In his book Deleuze: The Clamor of Being, Badiou focuses upon the theory of the virtual and directs his harshest criticisms of Deleuze at this theory. More to the point, Badiou argues that when Deleuze claims that the virtual is complete in itself and yet only part of an actual object, the indiscernible part, then Badiou believes that Deleuze stumbles because of his commitment to the univocity of One Being, or his commitment to affirming “a single and same voice for the whole thousand-voiced multiple, a single and same Ocean for all the drops, a single clamour of Being for all beings…” (DR 304). Badiou states his criticism as follows:
when the only way of saving – despite everything – the One, is by resorting to an unthinkable Two, an indiscernibility beyond remedy…one says to oneself that, most decidedly, the virtual is no better than the finality of which it is the inversion (it determines the destiny of everything, instead of being that to which everything is destined). Let us be particularly harsh and invoke Spinoza against his major, and indeed sole, truly modern disciple: just like finality, the virtual is ignorantiae asylum. (Clamor of Being, 53).
To respond to this criticism we can return to the master himself; namely, Spinoza, and especially to a problem many commentators have had with Spinoza’s Ethics – that is, the relationship of the attributes to the modes of these attributes. Badiou himself notes this problem, recognizing that ‘Although it is on the basis of which the attributive identifications of substance exist, the intellect itself is clearly a mode of the attribute “thought”’ (Badiou, Theoretical Writings, 2004, p. 84). Stating the problem baldly, Badiou asks, ‘how is it possible to think the being of intellect, the “there is intellect,” if rational access to the thought of being or the “there is” itself depends upon the operations of the intellect?’ (ibid.) This problem has long been recognized by Spinoza scholars and has received a number of solutions. Badiou’s particular solution is quite telling.
At the basis of Badiou’s understanding of the relationship between the infinite intellect, as an infinite mode of the attribute thought, and the attribute thought itself, is the premise that the intellect is identifiably distinct from the objects that are objects or ‘ideas of’ the intellect. For Badiou, then, since ‘every idea is an “idea of,” it is correlated with an ideatum,’ it follows that ‘the attributes of God and the modes of these attributes are objects of the infinite intellect’ (ibid. 86). With these assumptions at play, Badiou is naturally led to conclude that ‘the attribute of thought is not isomorphic with any of the other attributes,’ (ibid. 88) for the very reason that it is an infinite mode of this attribute that has, as its object, the other attributes that thereby constitute the essence of substance. Add to this claim Badiou’s extension of Spinoza’s argument, in the Demonstration to 2P21 that ‘the mind is united to the body from the fact that the body is the object of the mind,’ then it again follows for Badiou that there must then be ‘instances of union that straddle the disjunction between attributes. It is this union, the radical singularity proper to the operations of the intellect, which I call coupling.’ (ibid. 87). In other words, since the infinite intellect, as an attribute of thought, is united to the objects that are its ideas – the other attributes – then it is “coupled” to these other attributes, a coupling made possible by the attribute thought that is not ‘isomorphic with any of the other attributes.’
These arguments lead Badiou to a surprising conclusion. With the notion of coupling, a notion Badiou admits is not to be found in Spinoza but is necessary to make sense of Spinoza’s (supposed) understanding of the relationship between the infinite intellect and the objects that are the distinct objects of this intellect, Badiou claims a further consequence follows: ‘As a matter of fact, infinite intellect by itself constitutes an exception to the famous Proposition 7 of Book II: “The order and connection of ideas is the same as the order and connection of things”’ (ibid. 88). Because the intellect is coupled to the other attributes and to their modes, the order of the ideas in the infinite intellect is not the same as the order and connection of things for the infinite intellect is what makes possible the very actuality of attributes and things, and hence the parallelism between them.[i] Yet it is just this conclusion, that the intellect is an exception to Spinoza’s famous parallelism, that Spinoza himself would likely find unrecognizable.
