Sam Gillespie over Badiou’s #Spinoza [6]

De jonge Sam Gillespie (1970 – 2003) was buitengewoon goed thuis in de filosofie van Badiou. Hij schreef ook aan een dissertatie. Na zijn dood - hij pleegde op 32-jarige leeftijd zelfmoord - werd hem postuum in 2005 alsnog door de University of Warwick voor zijn The Mathematics of Novelty de graad van Doctor of Philosophy, toegekend. [Cf.]

Sigi Jöttkandt schreef in een themanummer “The Praxis of Alain Badiou” van Cosmos and History over Sam Gillespie: “Sam was a leading figure in introducing Badiou to the English-speaking world.” In 2001 verscheen van Gillespie:

Sam Gillespie, “PLACING THE VOID: Badiou on Spinoza.” In: Angelaki, Journal of the Theoretical Humanities, Volume 6, 2001 - Issue 3, Pages 63-77 – ik haal deze tekst hieronder naar binnen.

In datzelfde jaar, 2001, schreef hij “Badiou’s Ethics.” A review of Alain Badiou, Ethics: An Essay on the Understanding of Evil, trans. Peter Hallward (London: Verso, 2001).” In: Pli. The Warwick Journal of Philosophy, Vol. 12, 2001 [PDF]

Sigi Jöttkandt heeft mede de redactie gevoerd om Sam Gillespie’s Ph.D-thesis postuum uit te brengen:

● Sam Gillespie, The Mathematics of Novelty: Badiou's Minimalist Metaphysics. Melbourne: re-press, 2008 - 159 pages. Het boek is door de uitgever in open Acces uitgebracht [cf. PDF]. Het bevat een sterk 2^e hoofdstuk over Badiou’s Spinoza. Daar kom ik in het volgende blog op terug.

In dit blog breng ik de bijzonder informatieve tekst van Gillespie, “PLACING THE VOID: Badiou on Spinoza,” waarin hij Badiou uitlegt - mede door uit de verzamelingenleer te putten - en hem tevens kritisch bespreekt.
Als extra service aan de lezer breng ik hier in een apart PDF de eindnoten bij het artikel, zodat u niet steeds naar onder hoeft te scrollen, maar de noten desgewenst in een apart venster kunt bekijken.
De paginanummers van de oorspronkelijke uitgave staan tussen vierkante haken: [ met paginacijfer rood ].

Ik wijs hier op één foutje: op blz. 69 staat “in the order of thought, an immediate infinite mode would be "absolutely infinite extension." Dat moet uiteraard zijn "absolutely infinite understanding."

Verder heb ik ernstige twijfel over de formulering op p. 67: “insofar as modes constitute substance.” De eerste stelling van de Ethica luidt niet voor niets: “Een substantie gaat van nature vooraf aan haar aandoeningen.” Het kan dus niet zo zijn dat modi de substantie ‘constitueren’.
In de buurt van die passage staan vergelijkbare uitspraken en wordt in de noten 10 t/m 12 verwezen naar de idem dito benadering van Deleuze, waar ik dus vraagtekens bij plaats.

Many newcomers to the work of Alain Badiou will almost certainly have reservations concerning his assertion that mathematics, and particularly Cantorian set theory, is ontology. Badiou is not arguing that mathematical thought resembles ontological inquiry. Description or intuition are not properly ontological procedures for Badiou, and any understanding of his work will have to, at least in part, accept the principle that being as such is resolutely uncategorizable and multiple. It is furthermore not the case that mathematics is ontology insofar as it designates ontological objects for philosophical enquiry. Mathematics simply states what is expressible about “being-qua-being” to the extent that it is directly conveyed in mathematical thought. In other words, the content of being is given by way of the formal operations of mathematics: there is no pre-given domain of being upon which mathematics operates. It is only through the mathematical procedures of axiomatically constructing and ordering multiplicity that infinity is posited as set theory’s proper domain.

Badiou’s affirmation that mathematics is ontology extends from two criteria that rudimentarily define what ontology should be. First, following the dialogues of Plato’s Parmenides, Badiou affirms that being is pure multiplicity: no principle of unity is intrinsic to a definition of being-qua-being itself. Secondly, given that ontology is a pure thought of being-qua-being, there is no need to refer to the particular things of the world, or to any distinction between an actual and possible existence, in order to speak of being.

The present will be an attempt to analyze the implications of Badiou’s set-theoretical ontology through his reading of Spinoza. In his mammoth opus, L’être et l’événément [Being and the Event], Badiou reads Spinoza as a philosopher who “forecloses the void par excellance”.¹ Then ramifications of what the void exactly is for Badiou, and how it comes to be excluded from the lineage of Spinoza’s philosophy, can only be explicated in what follows. For the present, however, it should simply be enough to say that its absence will effect a double closure within Spinoza’s system: a closure that falls short of thinking multiplicity proper, on one hand, and novelty, on the other.

I ontology and the void

At a rudimentary level, set theory departs from a theory of an actually existing infinity. This is as true for Georg Cantor, the founder of set theory, as it is for Badiou. Even if the infinite may have an existing counterpart in the physical universe, the formal consistency of infinity within thought was, for Cantor, a sufficient enough criterion for it to exist. In other words, the ontological valid-[64]ity of the infinite was equal to a formalized thought of infinity. Mathematics, for Cantor, was thus a form of freedom insofar as its content was purely immanent to thought, with no need to conform to any objective content.² Also, early on in the development of set theory, Cantor was able to demonstrate formal proofs of the existence of infinite multiples: in particular, it could be shown that the set of real numbers was greater in sum than that of the positive integers, which themselves were infinite. Infinities of different sizes could thus be said to exist. Whilst departing from an actual infinite, set theory proved capable of deducing a formally consistent means with which the infinite could be spoken of through a theory of ordering multiples into denumerable collections, or sets. It did so, however, with the provision that not every multiplicity could be well ordered: not every element in a multiplicity could be ordered hierarchically in a set such that each element was greater than, equal to, or less than any other element in that multiplicity.³ Such multiples were deemed to be inconsistent by Cantor, and while the operations of classical set theory involved the ordering and collecting of multiples into sets, classical set theory did so with the knowledge that not everything could fall under the operations that determined a set’s formation. A final set containing every possible element in the universe is an impossibility of modern thought.⁴ A metaphysical importation of set theory is that being does not coalesce into a totality: the universe is not one. Or, as Badiou has more conclusively put it: “reason itself determines the impossibility of the whole as an intrinsic property of the multiple-existence of any being” (CT 190).

