics of the multiple is the thought of being qua being. In brief, I passed from a structural materialism that privileged the letter (the mark), to an ontological materialism that privileges the evidence of being-there [l’évidence du ‘il y a’] in the form of pure multiplicity.25
At the same time, I would add that this ontological materialism nonetheless fails to constitute a science of causes in the sense of the materialist critique of Spinoza or Marx, as Badiou himself seems to sense: ‘the fact that logical structures are valid for any model only signifies their real vacuity, the fact that they make possible thinking the transcendental form of different possible localisations’ in what he will eventually call a ‘world’ (in Logiques des mondes).
While the virtue of this later position, as we shall see in more detail in the following chapter, is that it limits logic, against all empiricist and idealist tendencies, to the rigorous description or science of the appearance of things in a world, I will nonetheless argue that it remains, as Badiou himself calls it, a mere materialism, one that, in the absence of a materialist axiomatic starting point, holds true only at the level of ontology as generic multiplicity; it is, in other words, a mere generic materialism that in its utter abstraction ignores the singular structural logic of any specific world, such as the logic of our world, the capitalist social form. Before developing this critique of Badiou’s generic materialism as a logic of worlds in the next chapter, I wish to first take stock of the real force of Badiou’s post-1988 ontological materialism, since it constitutes a powerful critique of logical idealism such as that of Frege (the object of Badiou’s explicit critique) and, implicitly, that of Hegelian Absolute Idealism more generally.
2 Bolzano and the Formalisation of Axiomatic Thought
Badiou’s turn after 1988 to an axiomatic orientation constitutes a structural materialism of the letter or the sign. This is a materialism in which ontology is strictly subordinate to logic in a philosophy of the concept, a tendency that in fact originates with the Czech logician, Bernard Bolzano, and only subsequently develops from Bolzano through Frege, through Cavaillès, Desanti, and the Badiou.26 Although Badiou engages explicitly with the latter figures, it is Bolzano who initiates and articulates the turn from Hegelian negative dialectical thought toward an axiomatic philosophy in the decades prior to his death in 1848, and given his relative invisibility in post-Althusserian thought, it is important to indicate his key role for thinkers such as Cavaillès and Badiou.
Badiou never mentions the pioneering, long-overlooked Czech-German logician Bernard Bolzano in the three volumes of Being and Event. In fact, his name only appears in passing on two occasions in Badiou’s oeuvre: once in Number and Numbers, in a list of the modern founders of the thought of number, and once, in a passing reference to Bolzano’s pioneering formalisation of the concept of the infinite in Paradoxes of the Infinite, in Badiou’s 1994–95 seminar on Lacan.27 Badiou has, moreover, admitted that his knowledge of Bolzano’s work is in fact limited and largely second-hand.28
Badiou’s neglect of Bolzano’s thought is hardly surprising, since the great Czech-German philosopher’s pioneering and foundational work, in set theory, in the critique of post-Kantian Idealism and intuitionism, in the semantic formalisation of mathematics and logic, in the formal nature of axiomatisation, his precocious articulation of a realist, mathematics-based platonism a century before Albert Lautman’s ‘transplatonism’, and in many other fields, remained little acknowledged and even less studied until quite recently.29 As late as 1993, Jacques Bouveresse could still decry this ‘historical injustice’ done to ‘the most gifted and original adversary of German Idealism’.30
Decades before Frege, Husserl, Cantor, Tarski, and Gödel, Bolzano founded or made possible many of the crucial discoveries of modern analytic philosophy and set theory, innovations for which the former would become famous. Following the prohibition of his publications and his early retirement to the Czech countryside, Bolzano’s discoveries remained overlooked after his death in 1848, and thus the breakthroughs of his major, posthumous works Paradoxes of the Infinite and Theory of Science were only belatedly recognised by Cantor and famously celebrated by Husserl in the Philosophical Investigations.31
Bolzano’s vast and still underexplored body of work announces Badiou’s thought in a series of crucial dimensions, of which I will briefly indicate three:32
1) Bolzano’s thought remains the most original and decisive critique of post-Kantian Idealism in the first half of the nineteenth century. While Badiou cannot be said to reject Hegelian dialectical modes of thought entirely, and in fact has returned repeatedly to interrogate its modalities, it is arguably Bolzano who initiates a tendency in European philosophy to supplement and complete philosophical investigations with apodictic demonstrations formulated in the precise, emphatically un-Hegelian mathematical terms of set-based theory. This mode of demonstration culminates in Badiou’s mathematical apparatus deployed throughout the three volumes of Being and Event.