The reason Badiou is led to what we believe is a mistaken conclusion concerning the relationship between the attributes and their modes is that he presupposes the identity of both the infinite intellect and the attributes and modes that are the identifiable objects of this intellect. For Deleuze, however, the best way to understand the relationship between the attributes and the infinite intellect is to argue for the primacy of the modes themselves.[ii] In other words, there is the necessity for the modification of an attribute – infinite thought – as that which perceives substance and constitutes its identifiable, actualized essence, precisely because the attribute is identifiable as such only as actualized in a mode. The attributes are thus not distinct identities or objects waiting for the infinite intellect to perceive them; rather, it is the very perception of the attributes by the infinite intellect (as infinite mode) that actualizes the identifiable essence of substance itself. Furthermore, if one understands Spinoza’s notion of substance as absolutely indeterminate, then the attributes can then be understood as the condition for determining the infinite and infinitely determinable essence of substance.[iii] This identifiable essence is made possible by the actualization of a mode of an attribute, and substance is therefore identifiable as such only when actualized within a mode – i.e. the infinite intellect. This conclusion, we argue, is not one Spinoza would find unrecognizable, unlike Badiou’s, but instead simply repeats Spinoza’s own definition of the attributes: ‘1D4: By attribute I understand what the intellect perceives of a substance, as constituting its essence.’
It is this relationship between the modes and attributes that is extended by Deleuze in his understanding of the relationship between the virtual and the actual. Just as the attributes are the conditions that allow for the possibility of determining, by way of the intellect, absolutely indeterminate substance, so too the virtual is indiscernible from the actual not as a distinct identity that is to be contrasted to the identity of the actual, but rather the virtual is the condition for identity itself. How, then, as Badiou might ask, can we know that the virtual is real, as Deleuze contends,[iv] if it is indiscernible? The reason Badiou might ask such a question, and why he finds the virtual problematic in its purported resort to an “unthinkable Two,” (Badiou 2000, 53) is because Badiou subordinates knowing to a conceptual knowing whereas Deleuze, in good Nietzschean-pragmatist fashion, subordinates knowing to the practical problems that are inseparable – indiscernible – from the actualities that are themselves the identifiable solutions to these problems.[v]
[i] Badiou is quite forthright on this role of the infinite intellect: ‘The infinite intellect provides the modal norm for the extent of modal possibility. All the things that it can intellect – “omnia quae sub intellectum infinitum cadere possunt” – are held to exist’ (ibid. p. 85).
[ii] Deleuze is quite forthright in his assertion that Spinoza, as he reads him, makes substance turn upon the modes. In correspondence with the translator of the English edition of Spinoza: Expressionism in Philosophy, Deleuze sees his original contribution to Spinoza scholarship being precisely his effort in ‘making substance turn on finite modes …’ (Deleuze 1990, 11).
[iii] H.F. Hallett has argued that Spinoza understands substance as “absolutely indeterminate,” and the reading offered here largely echoes Hallett’s position. For other, similar interpretations, see Pierre Macherey, Introduction à l’Éthique de Spinoza: La première partie la nature de choses (Macherey 1998), and for Macherey’s sympathetic reading of Deleuze, “The Encounter with Spinoza,” in Deleuze: A Critical Reader (Patton 1996), pp. 139-61; Charles Ramond, Qualité et quantité dans la philosophie de Spinoza (Ramond 1995); Lorenzo Vinciguerra, Spinoza (Vinciguerra 2001); and François Zourabichvili, Deleuze: une philosophie de l’événement (Zourabichvili 1994), and in particular Zourabichvili’s essay, “Deleuze et Spinoza,” in Spinoza Au Xxe Siècle (Bloch 1993), pp. 237-46.
[iv] That the virtual is real is one of Deleuze’s central claims and he states it on numerous occasions. See, for instance, Difference and Repetition (DR 208): ‘The virtual is opposed not to the real but to the actual. The virtual is fully real in so far as it is virtual.’
[v] A preliminary indication that supports this reading of the difference between Deleuze and Badiou can be seen in Badiou’s work itself, where, in the introduction to the Clamor of Being, Badiou claims that Deleuze did not want to have his correspondence with Badiou published for on rereading it ‘he found them too “abstract”’ (Badiou 2000, 6). It is also worth noting that the subtitle to Deleuze’s second book on Spinoza is ‘Practical Philosophy.’