Το κείμενο έχει το εξης ενδιαφέρον εύρημα.Διατυπώνεται πως η Μαθηματική "Μεταφυσική" του Badiou, βασίζεται σε μια διαστρεβλωτική ανάγνωση του Leibniz.Αναδεικνύεται πως η μοναδολογία του Leibniz έχει ενσωματωμένα στοιχεία δυναμικής και ρευστότητας τα οποία όμως ο ΑΒ δεν αναγνωρίζει, έτσι ώστε η δικη του Μαθηματική σύλληψη να εμφανίζει καινοτομίες οι οποίες όμως τελικά δεν υπάρχουν.Το συμπέρασμα είναι αρκετά επικριτικό:O Badiou κατηγορείται για μια "παθολογική άρνηση και σκόπιμη αποσιώπιση" του έργου του Leibniz.
Mis-readings of Leibniz: Deleuze and Whitehead against Badiou
James Juniper, Lecturer in the School of Economics, Politics and Tourism and Associate of the Centre of Full Employment and Equity, the University of Newcastle
The paper is motivated by the desire to identify exactly what Leibniz has contributed to Deleuze and Whitehead’s particular version of (non-organic) vitalism. This reading of Leibniz is compared with those of Badiou (with a little help from Heidegger, who specifically demonstrates the dependence of logic on ontology rather than of ontology on logic). The paper compares each of these philosopher’s interpretations of the fundamental principles that ground Leibnizian monadology, with the intention of highlighting the implications of these readings for political theory. In particular, Badiou’s notion of a schema of torsion is examined and distinguished from Deleuze’s notions of actualization and realization.
Leibniz on Substance and Knowledge___________________________________3
The Debate over Leibniz’s Principles____________________________________8
Badiou’s Reading of Leibniz__________________________________________11
The political motivation for this paper is straightforward. In his review of Logic and Existence, Jean Hyppolite’s reconstruction of Hegelian philosophy, Deleuze (1953) foreshadows the necessity to construct a philosophy of difference that does not “take things up to contradiction”. Along with his interpretations of Duns Scotus, Hume, Kant, Spinoza, Whitehead and Bergson, Deleuze’s analysis of Leibniz’s philosophy of expression makes a major contribution to this task of constructing an alternative and non-organic form of Vitalism, designed to ultimately displace the more familiar organicist tradition that can be traced from Rousseau’s conception of the social contract through to the German Idealism of Hegel and his contemporaries.
Under the latter form of vitalism, the distinction between the (externally caused and atomistic) machine and the (self-caused and internally related) organism carries over to that holding between the state and civil society respectively (Quadrio, 2009). Under the former, the genesis of products (Modes) from their respective constitutive essences (Attributes) is (integrated) through Substance as the infinite power to act, which in theoretical terms is conceived genealogically as both an immanent cause and as self-cause (Substance acting through its essence). A closely related paper (Juniper, forthcoming), examines how Deleuze constructs this genealogy from a close reading of Kant’s three Critiques (specifically, the Third Critique’s “Analytic of the Beautiful”, and both the Transcendental argument and the “Transcendental Dialectic” in the second half of the First Critique) distinguishing it from Badiou’s conception of Kantian philosophy as
a “subtractive ontology”
1. This paper will compare Deleuze’s reading of Leibniz with that of Badiou, with the objective of identifying the specifically Leibnizean sources of this (non-organic) vitalism contrasting this reading with that of Badiou. A more detailed examination of the political implications of such a vitalism, both in theoretical and practical terms, must remain the task of subsequent research2.
In his work on Leibniz, Heidegger (1984) comments explicitly on the diversity of interpretations of Leibniz’s monadological metaphysics, suggesting that diversity of this kind is true of all authentic philosophy. The result of any effort to distil the essence of Leibniz in such a way that it would be agreed upon by all, he reasons, would surely be something dead.
Alain Badiou (2005: 315), for one, finds in Leibniz the paradoxical combination of a “prodigiously modern thought” with a “conscious conservative will”. In actuality, however, he suggests that this will served as a prelude to Leibniz’s more radical anticipations because inventive freedom could only be exercised once an adequate foundation for thinking could be guaranteed.
Being and Event Badiou provides us with a series of philosophical, poetic and political examples of what he calls the “generic event”. Examples of such “truth-events” range from the October Revolution for Lenin, Crick and Watson’s discovery of the double-helix, and St. Paul’s revelatory “road to Damascus” experience of the truth of the resurrection, through to Picasso and Braque’s discovery of synthetic cubism. As Bosteel (2001, 2002) reveals, Badiou’s manner of grasping the event is closely related to his earlier thinking about ‘schemas of torsion’. For him, Rousseau’s notion of the social pact provides one of the clearest political examples of torsion at play. Badiou homes in on the apparent contradiction in Rousseau’s conception of the social pact as something that is both presupposed and constituted by the ‘general will’. He discerns in this paradoxical torsion the signature of the evental form: namely, once constituted, it’s being becomes what is always and already presupposed (Badiou, 2005: 345-6). Thus, for Rousseau the body politic operates as a supernumerary multiple for which the ultra-one of the event is the social pact! The prospect of a self-belonging of the body politic to the very multiple that it is, could never violate the pact as it would destroy itselfi! In this manner the pact supplements the state of nature insofar as it is interposed between nature (void) and itself.
