jesuve

This was just written as notes to myself but I thought it might be worth sharing. Let me know!

BADIOU’S OWN VOID IN HIS CRITIQUE OF SPINOZA

“In other words: the infinity of God, which is what singularizes him as substance and entails that he is the name for the ‘there is’, is only thinkable under the aegis of the multiple.”

Badiou proposes a reading of Spinoza’s ontology that brings to the fore his own concept of the void. Despite all of his Herculean efforts to present an ontological plenitude, in which there is neither excess nor chance, but that all potentiality is actualized, Badiou believes that the void returns within Spinoza’s philosophy vis-à-vis the infinite modes, the “gateway” between the infinite and the finite realm. The void returns here in the sense that, according to Badiou, the infinite and the finite intellect (as well as their extended counterpoints) cannot meet. Although the infinite intellect is necessary for the finite intellect to exist and function; the finite intellect cannot ‘know’ and recognize the infinite intellect so that, “we could say that the concept of an infinite mode is coherent but existentially undecidable;” or to use the language within Being and Event, the infinite modes are the “technical name of the abyss.”

However, one could charge Badiou with presenting only those aspects of Spinoza’s theory that are agreeable to his own vision, while acutely (or intentionally?) ignoring those aspects which do not create the void out of the infinite modes. In particular, Badiou either ignores completely or perverts Spinoza’s discussion of infinity and finitude. Hence, in what follows, I do not wish to merely give an exegesis of Badiou’s read of Spinoza; instead, I wish to, in part, also to challenge Badiou’s read of Spinoza. Is there something in Spinozistic philosophy that can undermine Badiou’s project and thus his reluctance to approach it? This is not to argue that Spinoza’s account of ontological unity, an ontology of one, is justified; a mere attempt at ‘saving’ my beloved Spinoza from the void. Rather, this being the first presentation paper of the seminar, I hope, through presenting a different notion of infinity and finitude than does Badiou, we ask ourselves, whether there is some other—perhaps equally adequate—route down upon which to travel.

Badiou’s read of Spinoza: Meditation 10 opens with “Quicquid est in Deo est. or: all situations have the same state.” If we translate this literally, we see that it is the first half of EIp15, “Whatever is, is in God.” We can, then, that for Badiou, a Spinozistic situation must be either the attributes or perhaps the finite mode, which are the plura individua or res singulares respectively, while the state is God/Nature/Substance. Thus, keeping with the definitions of the situation and the state, God is that metastructure which ‘guarantees’ the consistency of all multiples, i.e., the attributes and the modes, by counting-as-one the original count-as-one, thus assuring that everything which belongs is included and everything that is included belongs; “The consistency of presentation thus requires that all structure be doubled by a metastructure which secures the former against any fixation of the void.” Through this doubling anything which threatens to be unaccounted for in the first count-as-one, the inconsistent, “the pure will-have-been-counted,” is counted. Hence “it is clear that this is the philosophy par excellence which forecloses the void.”

Yet, it is exactly this relationship that Badiou wishes to question; “this hitherto unmentioned relation of inclusion has to do with what, in my opinion, constitutes the greatest impediment for Spinozist ontology: the relation between the infinite and the finite.” Spinoza’s answer? The infinite modes, which bridge the gap between the infinite and finite. Yet, while this bridge is necessary, according to Badiou, it is unthinkable within the present count-as-one, and therefore its existence is undecidable within that system. The origin of this trouble seems to stem from Badiou’s read that, “for Spinoza, the count-as-one of a multiple, structure, is causality.” For how can there be any relation between that which is absolutely infinite and that which is not? Moreover, Badiou hears the echoes of circularity; the plura individua are already presented as unified by a causation, since the metastructure (God) is also causality: A composition of multiple individuals (plura individua) is actually one and the same singular thing provided that these individuals contribute to one unique action, that is, insofar as they simultaneously cause a unique effect (unius effectus causa). Which Badiou clearly seems to be taking directly from Spinoza, EIp28: Every singular thing, or [sive] any thing which is finite and has a determinate existence, can neither exist nor be determined to produce an effect unless it is determined to exist and produce an effect by another cause, which is also finite and has a determinate existence; and again, this cause also can neither exist nor be determined to produce an effect unless it is determined to exist and produce an effect by another, which is also finite and has a determinate existence, and so on, to infinity. The state (God), then, seems to be constituted by a never ending series of finite modes (every operation of the count-as-one relies upon another previous action qua cause) while at the same time, in order that the plura individua can be considered to be counted-as-one, the composition of the infinite sum must be presupposed. The unity of a singular thing, then, is already being supposed in its definition.