It is from a theory of inconsistency, of what cannot form a unified multiple, that Badiou departs when outlining the parameters of his ontology. Now in order to do ontology (at least for Badiou), a foundation for speaking of the pure inconsistency of being-qua-being must be given at the outset. Badiou’s ontology is thus forced to split itself into two domains: one as the origin where being comes to be presented (which adheres to the principles of ordering multiplicity through presentation), and another domain where the pure inconsistency of what escapes the count is posted qua subtraction. We could call the former a local presentation of multiplicity/being (in Badiou’s terms, a “situation”), while the latter would simply be the pure inconsistency of being-qua-being which escapes presentation. In the same way that a formalization of being is effected through the settheoretical operations of well-ordering (whereby multiples come to be composed of discrete, consecutively ordered elements), so too does being-qua-being present itself locally in an ontological situation, where multiplicity falls under the logic of the “count-as-one.” This is to say that if Badiou refuses totality at the level of pure being-qua-being (which is indifferent to totality), it reappears under the banner of ontological presentation, where everything obeys the law of the count-as-one. Nonetheless, it is important to remember that the count-as-one is a pure operation of formalization and not a principle inherent to being itself. It follows that not everything can be unified under the count - there will always be something that cannot come to be consistently presented.

At this point, the void enters Badiou’s lexicon. Given that being-qua-being is not directly isomorphic to what is presented in a situation (that is, if everything cannot be presented qua counting), the operations of presentation necessitate a second operation of unpresentation, or subtraction, insofar as the inherent inconsistency of being-qua-being is subtracted from the logic of the count, yet determined to be subtracted as such. The count, which only tolerates the assertion that the one is, operates at odds with inconsistency, which entails that the one is not. It follows, for Badiou, that “inconsistency as pure multiple is solely the presupposition that before the count, the one is not.” (EE 65). But the particular paradox of set theory is that what is ordered within thought can only be given through the act of ordering itself: there is nothing that pre-exists the count if the count is no longer conceived in terms of a form acting upon a content. On the contrary, the content is given through the form itself. There is thus a double assumption at play in Badiou’s logic: on one hand, something falls outside the logic of presentation (or the count), and could be said to pre-exist it qua subtraction. [65] On the other hand, nothing could be said to be given prior to presentation, insofar as presentation is a presentation of nothing. It follows that the presented multiples are multiples of nothing (they “contain” no pre-operational content), and are thus derived from the void. “The sole term from which ontology’s compositions without concept are woven is inevitably the void.” (EE 70).

The void is not a physically existing vacuum, or a lack, or an existential wound at the center of experience. It is simply Badiou’s name for what is subtracted from presentation. And since nothing pre-exists presentation (no pre-operational content of sorts), the inconsistent unpresented of any situation is named the void. One can think the void as an impasse of thought that is internal to thinking the totality of being, rather than as a name for some failure of thought to be adequate to some pre-operational content.⁵ It is thus important to distinguish the void from inconsistency: the void is a localized effect of presentation (the unpresented of presentation) whereas inconsistency is what is not presented (and thus truly neither one nor multiple, neither consistent nor inconsistent). Nothing is inconsistent in and of itself: the term inconsistency applies only to what can or cannot follow the external applications of a given rule of well-ordering.⁶

I’ll make a leeway here to the implications this theory has for a reading of Spinoza. If the void is the primary name of being for Badiou, it is because the multiplicity that presentation presents has no qualitative being in and of itself: multiplicity is not a constitutive determination of being at any sort of substantial level. It is rather the result of an impasse internal to formalization. Or rather, presentation inscribes the existence of what cannot be directly presented. With regard to Spinoza, for whom infinity is a non-mathematical quality of substance, the existence of a void can only be introduced through the employment of an external determination of substance that modifies its proper content. For example, in a work pre-dating the Ethics by over a decade, Spinoza postulated that “it involves a contradiction that there should be a vacuum.”⁷ The existence of a vacuum would imply that there could be extension without corporeal substance. By virtue of the fact that Spinoza had previously proposed that “body and extension do not really differ” (DPP II.2, 267), having extension without corporeal substance (or a body) would be tantamount to having extension without extension, a self-contradictory statement if there ever was one. Spinoza’s rejection of a vacuum was thus necessary on two counts. In the first place, his geometrical method served as a model in which the rejection of a vacuum logically followed from the parameters of what was already outlined in an axiomatic system (that is, from what space, bodies, extension, substance - and the relations between them - exactly were). It was a model that contained its own criteria for verification, making recourse to any external term superfluous. Given this, it could secondly be said that the rejection of the void in Spinoza’s philosophy logically extended from the fact that nothing external to a geometrical method was necessary to ensure its internal consistency. Like the monism of his substance, Spinoza’s geometrical method was not a reflection upon being, or the world, or any external object or domain, but rather a system in which creation was fully immanent to the created.

If one is to assume that Spinoza is a thinker of multiplicity (a fairly uncontroversial conjecture), he is undoubtedly one who conceives it as a continuous whole that pre-exists any division into parts. Only abstractions from  the intricate relatedness of multiplicity would allow multiplicity to be divided into discrete sections. And the fact that there is no vacuum in nature for Spinoza is the direct result of the indivisibility of substance itself. To quote Spinoza fully on this count: “Since, therefore, there is no vacuum in Nature … but all its parts must concur that there is no vacuum, it follows also that they cannot be really distinguished, that is, that corporeal substance, insofar as it is a substance, cannot be divided.”⁸ The key point is that it is precisely as substance that a whole cannot be divided into parts. Parts inhere in matter only insofar as matter can be seen as something that is “affected in different ways, so that its parts are distinguished modally, but not really.’ (Ethics, Book I, Proposition 15). Like Deleuze and Bergson after him, Spinoza undoubtedly posits the actuality of [66] infinity at the outset, so that parts are merely abstractions or divisions extracted from the density of the whole. Only from a perspective that deems corporeal substance to be a discrete whole composed of parts could it then be inferred that substance is finite, and thus separate from God. The logical absurdities that follow from this are amply given in the Ethics,⁹ and I won’t labor their implication in detail. I will only say that the problem that extends from thinking infinity through the summation of discrete (or finite) divisions would introduce the problem of a void - something that Spinoza refuses on both logical and ontological grounds - the void in this case being the empty beyond that the infinite addition of parts would be directed towards in pursuit of infinity.