While Bolzano’s Theory of Science reiterates and refines the terms of Bolzano’s initial critique of post-Kantian Idealism, Jacques Laz has shown that Bolzano’s 1810 Beiträge zu einer begründeteren Darstellung der Mathematik [Contributions to an Exposition of Mathematics on a Firmer Basis], written when Bolzano was only twenty-nine, already sets forth the principal propositions of his thought.33 Key among these is his systematic critique of Kantian philosophy, attacked at its root via what Bolzano shows to be the contradictory nature of Kant’s claims for an a priori intuition that would ground the entire project of the Critique of Pure Reason.34 While the extraordinary brevity of the Appendix to Bolzano’s Contributions (‘The Kantian Doctrine of the Construction of Concepts by Intuitions’) articulates its powerful critique in a mere eleven dense and methodically parsed paragraphs,35 elsewhere Bolzano decries more generally the ‘love of imagistic language’, lack of expressive precision, and reliance upon ‘analogies, paradoxes, and tautologies’ dominant in the Schellingian and Hegelian thought of the age.36
Bolzano unequivocally condemns what he views as a catastrophic tendency of philosophy, ‘the essence of [which] consists in … playing with images and passing off the slightest superficial analogy between two objects as an identity’.37 The core of this limitation, Bolzano concludes, is that ‘the thinkers of our age do not feel themselves in the least subject to … the rules of logic, notably to the obligation always to state precisely and clearly of what one is speaking, in what sense one takes this or that word, and then to indicate from what reasons one affirms this or that thing’.38 Bolzano’s critique proved decisively productive for his invention of what Jean Cavaillès would famously call a ‘philosophy of the concept’.39 Badiou can be said in turn to have taken from Cavaillès’ critique a positive notion of ontology in its intrinsic relation to science and to mathematics in particular as the adequate language of being as being.40
2) Bolzano, decisively influenced on this count by Leibniz, is arguably the first modern philosopher to clearly define mathematics as the adequate language of ontology in the form of a mathesis universalis based upon predicate logic derived from Aristotle’s Posterior Analytic.41 Bolzano argues in the Contributions that philosophy is the science addressed to the question ‘what things are necessarily real’, while mathematics, in contrast, addresses the question ‘What properties must things necessarily possess to be possible?’42 While philosophy attempts to prove the reality of particular objects a priori and unconditionally, mathematics, in Bolzano’s formulation, constitutes the a priori science of the set of universal laws to which all possible objects are subject.43
Scientific method in general is for Bolzano coterminous with the logical rigor of mathematical method.44 While for Bolzano philosophy seeks to deduce the real existence of things (analogous to Badiou’s project to define an asubjective phenomenal logic in Logics of Worlds), mathematics applies its analysis, Bolzano argues, to the possible existence of all objects as governed by general laws. Bolzano can in this sense be said to announce Badiou’s demonstration of the laws governing the phenomenal appearance of things in Logics of Worlds (to be discussed in the next chapter): mathematics, Bolzano affirmed, develops a general theory of forms, which he defined as ‘a science that treats of the general laws (forms) to which things must conform in their existence’.45 While for Bolzano this constitutes an ontological affirmation, Badiou will reject categorial logic as identical with being as such, to argue instead that while mathematics constitutes the adequate language of what is dicible (sayable) of being, a categorial logic offers the means to conceptualise an asubjective phenomenology of worlds.
3) Finally, Bolzano crucially announces the axiomatic position Badiou will develop in Being and Event: ‘Axiomatisation’, Badiou writes there, ‘is not an artifice of exposition, but an intrinsic necessity. Being-multiple, if entrusted to natural language and to intuition alone, produces an undivided pseudo-presentation of consistency and inconsistency. … Axiomatisation is required such that the multiple, left to the implicitness of its counting rule, be delivered without concept, that is, without implying the being-of-the-one’.46 While, as David Rabouin points out, Badiou’s notion of axiomatisation draws upon Hilbert and Bourbaki, one might note that Bolzano already presents in the second section of the Contributions the first explicit model of axiomatisation, decisively rejecting Kantian intuitionism.47
There, Bolzano does not proceed via a demonstration of the nature of the axiom, which would return precisely to the very logicism axiomatisation seeks to overcome (and for which Badiou takes Frege to task in both Being and Event and Number and Numbers). The axiom, Bolzano argues in terms that decisively announce those of Badiou, is derived neither through an intuition, nor even as a minimally and generally acceptable common notion, which would rely on a psychological recognition and agreement, but is instead, he argues, indemonstrable, and objectively so. Bolzano argues that it is precisely and minimally the indemonstrability of an axiom, rather than its essential nature, that can in fact be proven. This minimal proof is merely the verification that allows axioms to found the subsequent propositions subject to apodictic demonstration. ‘Neither deduction, nor demonstration of the truth of a proposition’, Jacques Laz writes, ‘the [Bolzanean] Deductio of an axiom is the exposition of its status as principle [statut de principe] in an objective sequence of connections between propositions. It is the operation by which are revealed the propositions that are the principles for other propositions’.48 Objective without being a logical demonstration of the truth of an axiom, the Deductio founds the effective conditions of demonstration, deducing only that a given proposition possesses an axiomatic character, in the sense that it cannot be analytically reduced into subsidiary components.49
Bolzano can thus be said to announce not only central features of Badiou’s thought, but more generally the structuralist analysis of what Marx called ‘social form’ that is the topic of this book as a whole; structuralist analysis, that is to say, in the quite specific sense in which Louis Althusser and Pierre Macherey developed it in Reading Capital. Here, Bolzano’s concerted critiques of intuitionism, psychologism, and empiricism, and above all his concept of propositions in themselves can be said to second and further develop the Spinozist critiques that Althusser, Rancière, Macherey, and Balibar deployed in their readings of Marx’s Capital.