Badiou discerns the presence of a similar “schema in torsion” at play in the work of other philosophers and poets, including Leibniz. In the work of the latter philosopher, Badiou suggests that torsion is instituted by the Leibnitzian question,
par excellence, “Why is there something rather than nothing?” On the basis of there being something rather than
Similar interpretations of Deleuze along these Kantian lines can be found in Kerslake (2002), Shaviro (2009) and Smith (1997). Badiou’s work, however, is not examined in any of these papers.
In Juniper (forthcoming) it is argued that Deleuze’s notion of double causality provides vitalism with a materialist framework for transforming the traditional organicist dichotomy between the freedom and autonomy of noumenal spirit and the mechanism of phenomenal nature. Moreover, it is shown that this transformative notion can be infused with a mathematical robustness through the (non-metaphorical) deployment of the category theoretic concept of an adjunction, insofar as the latter is assigned the role of an Idea in both the Kantian and Lautmanian sense of this term.
nothing, he observes that Leibniz is able to infer that essence, in and of itself, strives for existence or that logic desires the being of what conforms to it. While the axioms or principles that Leibniz constructs impose the question, Badiou observes, the complete response afforded by the Leibnizian system of monadology, which supposes the axioms, also confirms them. By way of justifying this observation the following section of the paper will largely draw on Heidegger’s reading of Leibniz, examining the latter’s conceptions of substance and knowledge. It will lay bare Heidegger’s core objective, which is to demonstrate the dependence of logic on ontology rather than of ontology on logic. This section sets the context for an interrogation of different interpretations of Leibniz’s underlying principles or axioms on the part of Heidegger, Russell, Broad, and Deleuze. Badiou’s reading of Leibniz is examined in the fourth section of the paper and conclusions follow.
Leibniz on Substance and Knowledge
This section of the paper draws on Heidegger’s masterful interpretation of Leibniz for two purposes. First, Heidegger clearly demonstrates how Leibniz takes over from Thomas Aquinas and the Scholastics the crucial distinction they make between active and passive power. Specifically, Heidegger shows how this distinction informs Leibniz’s crucial notion of
conatus or striving, the conceptualisation of pre-hension as a “gripping-in-advance”, and his subsequent analysis of processes of actualisation and realization. Second, in clarifying the step-by-step unfolding of knowledge and judgement in Leibniz’s logic, Heidegger argues, against both Hegel and the seemingly opposed tradition of logical positivism, that logic must be grounded in metaphysics rather than metaphysics in logic. This claim justifies the efforts of Deleuze and Whitehead to fashion a metaphysics of difference that does not take things up to contradiction.
Heidegger contends that, at the centre of Leibniz’s monadology is an attempt to construct a positive rather than a negative definition of substance. While Descartes had defined substance as the thing, which so exists that it needs no other thing in order to exist, Spinoza had, in like manner, defined substance as that which is in itself and is conceived by itself, that of which the concept does not require the concept of another thing from which it needs to be formed. Leibniz discovered the positive conception that he required in Giordano Bruno’s notion of the monad (μοναδ ): a Greek term conveying the characteristics of simplicity, unity, oneness, individuality, and solitude.
Monads are conceived as formal “atoms”, ‘little gods”, or “animating points”: far from requiring any unification in themselves, they are that which gives unity insofar as they are primordially simple points of active force (
vis primitiva) or principles of formation (forma or ειδοσ) (Heidegger, 1984, 77; citing Leibniz, 1969, 482). Monads grasp themselves along with perception, presenting the world from a unique viewpoint so that each monad is the universe in concentrated form. Crucially, although monads are oriented in advanced towards a pre-disposed harmony, they share with all finite substance a passivity or resistance, which is correlated with what the monad is not but could well be. This negative and finite aspect of the drive characterises what Leibniz understands by prime matter (materia prima) and, in addition, conditions the monad’s relationship to the resistance or weight associated with secondary matter (materia secunda, massa).
For both Leibniz and the Scholastics Divine knowledge becomes the cognitive ideal for humans. This knowledge, however, includes both what is possible and what is or will become actual. The distinction Aquinas made between the active disposition to act and the passive disposition towards being formed carries over to a twofold distinction between active and passive forms of power or potentia. In Leibniz, this active force (vis primitiva) is embodied in his conception of the drive (conatus), conceived as a self-propulsive striving