As Badiou sees it, Spinozian being (substance) is founded upon an exclusion of the void in a very specific manner. It is not simply that there is no vacuum in nature (which could merely expel a physically existing void); it is rather that everything that is substance (which would in fact be everything) falls under the logic of a unified presentation insofar as everything is either a finite mode (counted as one) or a singular substance (which is only ever the one as totality of what is). The only exceptions to these principles could be found in infinite modes, something that Badiou will read as the reappearance of the void (qua inconsistency) in Spinoza’s axiomatic. How successful Badiou is in his attempts will ultimately depend upon the manner in which the reader accepts Spinoza’s initial positing of infinite modes. I would hope that my brief allusions to Deleuze’s interpretation of infinite modes leave their legitimacy open to further questioning. For the present, however, the important thing to follow is the manner in which infinite modes exceed the principle of unified presentation that otherwise informs Spinoza’s axiomatic.

II foreclosing the void: spinoza

Spinoza is one of the earliest thinkers to be introduced in the lineage of Badiou’s L’être et l’événement (with the exception of Plato and Aristotle), and the relative economy of Badiou’s analysis of Spinoza will lay the groundwork for the more difficult issues that bear upon the relations between Badiou and Deleuze, which we will no doubt hear much of in the future. Badiou begins his analysis not with what most commentators usually begin with (that is, singular substance), but rather with the multiplicity of singular things. It is a curious choice for Badiou, given that this is not necessarily the manner in which Spinoza organizes the Ethics.¹⁰ But Badiou’s unique nuance on this is to complicate the manner in which the unifying principle of substance - equivalent to the cause of singular things -  can be derived from the multiplicity of what Deleuze calls “extensive parts” (as we will see): “In effect, a composition of individual multiples (plura individua) is one and the same thing if those individuals work toward their unique action - that is to say if they are simultaneously the cause of a unique effect.” (EE 129). It isn’t difficult to see a bizarre reversal of the principles one commonly uses to understand Spinoza: why would it be the case that an individual would be the cause of an effect of unity if unity itself (qua substance) was the underlying cause of singular things? For Badiou, this may be clearer if we understand that the count-as-one (the individuation of singular modes from the multiplicity of substance) is causality. “A combination of multiples is a multiple-one of what is the one of a causal action.” (EE 129). This logic could just as easily be read backwards: the one as causal effect of the counting of multiples comes to be that which validates the one as cause of a singular thing.¹¹

The most immediate objection to Badiou’s equation of counting with causality is that number for Spinoza is only an external determination of an existing thing. For 20 men to exist in the world, the number 20 must “necessarily be outside” the 20 men themselves (Ethics I.8). Whatever then exists as a number of individuals must have an external cause to exist. It is substance itself that determines that number, and thus the count itself. The problem with this, for Badiou, is that it is circular. Two principles of unity must be presupposed to make sense of this: one as the effect of the count, and another one as the supposition of that effect (the one of causality). But the latter, defined as the cause of the [67] count, is retroactively generated as the effect of the count. If it was difficult to see what the count had to do with causality (insofar as the latter was not yet distinct from the unity of substance), Badiou’s intentions should now be clear: what must assure the consistency of the count is nothing other than the unity of God or substance itself insofar as it is inseparable from the internal determination of substance as a singular situation. Herein lies the unique character of Spinoza’s monism: substance is both metastructure and structure insofar as substance posits both itself (qua metastructure, determination of the whole) and its singular modes. If no term outside substance accounts for the manner in which it is cause both of itself and of its singular modes (such a determination being endemic to substance itself), then Badiou will maintain that “Spinoza’s is the most radical ontological attempt ever for identifying structure and metastructure, belonging and inclusion.” (EE 130).

The immediate consequence of this is that Spinoza’s is a philosophy that “forecloses the void par excellance.” (EE 130). While Badiou will go on to show that this foreclosure fails, I wish to stick, for the moment, with what is implicit in the conflation between what Badiou calls “belonging and inclusion.” If these set-theoretical terms are to be mapped onto Spinozism, the fact that there is a perfect transitivity at work in Spinoza ensures that everything presented in substance is also represented (individuated) as singular modes, and everything individuated as a mode is presented as well (insofar as modes constitute substance). It is a fairly straightforward point of Spinoza’s that the only things that exist are substance, on one hand, and modifications of that substance - that is, modes - on the other (attributes only being expressions of essence).¹² Now the latter clearly belong to the former, given Spinoza’s axiom, in the first book of the Ethics, that “whatever is, is in God, and nothing else can be conceived without God.” (Ethics I.15). For Badiou, the “in” of the belonging to God is the universal relation for Spinoza - there is no other relation than belonging. “If in effect you combine several things - several individuals for example - according to the causal count-as-one (departing from the one of their effect), you never obtain but an other thing, that is to say, a mode that belongs to God.” (EE 130). Thus, if a collection of things themselves forms a thing that does not qualitatively differ from any one of its parts, the counting of terms never amounts to anything excessive to substance, given that the count of terms is nothing other than the “inexhaustible immanent productivity of substance itself.” (EE 130).

To frame the point Badiou is making, and perhaps to allude to what will only later become apparent, consider the manner in which Deleuze handled the problem of Spinoza’s monism. It is clear that Deleuze privileged Spinoza over Descartes because substances in the latter were distinguished from each other only in distilled, mathematical terms - that is, only through abstracting from the substantial differences between the attributes of thought and extension are the primary differences between the two determined on the more elevated register of two substances (res cogitans, res extensa). But for Deleuze-Spinoza, this amounts to nothing more than a denial of difference as something that is real. Not only does Spinoza’s monism successfully affirm actual multiplicity; it internally differentiates the singularities inherent to it without having recourse to external criteria (for example, number) for that differentiation. “Detached from all numerical definition, real distinction is carried into the absolute, and becomes capable of expressing difference within being, so bringing about the restructuring of other distinctions.¹³

Now if Deleuze’s point is that the singularity of substance is precisely what allows for a real difference among attributes, this point is not lost on Badiou. He clearly concludes that Spinoza does not fail to distinguish multiple “situations.” The singularity of God is what allows him to be identified in an infinity of different manners, in attributes. “We must here distinguish between being-qua-being (the substantiality of substance) and that which thought is in a condition of conceiving as constituting the differentiable identity (Spinoza says essence) of being, which is plural.” (EE 131). Furthermore, Badiou makes the rather Deleuzian point that the multiplicity of situations (that is, the attributes of substance) is [68] what upholds the unity of substance insofar as that unity, were it to be thought in only a single one of its attributes, “would have in this way difference external to itself, that is to say, it would be counted, which is impossible, since it is the supreme count. “ (EE 131).