If Althusser and Macherey in particular looked back three hundred years prior to Spinoza in order to develop their critiques of Hegel and Hegelian Marxism, it is surely no less plausible to suggest that Bolzano, who developed the single most rigorous critique of Kantian and Hegelian Idealism prior to 1848, might offer compelling theoretical arguments to further develop this anti-Hegelian line of thought. Bolzano argued for an objective semantics governing not subjective, hermeneutic knowledge of objects, but their objective properties and relations. He inaugurates, this is to say, the affirmation that Badiou will formalise in 1988 as the governing imperative of Being and Event: that mathematics ‘writes that which, of being itself, is expressible [dicible]’.50 This, Bolzano argues, implies the independence of these concepts apart from conscious representation. Their meaning, he argues, is rigorously objective and independent from acts of judgement. In fact, I would willingly push this argument even further, to suggest that Bolzano can rightly be said to formulate crucial theoretical resources in the path leading to the Lacanian theory of the symbolic and real, above all perhaps via his realist, semantic critique of the Kantian thing in itself. As Badiou writes of Lacan’s notion of the real,
Lacan is not a critic. To be sure, the real differs from reality, which attaches its regime to knowing. But Lacan immediately says: I don’t mean to say the real is unknowable. I’m not a Kantian. … Although the real, as distinct from reality, is exempted from the knowable, which is the essence of reality, the real nevertheless does not end up being the absolute unknowable but is instead exposed to being demonstrated.51
Bolzano’s asubjective order of propositions and representations – in a precise and limited sense analogous to what Lacan will call the symbolic order (in what Badiou calls Lacan’s ‘hyperstructural axiomatic’ phase of the 1950s) – is eminently knowable through acts of formalisation and judgement, in contrast to Bolzano’s anti-Kantian notion of the thing in itself as much as the Lacanian real.52 While this objective order presents things as they are in what Bolzano calls the matter [Stoff] of a semantic, symbolic order, it is for Bolzano (unlike Kant) the real, as Lacan famously stated, that constitutes the impasse of formalisation.53 Or as Laz writes, for Bolzano, ‘we will never be able to grasp the objects of our representation, but only their [objective] meaning through which we represent them’.54
To suggest a Bolzanian reading of Badiou along the lines that I am suggesting here is surely no more implausible than was Macherey’s reading of Hegel.55 It is to articulate a transversal relation; unlike that which Macherey articulates, however, in Badiou’s case, there is no obscure disavowal on his part of a hidden proximity to Bolzano’s historically prior thought, but rather a complex field of relations and implications that remains to be developed and articulated, an investigation that Badiou himself might be the first to welcome.
3 Ontological Materialism in Its Limits
That said, the explicit referent for Badiou’s critique of idealist ultra-formalism is not Bolzano, but Frege, a thinker with whom he engages repeatedly across his work – in ‘Mark and Lack’, in Being and Event, and again in Number and Numbers. Already the object of Badiou’s critique in ‘Mark and Lack’, the inventor of formal logic will become, in both the Meditation Three of Being and Event and the second chapter of Number and Numbers, the object of a critique of formalist idealism that will motivate and justify Badiou’s essential turn from his initial logicism of 1967–68 to an axiomatic of Being as the pure presentation of inconsistent multiplicity prior to all logic.
The key moment in the development of Alain Badiou’s thought, the crucial turn is undoubtedly this conceptual decision to reorient ontology around an axiomatic, anti-logicist, anti-Fregean position. This takes form in Badiou’s axiomatic displacement and debasement of logical formalism, the destitution of the entitlement of Logic to legislate over Being classically sought after by Frege and David Hilbert. Badiou instead relegates logic to an unimpeachably secondary status in strict subordination to an ontological materialism, the inaugural presentation of Being as inconsistent multiple without a One.