Thus far we cannot find anything incorrect in Badiou’s account of Spinoza’s world, per se, as he has simply relayed to us the two types of causality in Spinoza. But his mistake comes into play when he states that it is within the gap between these two types of causality that the void (re)emerges. The infinite modes, for Badiou, bifurcate Spinoza’s ontology of the finite and the infinite. They seem to sit precariously on the hinge of the finite and infinite and thus are torn asunder by the two causal chains, given that “the immediate case of a singular finite thing can only be another singular finite thing, and, a contrario, a (supposed) infinite thing can only produce the infinite.” Consequently, “It seems that the excess of the causal source re-emerges at the point at which its intrinsic qualification, absolute infinity, cannot be represented on the same axis as its finite effect.” Thus, truly, it would seem, the infinite modes do in fact take the name of the void: Necessary, but inexistent: the infinite mode. It fills in—the moment of its conceptual appearance being also the moment of its ontological disappearance—the causal abyss between the infinite and the finite. However, it only does so in being the technical name of the abyss: the signifier ‘infinite mode’ organizes a subtle misrecognition of this void which was to be foreclosed, but which insists of erring beneath the nominal artifice itself from which one deduced, in theory, its radical absence.

Trouble in Badiou’s reading? Spinoza’s read of the finitude and the infinite: I think to get a handle on what is at stake here, and a possible misread of Spinoza, let us first turn the role of finite modes as Badiou understands it. As far as I can tell, and I may be entirely off base, for Badiou finitude is an essential predicate of singular things, perhaps reading Spinoza EIID7: “By singular things I understand things that are finite and have a determinate existence. And if a number of individuals so concur in one action that together they are all the cause of one effect, I consider them all, to that extent, as one singular thing.” It would seem that what individuates res singulares is their having a singular effect. But we must ask at this juncture, what is the finitude of finite things for Badiou? As far as I can tell in Meditation 10 Badiou gives no account of either Spinoza’s concept of the finite nor one of his own. I can only draw from this that either: Badiou is implicitly relying upon Spinoza’s definition at EID2—which will become vital below—or Badiou is employing his own definition while overlooking Spinoza’s. I believe that the latter is more likely.

Nor does Badiou give an account of the infinite in Being and Event, although he does, albeit inadequately, in the Theoretical Writings. We can perhaps already anticipate, following Badiou’s mathematical inclinations, that both the finite and the infinite are thought numerically. The finite in the sense of ordinals, i.e., there is always one more one can add. While the infinite is as follows: God is the ens absolute infinite. Badiou here claims that ‘infinite’ is the important term because it functions to determine the indeterminate, i.e., it is the metastructure, it functions as the ‘there is’. Badiou insists that, upon his reading of EID6—“as substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence”—this clearly shows that infinity is not qualitative, or itself indeterminate; “It refers back to an effectively plural, and hence quantitative, infinity…infinitum presupposes a denumberable infinitas…but then of course the concept of the infinite is covered by the law of difference…in other words: the infinity of God, which is what singularizes him as substance and entails that he is the name for the ‘there is’, is only thinkable under the aegis of the multiple.” This is certainly keeping in line with set-theoretic concepts of the infinite in terms of aleph-zero, aleph-one, aleph-two, etc. Badiou seems to be claiming that the existence of the infinite for Spinoza is axiomatic as well. Yet, whereas the finite is defined in EID2, the infinite is only predicated of God; and there are no axioms at all concerning the infinite. And whereas in EIp8 we have the demonstration that “every substance is necessarily infinite.” There is certainly no axiomatic indication of the infinite to be found in the entirety of the Ethics!

Moreover still, Spinoza explicitly writes that the infinite cannot be accounted for in terms of number (neither can the finite for that matter). Since Badiou has clearly read Spinoza’s correspondence, making reference to the letters in his own works, let us discuss a letter which will shed some light on this difficult subject, Ep12. This is the quite famous “letter of the infinite.” Here, Spinoza gives us three ‘types’ of infinity: From all that I have said one can clearly see that certain things are infinite by their own nature and cannot in any way be conceived as finite, while other things are infinite by virtue of the cause in which they inhere; and when the latter are conceived in abstraction, then can be divided into parts are be regarded as finite. Finally, there are things that can be called infinite, or it you prefer, indefinite, because they cannot be accurately expressed by any number, while yet being conceivable as greater or lesser. For it does not follow that things which cannot be adequately expressed by any number must necessarily be equal, as is sufficiently evident from the given example and from many others. The first of these infinites is most certainly God/Nature/Substance; we need only examine EIp8dem to understand this point. By the second type one can not only understand the attributes, but—and this is surprising—the infinite modes themselves, since it is by means of the causes that we understand them to be infinite as well. For the third, I would like to suggest that we can understand modal existence, “there are things that can be called infinite, or it you prefer, indefinite, because they cannot be accurately expressed by any number, while yet being conceivable as greater or lesser. For it does not follow that things which cannot be adequately expressed by any number must necessarily be equal, as is sufficiently evident from the given example and from many others.” The surprising upshot of all of this is that the modes themselves are infinite; the finite qua countable entity does not exist in Spinoza’s world—although Spinoza does give a coherent account of the nature of finitude as it is in relation on existent infinitely composed individuals without giving over to a discussion of number.