But despite the fact that an infinity of attributes exists, there are precisely only two attributes (‘two countable situations’ (EE 131)) that can be experienced by humans: thought and extension. And the uniqueness of a human is that even if he or she can inhabit two separate situations (mind and body, thought and extension), a human is also counted as one thing. For Badiou, this is the quintessential example of the subordination of statist excess (representation) to presentative immediacy. The mind and the body are included in a unified human being who does nothing more than belong to an ontological situation. Even if the mind and the body simultaneously belong to two separate situations or attributes, their inclusion in the singular mode of a human being ultimately subordinates their inclusion as two modes united in a human being to their belonging to an ontological situation.

I’ll briefly recapitulate this in set-theoretical terms in order to clarify the isomorphism Badiou is making here. Assume there is an original set of all the human beings in the world, each being counted as one, which could be called a situation. Now compose a list of all the various combinations of humans that could each be counted as subsets of the original set. For example, we can include in this set collections such as families, citizens of towns and countries, the set of all people named Mark, the set of all people with brown hair and blue eyes, etc.; as long as we follow rules of legitimate constructability (which is purely formal and not descriptive),¹⁴  we can generate a “power set” of the original situation (a set that will contain more members than the original set). Every person belonging to the original set will be represented (or included) in the second set (since we can construct a set in the second set that is comprised of “all the French philosophers named Gilles Deleuze”), as well as various other combinations these persons fall into (since Gilles Deleuze may also be a member of the subset “citizens of France,” which is also included in the power set). Now if the power set exceeds the magnitude of the original situation (which itself could be infinite), it follows, for settheory, that infinite magnitudes exist which cannot be incorporated into the consistent presentation of well-ordered multiples.

For Spinoza, however, given that the modes comprising the various affections of substance and its attributes belong to the ontological situation “substance” (alongside the humans who belong to that situation), there is no need to produce a power set of all the various combinations (for example, the humans that minds and bodies combine to make). Firstly, there is no place outside substance to posit such a set; secondly, the plurality of substance pre-exists the division of substance into discrete parts, thus making the application of a numerical measure (or cardinality) to the multiplicity of substance absurd. In other words, the minds and bodies that are elements of substance (qua modes) together form a subset that just as legitimately belongs to substance. Nothing exceeds presentation, either causally or ontologically.

The foreclosure of the void follows directly from this. The void neither belongs to an ontological situation (since it doesn’t result in being counted as one), nor is included in the metastructure as causality, or representation, that is excessive to presentation, since metastructure for Spinoza is nothing other than causal counting conceived this time as the immanent self-positing of substance in and through itself. Substance, as cause of itself, is what guarantees that nothing exceeds it precisely insofar as it posits itself as one substance. As Deleuze notes, correctly I believe, to apply external causality to substance in and through the positing of more than one substance would force substance to “operate outside the terms that legitimate and define it - to propose its operation in a sort of void - and quite indeterminately.”¹⁵

The fact that there is no vacuum in nature follows from the indivisibility of substance. A vacuum (or physically existing void) could only exist alongside a limitation of substance. But if substance is singularly indivisible, any limitation to substance could only occur through abstracting from the true nature of substance itself. It [69] will be in this disproportion between modes and substance, or the divisible and the indivisible, that a question of the void itself will re-emerge. If God, or substance, is the cause of modes (insofar as “modes can neither be nor be conceived without substance”), the question as to the measure between the count (substance, causality) and its result (effect of one, singular mode) necessarily reintroduces the void into Spinoza’s system qua “measurable non-rapport between its infinite origin and the finitude of its effect as one.” (EE 133). If only substance or modes exist, there will necessarily be an “excess of the causal source.” (EE 133) precisely insofar as the absolute infinite indivisibility of substance is not itself present at the same level as the effects it produces in the count of finite things. There will be a potential disruption in what would otherwise be seen as the complete immanence of Spinoza’s system.

III the problem of infinite modes

The crux of the problem directs the reader to Propositions 21, 22, and 28 of the first Book of the Ethics, where three points are established:

1.        Everything that follows from the absolute nature of any of God’s attributes must exist and be infinite. If an effect, or mode, directly results from the infinite nature of substance/God, it too must be infinite. These would be immediate infinite modes.

2.        Everything that directly follows from some attribute of God - that is, if it is modified by an attribute that exists necessarily and is infinite - must also exist necessarily and be infinite. These are mediate infinite modes.

3.        Any singular finite thing can neither exist nor produce an effect unless it is determined to exist and produce an effect by another singular finite thing which itself must be determined to exist by another singular finite thing, and so on to infinity.

The immediate implication of this, as has already been stated, is the complete disjunction between the finite and the infinite: one cannot directly ensue from the other, even if the recurrence of finite modes creates an infinite chain. “The flaw between the infinite and the finite, where the danger of the void lies, does not traverse the presentation of the finite.” (EE 134). Yet with regard to Propositions 21 and 22, it is a question of modes that, by virtue of following either from substance or from one of its attributes, are infinite. The question for Badiou (among others) is one of knowing the extent to which these infinite modes could be said to exist. What exactly are they? Drawing on a communication between Spinoza and a correspondent, Badiou proffers the following examples: in the order of thought, an immediate infinite mode would be “absolutely infinite extension,” in the order of extension, “movement and rest.” (EE 135). As for mediate infinite modes, he offers only one example in extension: “the figure of the entire universe” (EE 135).

The direct gap left in Spinoza’s system would evidently be the lack of a mediate infinite mode in thought. But this may be secondary to the actual problem Badiou finds in Spinoza’s positing of infinite modes: it is not that a lack of one of them leaves a void in his system - infinite modes, as Juliette Simont notes, are themselves void by definition.¹⁶ I want to be very clear on what this problem is for Badiou. He is not simply dismantling Spinoza by locating a certain indeterminate nothingness in the circularity of his method. It is rather that infinite modes are posited to provide a leeway between the presentative immediacy of finite modes and the indivisible infinity of substance. Of course, a leeway for Badiou exists, but only through an operation of subtraction, which is obviously at odds with the immanent productivity of Spinozist substance. More specifically, with regard to infinite modes, it could certainly be argued that the totality of the universe is composed of modes at the same time that it can be read (at least by Spinoza) as infinite. But there is a difference between a modal infinite unity established through “summation ad infinitum.“ (EE 135) and the principle of unity that operates as the causality of modes in general. The former would depart from modes to posit totality as one, whereas the latter would be inherent to the causal operations of substance (from which modes are produced). Why, then, is it legitimate to call infinite modes modes at all? [70]

The totality of the figure of the entire universe, for example, while being an immanent production of substance, cannot be said to be presented as one in the same manner as a finite mode. It departs from the finite onto the infinite, which is the direct opposite of the manner in which infinite substance could be said to be the cause of finite modes. The question that would need to be asked is if infinite modes are even presented at all since “the principle of the all that one will obtain through summation ad infinitum has nothing to do with the principle of the one through which substance guarantees the counting of all singular things in radical statist excess, which is nonetheless immanent.” (EE 135Ð36).