What we observe is a movement between Badiou’s initial logical materialism, a culmination of this long tradition, an anti-phenomenological tradition in thought from Bolzano, Cavaillès, and Althusser to Badiou – and an axiomatic formalism, in which the process of formalisation in Badiou’s works, such as Being and Event and Logics of Worlds, is retained, but to become strictly subordinate to ontology and philosophy. Mathematics, that is to say, reduced to the status of a subordinate, proper, and adequate mode in which to speak of being, longer assures the being there of being itself, as with Frege.
We find this Bolzanean, axiomatic turn or reorientation of Badiou’s thought at work, drawn and measured against the demonstrative force of Frege’s logicism, in the key founding ‘Meditation Three’ of Being and Event. If ‘Meditation One’ sets forth the absolute necessity of inconsistent multiplicity, it does so in the philosophical rhetoric of natural language. ‘Meditation Three’, in contrast, indexifies the necessity of inconsistent multiplicity not only to Bertrand Russell’s paradox, a merely negative presentation of the limits of natural language, but to the actual demonstration of these limits via Gödel’s proofs of completeness and incompleteness.
This is the moment in which Badiou affirms the contingent, axiomatic orientation of his thought as a refusal of all first principles, even those of logic as they were first systematised by Frege in his 1879 Begriffsschrift. There Frege sought to construct a comprehensive language for formal logic:
It is necessary [Badiou writes,] to abandon all hope of explicitly defining the notion of set. … Axiomatisation is required such that the multiple, left to the impliciteness of its counting rule, be delivered without concept …. [Contrary to Frege,] language cannot induce existence, solely a split within existence .… The power of language does not go so far as to institute the ‘there is’ of the ‘there is’. It confines itself to positing that there are some distinctions within the ‘there is’.56
Frege’s effort to secure the concept of set ‘guaranteed by a well-constructed language’57 such that the ‘control of language (of writing) [would amount to] control of the multiple’58 founders on the shores of Russell’s paradox, and this limit to a totalising symbolic formulation is then formalised in Gödel’s proof of, first, the completeness of first-order logic as the predicate calculus – the proof, in other words, that ‘every consistent formal system has a model’ – along with Gödel’s proof of the existence of arithmetically true but unprovable statements, the effective separation of the criteria for semantic truth from those of provability.59 Gödel demonstrates that ‘there are provably unprovable, but nevertheless true, propositions in any formal system that contains elementary arithmetic, assuming the system to be consistent’.60
Badiou draws the ontological implication of incompleteness as the destitution of monism with remarkable force: Since given not just Russell’s paradox, but above all incompleteness, ‘it is necessary to abandon all hope of explicitly defining the notion of set, … axiomatisation is required such that the multiple, left to the implicitness of its counting rule, be delivered without concept, that is, without implying the being-of-the-one’.61 Even more strongly, we read in the concluding lines of ‘Meditation Three’ this summation of the ineluctable ontological conclusion to be drawn from incompleteness: ‘The power of language does not go so far as to institute the “there is” of the “there is”. It confines itself to posing that there are some distinctions within the “there is” ’.62
For what, after all, is Zermelo’s axiom of separation if not the restrictive warrant of the symbolic to operate critically upon a necessarily prior given in its merely provisional totality, counted-as-one? Under the aegis of Separation, it is the case, Badiou tells us, that ‘a property only determines a multiple under the supposition that there is already a presented multiple’.63 There is always already a presented multiple in Badiou’s ontological materialism, a generic multiplicity prior to any counted-as-one. If this is the case, the ontological necessity of Zermelo’s axiom, required to save the operations of first-order logic from the proof of incompleteness, logically necessitates the initiation of any critique from the prior givenness of a world, as opposed to the idealist engendering of existence from the loins of logic.
The axiom of separation certifies the absolute necessity that apodictic critique begin not from the absolute of an esoteric logical demonstration of a logical structure as a closed, complete system, but, instead, as an ontological materialism, from the most universal and immediate, a multiplicity as the givenness, the il y a, of a generic plurality (for example, of commodities as an immense, undifferentiated heap, the underived axiom of an ‘ungeheure Warensammlung’). The axiom of separation, we could say, tells us that in our world, in the capitalist mode of production, in this world in which everything under the sun has its price, the world of commodities names a pure, perhaps the paradigmatic instance of a consistent multiple, in which each is counted, everything has its price, but counts in subtraction from any and all specific determination of singular form, any of the specific determinate use-values of various commodities in their differentiated multiplicity. Use-value, though necessary, is always secondary; from atom bombs to zaffre, the valorisation of value is the universal logic of our world.