From this letter we can at least understand that Spinoza gives us a prima facie alternative to Badiou’s account, i.e., existing infinitely composed things do not rely on number. What the three of these types of infinity show us is Spinoza’s insistence on non-denumerability, neither Substance nor the infinite modes are subject to counting; division is based upon the imagination and not the powers of Reason. Also, I think that it would be worthy of our collective intellectual powers to further contemplate the infinite nature of any existing mode, which while not being reducible to numbering or countability, are able to be “lesser or greater” infinities. We should think this especially in light of Cantor’s set-theory, which does give us denumerable infinities. Is there a rigorous Spinozistic alternative to Cantorian set-theoretic account of infinity? Must the ‘there is’, God, be only thinkable under auspices of the multiple, as Badiou insists? Certainly we cannot be to a definite answer here, but let nonetheless propose another path down upon which to stroll.

Another answer?: As stated before, Badiou does not provide for us a notion of finitude, let us give one now: That thing is said to be finite in its own kind that can be limited by another of the same nature. For example, a body is called finite because we always conceive another that is greater. Thus a thought is limited by another thought. But a body is not limited by a thought nor a thought by a body (EID2).

Thus, for Spinoza anyway, finitude does not suggest denumberability but rather limit. Hence, finitude is an account of the limitation imposed upon the composite modes by another mode that is greater or lesser. By “greater or lesser” we must hear Spinoza’s conception of expressive power. It is the amount of power that a mode has is what is determinate concerning the mode. The infinite modes are ‘infinite’ not because of some ontological principle of primacy, but simply because they are not limited by another mode of the same kind. Their lack of external limitations does not, however, suggest that there is no intrinsic differentiation. In our relationship between the finite and the infinite, we are not dealing with the denumerable and numerical, precisely because the numerical totality of an infinite mode is not what is expressing itself in finite modes, but rather the power to be expressed. Hence, while remaining one, the infinite modes are intrinsically differentiated in terms of intensity of expressive power. Consequently, the infinite modes do not straddle some obscure area between the infinite and the finite; they are descriptive and not intrinsic entities.

So Badiou’s insistence that the void creeps into the ‘gap’ between the finite and the infinite is misplaced. Modes are only finite insofar as they are limited by another of the same sort, and in some ontological sense, they are infinite by definition. However, the real question I would like to investigate with the seminar is that of individuation, how can a limited mode come to be within the determinations effected by an infinite God?

For Badiou it seems to me that individuation is a matter of causation “A composition of individuals (plura individua) is actually one and the same singular thing provided that these individuals contribute to one unique action, that is, insofar as they simultaneously cause a unique effect (unius effectus causa)…or una actio.” Or in other words, “for Spinoza, the count-as-one of a multiple structure, is causality.” It would seem that individuation stems form an external causation, thus giving Badiou the inroad to the void; there must always be something outside of the system, a constitutive lack (recall Badiou’s account of EIp28), hence the claims already quoted concerning the ‘there is’ is only thinkable under the auspice of the multiple. However, in relation to the subject of the greater and lesser, I think we can at least think something differently, whether it holds to a more rigorous investigation, I do not know.

Causation is neither the fundamental relation nor even a fundamental relation in Spinozistic philosophy. Although individuation in Spinoza is a tricky subject fraught with its difficulties, Badiou’s account seems to be missing the mark of Spinoza’s account, no matter how lacking the latter’s own account may be. This is not to say that causation is not an important term and notion in Spinoza’s philosophy, but rather I believe that motion and rest lie at a more fundamental relation to modes than causation as such. For example: When a number of bodies, whether of the same or of different size, are so constrained by other bodies that they lie upon one another, or if they so move, whether with the same degree of different degrees of speed, that they communicate their motions to each other in a certain fixed manner, we shall say that those bodies are united with one another and that they all together compose one body or [sive] individual, which is distinguished from the others by this union of bodies (EIILA2’’D). Causation is not that which portrays the res signulares; rather it is an internal amount of motion and rest, which is explicitly stated at EIILA’1, “All bodies either move or are at rest,” that defines the unified res signulares, or a given set of modes. For further evidence that it is motion and rest that define the individual, we need only look to the remainder of the lemmata. Thus, despite Badiou’s insistence that causality is the count-as-one, Spinoza’s individuals qua composite modes are less affected by causation than by motion and rest, so that we could say that for Spinoza, individuation does not presuppose differentiation, but rather gives rise to it.

Through this reversal of individuation and differentiation, through our removal of causality, and hinting at the intrinsic nature of expressive power, we are at least forced to question what an intrinsic individuation would look like, and whether it poses a real problem for Badiou. Let us take the entirety of extension (or even Nature itself), as Spinoza does. The whole of the whole, i.e., extension/Nature, remains the same and fixed (no void) insofar as the fixedness is the total quantitative proportion of motion and rest. What changes, what gives us differentiation, is not an external operation, but instead the composition and decomposition (or the coming-to-be and passing-away) of the relations of the modes. Does this reversal give us another read to Badiou’s critique of a philosophy of ‘the One’ in Spinoza? Is it the case that since differentiation is intrinsic, instead of an externally preformed operation upon the situation, that one could declare the ‘there’ is’ of the One? I leave it to our collective intellect to try to investigate these questions.