If it is true that all that exists is either a substance or a mode then it should be perfectly easy to test their existence. It pertains to the nature of substance to exist, whereas the existence of modes “cannot be inferred from the definition of the thing.”¹⁷ Modes, that is, exist a posteriori, through experience. Now, no single one of these modes can be given in experience: one cannot observe movement or rest directly (only things that move or are at rest), nor can the totality of extension be represented in experience. On the other hand, it cannot be said that these modes necessarily exist outside experience, for they would thus be qualified as substance, not as modes. Or, as Badiou writes, “at best, they will be the identifications of situations,” that is, attributes (EE 136). We are at an impasse. Infinite modes were introduced precisely in order to avoid having singular finite modes directly follow from infinite substance, since the void would emerge therein as the excess of causality over the singular thing, which is simultaneously immanent to, but incommensurable with, the infinite indivisibility of substance. But if infinite modes make amends of sorts for this excess (in that nothing finite can directly be caused by what is infinite), they are nothing more, for Badiou, than pure names whose existence cannot be proven. “One needs to propose either that these modes exist, but are inaccessible to thought as to experience, or that they don’t exist. “ (EE 136). If they exist, they do so purely as a name designating a certain outside to experience: the name ‘infinite mode.’ If they don’t exist, on the other hand, they directly create a void in the sense that they uphold infinity as such in the “causal recurrence of the finite.” (EE 137) (the totality of souls that comprises the universe as a whole, for example). This is an empty name as well: it is there “to put forward what the [geometrical] proof requires, to be successively annulled in all finite experience where it served to found unity.” (EE 137).

The lesson of Spinoza for Badiou is that, if the void is excluded from presentation, it will necessarily re-emerge in the form of an empty name. Perhaps this is Badiou’s own schematic take on Lacan’s famous dictum of the 1950s: “what is excluded in the symbolic reappears in the real”¹⁸ – Badiou’s very deliberate use of the Lacanian term “foreclosure” would suggest as much. “Infinite mode” would thus name the return of the void as a name for what cannot be consistently presented in Spinoza’s system. We can furthermore see how this initial foreclosure-exclusion was instilled on three counts:

1.      In the simple (almost axiomatic) proclamation of Spinoza in Book I: “the vacuum is not found in Nature” (Ethics I.15). As we have seen, this is a direct result of the indivisibility of nature at the level of its substantiality.

2.      In a point derived from Deleuze’s reading of Spinoza’s monism: there is nothing outside the terms of substance that can distinguish it from another substance, and thus serve as the cause of that distinction, for to do so, in Deleuze’s terms, would “propose its operation in a sort of void - and quite indeterminately.” This would be the foreclosure of the excess of metastructure (a term anterior to the immanent productivity of substance).

3.      The void finally remains absent from the disjunct relation between substance, as cause, and modes as effects. Ironically enough, this disjunction will be necessary for Spinoza if he is to avoid instilling causality as excessive to presentation. That is, the infinite can only directly result in modes that are infinite if it is to avoid appearing as a cause that is incommensurable with its effects.

If the void simply marks the place of an unacknowledged excess of infinite substance over the [71] finite modes of which it alone is the cause, this would, in the first place, follow from the fact that a direct correlation between infinite substance as cause and finite modes as effects has been established. Taken directly in this manner, infinite modes are void not simply because they have no existence that can be directly attested to in experience (and thus by the criteria of Spinoza’s system); rather, they secure the empty name of what is not directly accounted for in Spinoza’s causal operations. Deleuze, in contrast, found that movement and rest have a character that is particular to them alone, insofar as they are what allows for the unification of the extrinsic parts of a mode to form a complete whole. As he wrote:

The attribute of extension has an extensive modal quantity that actually divides into an infinity of simple bodies. These simple bodies are extrinsic parts which are only distinguished from one another, and which are only related to one another, through movement and rest. Movement and rest are precisely the form of extrinsic distinction and external relation between simple bodes. Simple bodies … are always grouped in infinite wholes, each whole being defined by a certain relation of movement and rest.¹⁹

From this, it is evident that movement and rest, far from being singular modes among others, comprise relations that make the existence of finite modes possible. Or, rather, movement and rest allow the infinite decomposable parts of a mode to determine a modal essence (which Deleuze characterizes, in terms too complex to outline here, as a degree of intensity). Now, Deleuze’s take on this is that it is only by virtue of these relations that the extrinsic parts that comprise a mode come to have an existence (that is, in Badiou’s terms, by virtue of belonging). “Thy have no existence of their own, but existence is composed of them: to exist is to actually have an infinity of extensive parts.”²⁰ Conveniently sidestepping the problem of defining movement and rest as modes, Deleuze maintains that movement and rest are what allows for “the conditions for modes to come into existence.”²¹ If we follow this point to its conclusion, we could infer that their modal existence directly follows from their essence, given that the means by which they act upon the extensive parts of finite modes mirrors the manner in which substance causes modes externally. Movement and rest could even be said to constitute the essences of things that don’t exist;²² they thus comprise a relation which is analogous to causality insofar as they enable the existence of modes in general. But the relation in question is nonetheless a different sort of relation than causality, strictly speaking. Thus, to return to an earlier point, it could be the case that relations other than causality are needed if we are to account for the workings of Spinoza’s system.

IV non-causal relations

In an article originally published in 1994,²³ Badiou acknowledged that Spinoza, not unlike Badiou himself, opts for an ontology founded upon the axiomatic of the decision. From this is derived the geometrical method, which “is not a form of thought --it is the written trace of an originally thought decision.” (CT 72). What Badiou rejects, however, is that the “there is” of the axiomatic decision, referring to the infinity of substance, or God, admits exclusively of causality as relation (CT 74). In effect, Badiou admits that two other relations are necessary to maintain the coherence of Spinoza’s system: coupling and, surprisingly, inclusion (CT 75).