The axiom of separation can be said to formalise the critical procedure itself as strict necessity. For the very meaning of critique – from the Greek kritikē, krinein, becoming after 1838 the French neologism criticité, to designate after Kant the examination of the rational foundations of knowledge – indicates precisely the operation of discerning, sorting, dividing, in a word, separating, that very procedure the axiom of separation formalises as absolute necessity. Here is Badiou: ‘Language cannot induce existence, solely a split [scission] within existence’.64 The logical requirement of an axiom of separation formalises the critical operation itself as absolute necessity. As Badiou writes in Number and Numbers, ‘We can only move to an existence that is somehow carved out of a pre-given existence. We can “separate” in a given domain those objects within it that validate the property exposed by the concept’.65
Critique in these terms is precisely the operation Marx deployed as the systematic destruction of the fetishistic illusion of totality, of the illusion that there are, in other words, natural beings we call commodities, in the pure inviolability of their self-same identity. There are only inconsistent multiples prior to the localised, provisional presentation of any One. ‘The existence-multiple anticipates what language retroactively separates out from it as implied existence-multiple’.66 In sum, the priority of being as inconsistent multiplicity, confirmed and supported by its axiomatic separation from the demonstrative critique that is the power of language, assures for Badiou the priority of an ontological materialism against all Hegelian and Fregean Idealisms alike.
A turn occurs, following the 1988 publication of Badiou’s first major ontological work, Being and Event: from that point on, Badiou recognises the imperative to retain a process of formalisation and reflection at a conceptual level, a ‘certain’ structuralism, a certain variant of structuralism as an axiomatic formalism. Nonetheless, this new form of thought is not a formal combinatory of fixed, unchanging structural essences as in the structuralism of Lévi-Strauss, but rather an axiomatic one, one in which politics and the critique of capitalism more specifically takes any given orientation as a decision, as a process of decision, one that allies with that orientation a formal process of reflection.
This is to say, literally and specifically: with 1989 and the coming neoliberal ‘triumph’ or generalisation of capitalism as a global sequence, it suddenly becomes imperative for Badiou to carry forward political thought axiomatically, and to invent a critique and politics adequate to the vast and encompassing generalisation of capitalism after 1989 as the tendential totalisation of global society. What we see is precisely the necessity of revisiting, and carrying forward into the post-’89 period, both a contingent axiomatic orientation toward the critique of capital, based not on an a priori moralism, or pre-given norms or normativity, but one that refers instead to the capacity to orient oneself in relation to universal categories – justice as equality, for example. The enormous difficulty of comprehending the rapidity with which capitalism dominates and transforms our experience (particularly since the turn of the century) is so overwhelming, that it becomes very difficult, if not impossible, to conceive of a politics that would truly be not just local politics, but also veritably anti-capitalist, given our existing and lingering categories of political critique from the twentieth century; to understand what that might mean implies, of course, understanding the forms, limits, structures of capitalism itself.
It is precisely in revisiting the conceptual categories that Marx developed in his critique of political economy in the three volumes of Capital, that we can recover the basic elements that still today define the structure of structures that is capitalism, a social form that is, nonetheless, a contingent structure: a structure of structures in which we see contemporary mutations of the orientation, the domination, and the subordination of those various categories in ways that require us to step back to invoke a conceptual moment and process of reflection in order to grasp precisely what it means to live in a period that I would call ‘posthuman capitalism’, in which there unfolds a general devalorisation of the capacity of labour power to create surplus value, the very substance of capital. To grasp that process, and then to put forward and to think politics in the contemporary conjuncture is precisely to require what I am calling an axiomatic formalism. This would constitute an effect or derivation from a general philosophical project, an ontological project that following Badiou sutures the axiomatic to the process of formalisation and conceptual reflection, to provide resources to begin such a re-foundation, reconceptualisation, and reorientation: the initiation of a critique adequate to our contemporary conjuncture of posthuman capitalism.
4 The Displacement of Capital
As such, among the most striking features of Being and Event and Number and Numbers is their reiteration and further development of the association noted above in ‘Mark and Lack’ and Concept of Model, as the pressing refiguration of Marx’s critique. Here too, these later texts schematise the logical reduction and restatement of Marx’s initial derivation of the concept of exchange-value and the commodity in Chapter One of Capital, Vol. 1. Here is Badiou on Frege: ‘To say that two concepts are equinumerate is to say that they have the “same quantity”, that their extensions are the same size, abstracting from any consideration as to what the objects are that fall under those concepts’.67
And here, beside that formal statement of equinumeracy, is a passage from Marx’s famous presentation of exchange-value in the first chapter of Volume I of Capital:
Let us take two commodities, such as a coat and 10 yards of linen, and let the value of the first be twice the value of the second, so that, if 10 yards of linen = W, the coat = 2W. … Just as, in viewing the coat and the linen as values, we abstract from their different use-values, so, in the case of the labour represented by those values, do we disregard the difference between its useful forms, tailoring and weaving [etc ….]68
The essence of Badiou’s critique is that while Frege’s idealism claims to conjure the self-same object – zero, that is – through the pure powers of logic, for Marx and Badiou both, the thought-object can only be the production of an entirely secondary operation. Marx calls this process in the 1857 Introduction the reproduction of the concrete as materialist thought-concrete, while Badiou names this secondary derivation, more generally, the operation of the count-as-one.69
5 A Materialist Axiomatic
In what sense then can we say that Marx’s beginning to Capital (‘The wealth of societies in which the capitalist mode of production prevails appears as an “an immense collection of commodities” ’) constitutes a materialist axiomatic? It is axiomatic, to begin with, in the minimal sense Lalande gives the term, as ‘a premise considered evident, and taken as true without demonstration by all those who understand its meaning’.70 Marx chooses as his starting point just such a ‘premise considered as evident’; he proposes a minimal, true idea, that all its subjects, he wagers, already possess of the nature of capitalism: that it appears as the general commodification of things.
Throughout this book, however, I have argued that the first sentence of Capital furthermore functions in a stronger, logically determinant sense, firstly that of an axiom as Lalande further defines the concept as ‘every proposition, in a hypothetico-deductive system … that is not deduced from another, but which is posed by a decisionary [décisoire] act of thought, at the beginning of a deduction’.71 This emphasis on the decisionistic aspect is precisely the sense in which Badiou qualifies axioms, ‘which must’, he argues, ‘be affirmed, taken into account [assumés], explicit, and which, as such, introduce into every rational system an element of decision’.72 Marx explicitly addresses the contingency of the starting point of his critique, for example in the Grundrisse, when he rejects the seemingly obvious option to begin the critique of political economy from the fact of ground rent.73
Yet this leaves in suspension a third aspect of the axiomatic starting point, the axiom as what Lalande calls ‘a general rule of logical thought’, which is to say, the manner in which the choice of this axiom prescribes and determines the nature of the exposition that follows from it. I have repeatedly emphasised, in the previous chapters, the way in which the starting point of Capital determines the course of the demonstration that follows from it: for example the necessity, in a society of general, as opposed to occasional, exchange, that that exchange be mediated by a general equivalent (monetary) form of value.74
While Marx’s demonstration of the ‘simple’ form of value is logically coherent and non-contradictory in the case of two commodities (coats and linen in Marx’s example), it is nonetheless ‘insufficient’ or inadequate to account for a society characterised by the general exchange of all things of value as commodities, as Marx has defined the capitalist social form in the first sentence of Capital, and it is this axiomatic insufficiency (rather than some internal contradiction) that compels his exposition in the first chapter of Capital to move from the simple to the general form of value.75 Marx’s axiomatic demonstration shows that if capitalism is a social form of general commodification, then it necessarily and by absolute implication requires a general, monetary form of value for that exchange.
Badiou’s ontological materialism, in its refusal critically to investigate the parameters of an actual, given world (such as that of capitalism), suffers from a materialist deficit. While its axiomatic orientation determines the necessity governing its ensuing demonstration, the choice of a given starting point remains indeterminate, even arbitrary. It is, in other words, a mere generic materialism, applicable to any world whatsoever. In contrast, Marx’s apodictic exposition in Capital derives its starting point from the capitalist real itself: ‘I do not start out from “concepts” ’, Marx writes in his ‘Notes on Adolph Wagner’, ‘hence I do not start out from “the concept of value”, and do not have “to divide” these in any way. What I start out from is the simplest social form in which the labour-product is presented in contemporary society, and this is the “commodity”. I analyse it, and right from the beginning, in the form in which it appears’.76
Marx’s painstaking analytical enquiry into the nature of the capitalist social form extended from the 1850s to the end of his life, to constitute the materialist determination not only of his additive synthetic exposition, but of the axiomatic starting point that initiates and determines that demonstration.77 This materialist determination is evident, for example, in Marx’s crucial finding in the final paragraph of Grundrisse, when, nearly 900 pages into his analysis, Marx at last determines the proper starting point for his exposition. Not, for example, ground rent, a beginning point he explicitly rejects already in his 1857 Introduction (as noted above), but ‘Value’, the analysis of which, he adds in a note to himself immediately following this section title, should necessarily constitute his materialist starting point: it is the ‘section to be brought forward’ to the beginning of what will become Capital.78
In contrast to Badiou’s generic materialism, Marx’s science of causes in Capital begins from the materialist position he develops not from empirical reflection on the lived experience of capitalism, but from his critical analysis of the contradictions and insufficiencies of classical political economy and French socialism. Despite this comparative insufficiency of Badiou’s ontological materialism, it is nonetheless possible and even fruitful, I wish to argue, to continue to read Badiou’s abstract logic as the objective displacement (Verschiebung, in the Freudian terminology) of Capital, as a body of work that in its incessant commitment and faithfulness to the Marxian political project of communism, objectively reinscribes Marx’s critique of political economy within terms that raise to a point of extreme abstraction and schematisation that same initial tendency to formalisation identifiable (as I argued in the previous chapter) in Marx’s own revision process of his manuscript.