The crux of Badiou’s conclusion encompasses a problem that was encountered earlier: the circularity of Spinoza’s system. If we enquire as to the resources with which thought can have access to infinity, and if the intellect offers the means (or “singular localization” (CT 79)) with which divine infinity can be conceived (along with the ”there is” of pure positing itself), then we are faced with what Badiou will call a “torsion.” For it is not simply the case that the intellect is that  through which one grasps divine infinity; it is also what attributes to substance its nature as an infinite thing conceived through itself.²⁴ The circularity is introduced as such:

To think this torsion is to say: how can the Spinozist determination of the “there is” return to its interior fold which is the intellect? Or, more simply, how can one think the being of the intellect, the “there is” of the intellect, if [72] rational access to the thought of being, or of the “there is” itself, is itself dependent upon the operations of the intellect? Or: the intellect operates, but what is the status of its operation? (CT 78)

The difficulty is not particular to Badiou’s interpretation. Following the lineage of Hegel’s objections to Spinoza, Pierre Macherey has observed that the attribute thought, as an essence of substance, must precede the intellect as a mode if Spinoza’s system is to have a logical order. Yet, as a mode, it is the intellect that perceives the attribute as constituting the essence of substance. If abstract reasoning supposes a circle, it does so by definition, not through any procedure of realization. Thus, the circularity of Spinoza’s logic explicates itself, for Macherey, through the fact that the definition of an attribute “makes the nature of an attribute depart from the existence  of the mode without which it would not only be incomprehensible, but even impossible.”²⁵

The fact that this will foreshadow an acknowledgement of non-causal relations is what, in effect, allows Badiou to avoid the necessity of resolving the aforementioned enigma through placing the void. First, in acknowledging that the relation between an idea and its object is not directly causal, Badiou introduces another relation called coupling, whereby “an idea of the intellect is coupled with an object.” (CT 82). Or, by extension, “a mode of thought is always coupled with another mode, which could be extension, or thought, or a whole other attribute entirely.”²⁶ Now to conceive this as a coupling between two distinct attributes is one thing; clearly, this is how Spinoza’s familiar definition of the mind as the idea of the body is usually received. But if one acknowledges the theorem that “the order and connection of ideas is the same as the  order and connection of things” (Ethics II.7), how can one then account for the intellect being coupled with a mode of thought? Clearly, thoughts have connections with other thoughts in a manner that is not isomorphic to the relations among extended modes. For the intellect, two infinite recurrences have to be posited to account for this particular relation: one of causality, and one of coupling. Thoughts could be said to be the cause of other thoughts (and even of God’s essence) at the same time that they are coupled with thoughts and objects that have no causal bearing upon them. And, unlike extension, the attribute of thought has a structure that is isomorphic to itself - insofar as the idea of an idea is the object of an idea. The connection between ideas and ideas of ideas is not isomorphic to the “order and connection of things” in extension. Thus, the attribute thought, or the intellect, remains radically singular in Spinoza’s system insofar as modes of thought can be coupled with other thoughts. As such, substance can think itself through the mode of thought.

Things are even more complex with regard to the finite intellect (human mind). Badiou immediately asks how the finite intellect “can conceive itself as a modification or affection of the infinite intellect” (CT 84). If everything that follows from an infinite mode (the infinite intellect) is infinite, then there is simply no way the finite intellect can directly ensue from the infinite. But neither is it the idea or object of the infinite intellect, as would be the case in a relation of coupling. A third relation is necessary, and Badiou is quick to name this relation, curiously enough, inclusion. “Certainly,” writes Badiou, “the finite intellect is not an effect of infinite intellect, but it is a part” (CT 85). It hardly seems arbitrary that the choice word for part will be partie, French for subset. For the inclusive relation between the finite and infinite intellect (such that the finite intellect is included in the infinite intellect) could just as well reciprocally be viewed in set-theoretical terms: the infinite intellect is the sum total, or collection (or power set), of finite intellects, as Badiou keenly observes in quoting from Book V of the Ethics: “Our mind, insofar as it understands, is an eternal mode of thinking which is determined by another eternal mode of thinking, and this again by another, an so on, to infinity; such that together, they all constitute God’s eternal and infinite intellect.” (Ethics V.40). The uniqueness of inclusion is that it names what specifically constitutes the content of the infinite intellect (being the “limit point for the finitudes it totalizes”) and, simultaneously, the being of the finite intellect (a “point of composition for the infinite summation” of the intellect) (CT 85Ð86). More generally, inclusion alone is what [73] accounts for the cyclic relation between the finite and the infinite intellect which causality, in its strict linear movement from substance to modes, cannot justify.

Now - cutting across Badiou’s analysis of “common notion” in Spinoza - we are in a position to see the manner in which these two extra relations, rather than opening Spinoza’s ontology to its own meta-ontological grounds that exceed substance as such, effect a closure that is necessary to sort out the different determinations (the “multiple and complex muddling” (CT 74)) of the positing of substance. If Spinoza’s system only admits the existence of singularities as the immanent effects of the postulation of substance, the criteria of assessing the truth of singular propositions can only be attributed to notions that are common to all singularities. If the relations between the human intellect (which is included in the infinite intellect) reintroduce coupling at the level of relations between an idea and its object (for example, the body), the singularity of such an assertion is traversed by what is common to all bodies. Badiou’s unique contribution to the theory of common notions is that their commonality is no longer justified through what is singular to all bodies, but through the geometrical method itself, which - otherwise stated by Badiou - would entail that all truth is mathematical. This expression could be easily exchanged with another: all being is mathematical.

At the end of the essay that has just been recapitulated, we find a point that is resolutely singular for Badiou: Spinoza lacks anything that exceeds, or supplements, the presentation of being - a conception of the event (CT 92). A theory of the void - that is, of something that remains on the fringe of any situation – is required for an event to occur. It seems rather abrupt for Badiou to introduce the category of the event within an analysis which, up to this point, has been exclusively concerned with the relations that sustain the consistency of Spinoza’s ontology. The event, for Badiou, is not an ontological category, insofar as it is never posited or presented in a situation through any normative or regulative act of formalization: it is resolutely meta-ontological and as such cannot be reduced to an analysis of Spinoza. Unlike Deleuze, for whom an event is an expression of the world (whether understood as an expression of continuity or disruption),²⁷ Badiou’s event is always detached from the world, from substance, and thus dependent upon something transitive to substance. Badiou’s later analysis ultimately ends up assuming that the impossibility of an event in Spinozism is a consequence of the closed nature of substance. His conclusion is thus fully relevant to the analysis in L’être et l’événement. I will conclude with a brief outline of what the implications of this conclusion are to be.