RC, p. 52. See above, note 55.
Laplanche and Pontalis define ‘Displacement’ as ‘The fact that an idea’s emphasis, interest or intensity is liable to be detached from it and to pass on to other ideas, which were originally of little intensity but which are related to the first idea by a chain of associations’ (2018, p. 121).
Badiou 2012, p. 159.
Marx 1973, pp. 109–21. See also Iñigo Carrera 2013; Nesbitt 2019.
Badiou 2012, p. 159.
Marx 1973, p. 101. See RC, p. 41.
Badiou 2012, p. 165.
See above, pp. 53–4.
Hegel had already formulated in the Logic’s ‘Doctrine of Concept’ an analogous critique of empiricism as the mere abstract reflection of appearances: ‘Since the predicates immediately drawn from the appearances still belong to empirical psychology, so far as metaphysical consideration goes, all that is in truth left are the entirely inadequate determinations of reflection’. Hegel then continues – and here one should simply replace the more general ‘metaphysics of the soul’ that Hegel criticises in this passage for Adam Smith’s more specific search for a metaphysics of man’s economic nature that is the object of Marx’s critique – with the point that such empiricism is ‘intent on determining the abstract essence of the soul; it went about this starting from observation, and then converting the latter’s empirical generalisations, and the determination of purely external reflection attaching to the singularity of the actual, into the form of the determinations of essence’ (Hegel 2021b, pp. 689, 690). It is no coincidence, then, that this chapter of the Logic (‘The idea of cognition’) appears to be precisely the section of the Logic that most decisively influenced Marx’s formulation of the 1857 ‘Introduction’ (Meaney 2015, p. 45).
Badiou 2012, p. 165.
RC, pp. 40–2.
Badiou 2007 [1968].
See Hallward and Peden 2012.
Foucault and Deleuze 1977, pp. 205–17.
Althusser 2005; Badiou 2013 [1988].
See above, pp. 72–4.
Badiou 2007, 19.
RC, p. 37.
Badiou 2007, 23.
Lévi-Strauss, cited in Badiou 2007, 25.
Badiou 2007, 25.
Badiou 2007, 30.
Badiou 2007, 31.
Badiou 2007, 40.
Badiou 2007, 19.
See Lapointe 2011.
‘Les noms de cette première modernité [de la pensée du nombre] ne sont pas Proust et Joyce, ce sont Bolzano, Frege, Cantor, Dedekind, Peano’. Badiou 1990, p. 24. ‘Après que l’infini eut reçu dans la mathématique un statut clair, grâce à Bolzano, Weierstrass et Cantor, il cesse de jouer un rôle dans l’argumentation philosophique’. Badiou 2013b, pp. 256–7. In English: Badiou 2008. Badiou 2018. See also Bolzano 1950 [1851].
Personal communication, New York, 18 October 2017.
Badiou 2013a, p. 12.
Bouveresse, ‘Préface’, in Laz 1993, p. iv.
‘Bernhard Bolzano’s Wissenschaftslehre, published in 1837, a work which, in its treatment of the logical ‘theory of elements’, far surpasses everything that world-literature has to offer in the way of a systematic sketch of logic’. Husserl 2001 [1900], p. 68. See Bolzano 2014; 2011. On Bolzano’s life, see the biographical information in Rusnock and Šebestík 2019. Bolzano publicly articulated as radical a critique of Viennese militarism as was perhaps possible in his Austro-Hungarian milieu, and it was this in particular that led to the banning of his publications and his forced early retirement from Charles University.
I develop other points at which Bolzano announces Badiou’s thought, for example on the concept of the infinite, in Nesbitt 2021.
Bolzano 2010.
Kant 1998.
See Bolzano 2010.
Cited in Laz 1993, p. 33.
Cited in Laz 1993, pp. 32–3.
Cited in Laz 1993, p. 32.