V conclusion: enabling the event

In outlining the principles of Badiou’s ontology, I have emphasized the dual nature of presentation: while it comes to organize everything internal to the situation under the unifying principles of the count, it furthermore contains an operation of unpresentation, whereby the void names the ontological inconsistency that presentation cannot exhaust. Any situation can contain elements,²⁸ or presented parts, that inhabit the margins of that situation, and are thus on the “edge of the void.” Only subjective action can bring the effects of the unpresented to bear upon any situation in order to fundamentally change it. Or, rather, it could be said that from the inconsistency of the void, subjective action re-decides the consistency of any situation. It has already been emphasized that any situation contains an excess of subsets over elements, and thus always contains a profusion of trans-situational multiplicity for which questions of quantity are fundamentally undecidable on both ontological and epistemological grounds. To bring this undecidability of the inconsistent excess to bear upon the regulative principles of the situation thus extends from a local decision that an event has occurred. As Ray Brassier has succinctly put it, for Badiou, “subjectivity originates in the event as that eruption of consistency through which the void’s inconsistency is summoned to the surface of any situation.”²⁹

For a reading of Spinoza, the problem with this analysis is that nothing in Spinozism exceeds presentation. Not only is there no void in Spinoza, there is nothing external to the situation [74] “substance” for which questions of belonging or non-belonging, and thus decidability and undecidability, can even apply. The implications of this for the present discussion are crucial: if the regulative principles which determine the “belonging to” of substance are everywhere immanent to substance, then it becomes impossible to distinguish what is globally determined to exist and what can become a local site of intervention through the fleeting appearance of an event, which the void alone inaugurates.³⁰ On the contrary, for Spinoza, belonging is not an issue because substance cannot be determined by anything other than what belongs to it: nonbelonging does not emerge as another relation that could have measurable effects for the determination of substance.

The three Spinozist relations that Badiou engages with (causality, coupling, inclusion) were introduced to resolve certain problems in Spinoza’s ontology. With regard to causality, it should be asked how it is that the principle of the unity of substance comes to engender modes through a unifying principle of causality. Is there not a certain circularity in this theory, if a principle of unity as cause is attributed to the effects of the appearance of modes? Of course, given that Deleuze views substance as simply a capacity to exist, the unity of substance is what allows for the best possible multiplicity, but it is for the less imprudent to conclude that the modes (as liberated differences within multiplicity) come to deplete the univocal totality of substance. Secondly, does the problem of the intellect’s ability to think itself not introduce another impasse into the framework of the Ethics: the need to account for something extrinsic to modes in order to think them properly? If coupling or inclusion successfully come to describe the manner in which thought can think itself, they do so at the expense of necessarily introducing another void into the operations of Spinoza’s method: the void of the incommensurable disjunction between the continuous infinity of substance in itself (qua thought as attribute) and the discrete multiplicity of finite thoughts.

Indeed, this above point necessarily illuminates the often unnoticed slippage Spinoza frequently makes between two types of infinities. On one hand, there is the indivisible, infinite totality of substance, which can only be divided into parts through extrinsic action. On the other hand, the figure of the entire universe, the commonality of all bodies, or even nature as totality, are multiples composed of discrete modes. On one hand, positing the infinity of substance at the outset allows for an actual infinity, a means of thinking multiplicity beyond the successive addition of finite parts towards its impossible “infinite” goal (for which the void would be the empty beyond of repetition). On the other hand, if we conceive the infinity of substance as its capacity to continually affect itself, then it is only through the differential relations established by finite modes - that is, their continual generation - that we can truly have an ontology founded upon a principle of becoming (for which the void would be “substance” as abstract totality of actual differences).³¹ Clearly, Deleuze aligned himself with the latter tradition when he wrote: “what interested me most in Spinoza wasn’t his Substance, but the composition of finite modes.”³³ If we accept the existence of both continuous and discrete multiples in defining infinity, we could then be said to have the best of both worlds. However, if one is to assume the causal reciprocity between substance and modes, one is forced to account for what transpires in the causal movement from the finite to the infinite, the movement of thought as it thinks itself above and beyond the immediacy of presentation. And for an effective decision to ensue from this process, an act of subtraction (or negation) is required. Foreclosed from Spinoza’s system, the void becomes the necessary precondition not only for thinking multiplicity, but for thinking itself. The price to be paid for its foreclosure is a philosophy that can only take recourse in a descriptive affirmation of what always already is.

notes

Many thanks to Nina Power and to Angelaki’s reviewers Peter Hallward and Daniel W. Smith for their invaluable efforts in reading different versions of this article. I would also like to [75] acknowledge Oliver Feltham’s help with my translations from L’être et l’événement.

1 Alain Badiou, L’être et l’événement (Paris: Seuil, 1988) 130. Hereafter cited in the text as EE. Translations are mine.

2 The most succinct presentation of Cantor’s belief in an actual infinite is given in chapter six of Joseph Warren Dauben’s George Cantor (Princeton: Princeton UP, 1979) 120–48. In particular, see 132.

3 Consistency for Badiou seems analogous to a principle of well-ordering whereby a set can have every element presented. As defined by Shaughan Lavine: “Cantor regarded the process of ordering a set, thereby specifying a definite succession of the elements of the set, as giving a way of counting the members of a set.” Lavine, Understanding the Infinite (Cambridge, MA: Harvard UP, 1994) 53.

4 Well-ordering, or consistency, is the backbone of nature for Badiou. Well-ordered situations are those that subscribe to a unified presentation of discrete elements that are collected with an aim towards completion. In the genesis of L’être et l’événement, it is Spinoza who provides the leeway between ontology proper and nature.

5 I borrow this formulation from Joan Copjec.

6 The principle of well-ordering thus displaces the question of size or quantity from that of forming a set without paradoxes. In particular, the limitations introduced by Russell’s paradox are not, strictly speaking, limitations of size. As Lavine writes: “it is not at all clear how size could be relevant to the question whether a multiplicity forms a set – the elements, after all, are not gathered, they simply obey a rule.” Understanding the Infinite 97. At a certain point in his career, Cantor was forced to abandon well-ordering as a principle established prior to the fact of forming a set, thus introducing the theory that sets could be wellordered because they were sets, and not vice versa. For Badiou, the question of ordering multiples that are not subsumed by the operations of the count emerges only at a meta-ontological level of fidelity to an event.