Cavaillès 2008. Note that beginning with his critique of Fregean logicism in ‘Meditation 3’ of Being and Event, Badiou decisively rejects the notion of logic as a purely syntactic operation: ‘Logic is not a formalisation, a syntax, a linguistic apparatus. It is a mathematised description of possible mathematical universes, under the generic concept of Topos’. Cited in Hallward 2003, p. 109. I will return to this point below, in reference to Bolzano’s innovative formalisation of axiomatic method. While Cavaillès celebrates, in On Logic, Bolzano’s rigorous attention to the necessary modalities of adequate, apodictic demonstration, he nonetheless criticises the ahistorical nature of these conditions, to offer instead a historically developmental concept of adequate demonstration. Hourya Benis Sinaceur has argued that Cavaillès’ critique of Bolzano indicates a subterranean Hegelianism latent in Cavaillès’ thought. Sinaceur 2013, pp. 114–16.
Thanks to David Rabouin for clarifying this point.
On Leibniz’s influence on Bolzano, see Laz 1993, pp. 33–5; and on Bolzano’s reconfiguration and critique of Aristotelean logic, see Laz 1993, pp. 27–30.
Cited in Laz 1993, p. 29.
Cited in Laz 1993, p. 45.
Laz 1993, pp. 46–8.
Cited in Rusnock and Šebestík 2019, p. 417.
Badiou 2005, p. 43, translation modified.
David Rabouin, personal communication.
Laz 1993, p. 55.
Laz 1993, pp. 52–6.
Badiou 2005, p. 5, translation modified.
Badiou 2013b, p. 151.
Badiou 2013b, p. 237.
Badiou 2005, p. 5.
Laz 1993, pp. 121–2.
Macherey 2011 [1979].
Badiou 2005, pp. 43, 47.
Badiou 2005, p. 39.
Ibid.
See Goldstein 2013, pp. 186, 160.
Goldstein 2013, p. 168.
Badiou 2005, p. 43.
Badiou 2005, p. 47.
Badiou 2005, p. 45.
Badiou 2005, p. 47.
Badiou 2008, p. 20.
Badiou 2005, p. 47.
Badiou 2008, p. 17.
Marx 1976, p. 132, emphasis added. The formal resemblance of these two texts grows even greater if we then consider Badiou’s schematic reduction of Frege’s idealist derivation of number in Number and Numbers: ‘Concept→ Truth→ Objects that fall under the concept (that satisfy the statement attributing the concept to the object) → Extension of the concept (all truth-cases of the concept) → Equinumeracy of two concepts (via biunivocal correspondence of their extensions) → Concepts that fall under the concept of equinumeracy to a given concept C (that satisfy the statement ‘is equinumerate to C’) → The extension of equinumeracy-to-C (the set of concepts from the preceding stage) → The number that belongs to concept C (number is thus the name for the extension of equinumeracy-to-C)’. Badiou 2008, p. 18.
One could, I think, follow through nearly every step of this presentation to translate and formalise Marx’s discursive analysis of exchange-value into Badiou’s more logically adequate form, in which each logical step of derivation is indicated, beginning with the famous initial postulation of the concept of commodities as given, as pre-existent materialist fact in the first sentence of Capital: ‘The wealth of societies in which the capitalist mode of production prevails appears as “an immense collection of commodities” ’ (Marx 1976, p. 125). From this follows the proposition that there are, in fact, commodities that fall under that concept; this is followed by the extension of the concept of the commodity to name the set of all commodities; to assert in turn the equinumeracy of all such concepts in their consistent multiplicity, as differing quantities of use-values that relate to one another as equivalent exchange-values (1 coat = 2 yards of linen); next the set of concepts that is the consistent multiplicity of use-values that fall under the concept of equinumeracy, etc.
Lalande 2010, p. 105.
Lalande 2010, p. 105, emphasis added.
Badiou 2007, p. 40. Similarly, Macherey emphasises how Spinoza’s definitions in their axiomatic contingency forgo ‘all attempts at rhetorical persuasion, since these truths proposed for examination are to take or leave as such, addressed to [the reader’s] completely free mind, free to pursue – or not – the path they open’, (1998, p. 30).
‘Nothing seems more natural than to begin with ground rent, with landed property, since this is bound up with the earth, the source of all production and of all being, and with the first form of production of all more or less settled societies – agriculture. But nothing would be more erroneous …. Capital is the all-dominating economic power of bourgeois society. It must form the starting-point as well as the finishing-point, and must be dealt with before landed property. After both have been examined in particular, their interrelation must be examined’ (Marx 1973, pp. 106, 107).
Analogously, Macherey emphasises the determination Spinoza’s initial starting point, the definition of causa sui, governs the entirety of his ensuing exposition: ‘the concept [of causa sui] sustains from beginning to end Spinoza’s entire philosophy, which one could present in a general manner as an effort to explain all things by their causes’ (1998, p. 31).
Marx 1976, p. 154. See the previous chapter on this point.
Marx 1996, p. 241.
Musto 2020. On Marx’s materialist enquiry as a guarantee against Hegelian idealism, see Heinrich 2022, p. 170.
Marx 1973, p. 881.