7 Proposition 3 of Book II of “Descartes’s ‘Principles of Philosophy’” in vol. I of The Collected Works of Spinoza, ed. and trans. Edwin Curley (Princeton: Princeton UP, 1985) vol. I, 268. Hereafter cited in the text as DPP.

8 Spinoza, Ethics, in The Collected Works of Spinoza, Book I, Proposition 15. Hereafter all citations from the Ethics will be given in the text, with book and proposition numbers.

9 On one hand, if corporeal substance is infinite and divisible, it could be divided into two parts, which could either be infinite or finite. If both parts are finite, one would have an infinity composed of two finite parts. If both are infinite, one would have more than one infinity, which is absurd. Or one could be infinite, and the other finite, and thus it would be the case that infinity is missing a part, which is equally absurd. Either one must conclude that corporeal substance is finite, or that it is not divisible into parts. Spinoza clearly opted for the latter position.

10 Deleuze is not far from this approach when he writes: “substance, by virtue of its power, exists only in its relation to modes.” It should be noted that, for Deleuze, substance exists only as the puissance that enables the existence of modes. Expressionism in Philosophy: Spinoza, trans. Martin Joughin (New York: Zone, 1991) 95.

11 Again, even Deleuze is close to this interpretation when he writes that for Spinoza “to exist is to actually possess a very great number of parts.” See Expressionism in Philosophy 201.

12 Deleuze, Expressionism in Philosophy 95: “[substance] has an absolutely infinite power of existence only by exercising in an infinity of things, in an infinity of ways or modes, the capacity to be affected corresponding to that power.”

13 Ibid. 39.

14 This, of course, acknowledges the serious limitations of the example I have given of actually existing people in the world, since the present example would almost certainly require formal limitations to prevent various random absurdities (such as “set of all people with orange skin”) which  depend upon descriptive characteristics of the original elements involved.

15 Gilles Deleuze, Expressionism in Philosophy 32.

16 Simont, “Le Pur et l’impur (sur deux questions de l’histoire de la philosophie dans L’être et l’événement).” Les Temps modernes 526 (May 1990): 32. Simont sees Badiou’s reading of Spinoza as an argument for infinite modes’ lack of existence, [76] which is not the case at all. Infinite modes for Badiou are simply not consistently presented in experience as modes.

17 See “Spinoza’s letter 10 to Simon de Vries” in The Collected Works of Spinoza, vol. I, 196.

18 The Seminar of Jacques Lacan, Book III: The Psychoses, trans. Russell Grigg (New York: Norton, 1993) 71.

19 Deleuze, Expressionism in Philosophy 205.

20 Ibid. 205.

21 Ibid. 236.

22 Ibid. 235.

23 “L’ontologie implicite de Spinoza,” Spinoza: puissance et ontologie, ed. Myriam Revault d’Allones (Paris: Kimé, 1994). Reprinted in Badiou’s Court trait d’ontologie transitoire (Paris: Seuil, 1998). Hereafter cited in the text as CT. Translations are mine.

24 See Spinoza’s March 1663 letter to Simon de Vries: “By substance, I understand what is in itself and is conceived through itself, that is, whose concept does not involve the concept of another thing. I understand the same by attribute, except that it is called attribute in relation to the intellect, which attributes such and such a definite nature to substance.” The Collected Works of Spinoza, vol. I, 195.

25 Pierre Macherey, “The Problem of the Attributes,” The New Spinoza, eds. Warren Montag and Ted Stolze (Minneapolis: U of Minnesota P, 1997) 65.

26 This almost certainly bears resemblance to Deleuze’s interpretation of parallelism in Spinoza. See Expressionism in Philosophy 99–111.

27 Badiou’s interpretation of Spinoza departs significantly from that of Deleuze, for whom the geometrical method served precisely as a method of invention. As Deleuze writes, “the geometrical method ceases to be a method of intellectual exposition; it is no longer a means of professional presentation but rather a method of invention. It becomes a method of vital and optical rectification. If man is somehow distorted, this torsion effect will be rectified by connecting it to its cause more geometrico.” Deleuze, Spinoza: Practical Philosophy, trans. Robert Hurley (San Franscisco: City Lights, 1988) 13.

28 Badiou here distinguishes historic situations (which contain a site for an event) from natural situations (where no such site is present). The site of the event could be said to be presented in a historic situation, but its elements are not. It is thus a site “on the edge of the void.” See EE 193–98. Badiou is slightly ambiguous on this point. On one hand, he firmly maintains that “at the heart of every situation, as the foundation of its being, there is a ‘situated’ void, around which is organized the plenitude (or the stable multiples) of the situation in question.” Badiou, Ethics: An Essay on the Understanding of Evil, trans. Peter Hallward (London: Verso, 2001) 68. It would seem that every situation could contain the possibility for an event insofar as an event names the void of the situation. On the other hand, Badiou firmly maintains a distinction between historic and natural situations (in which events do not or cannot occur).

29 Ray Brassier, “Stellar Void or Cosmic Animal: Badiou and Deleuze on the Dice-Throw,” Pli: The Warwick Journal of Philosophy 10 (2000).

30 See Badiou’s Deleuze: The Clamor of Being, trans. Louise Burchill (Minneapolis: U of Minnesota P, 2000) 91: As for myself [Badiou], however, I cannot bring myself to think that the new is a fold of the past, or that thinking can be reduced to philosophy or a single configuration of its act. This is why I conceptualize absolute beginnings (which require a theory of the void) and singularities of thought that are incomparable in their constitutive gestures (which require a theory – Cantorian to be precise – of the plurality of the types of infinity)…

31 Mary Tiles has suggested that the presupposition of a continuous whole poses problems for a philosophy of becoming. For it would follow from such a perspective that “time too would have to be actually, not potentially, infinite and thus in some sense wholly actual even though not simultaneously present. It is from this point of view that the reality of time as associated with change and becoming is questionable.” The Philosophy of Set Theory (Oxford: Blackwell, 1989) 29–30.

32 Martin Joughin’s Introduction to Expressionism in Philosophy 11. I thank Daniel W. Smith for bringing this quote to my attention. Deleuze continues: [77] “the hope of making substance turn on finite modes, or at least of seeing in substance a plane of immanence in which finite modes operate, already appears in this book [Ethics].”

 

Colofon

Sam Gillespie, “PLACING THE VOID: Badiou on Spinoza.” In: Angelaki, Journal of the Theoretical Humanities, Volume 6, 2001 - Issue 3, Pages 63-77