Sam Gillespie nogmaals over Badiou’s #Spinoza [7]

Zoals ik al tweemaal in vorige blogs - o.a. in het vorige blog over Sam Gillespie -  aankondigde, kom ik hier nog eens terug op

● 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].

Description: The Mathematics of Novelty: Badiou’s Minimalist Metaphysics tackles the issue of philosophical materialism in Gilles Deleuze and Alain Badiou, enquiring after the source and nature of the ‘novelty’ that both philosophers of multiplicity claim to discover in the objective world. In this characteristically erudite analysis, Sam Gillespie maintains that where novelty in Deleuze is ultimately located in a Leibnizian affirmation of the world, for Badiou, the new, which is the coming-to-be of a truth, must be located exterior to the ‘situation’, i.e. in the void. Following a lucid presentation of the central concepts of Badiou’s philosophy as they relate to the problem of novelty (mathematics as ontology, truth, the subject and the event), Gillespie identifies a significant problem in Badiou’s conception of the subject which he suggests can be answered by way of a supplementary framework derived from Lacan’s concept of anxiety. Gillespie’s intent to illuminate the relation of philosophy to the four truth procedures (art, love, science, politics) leads him to the polemical conclusion that, as a transformative rather than descriptive or reflective project, Badiou’s philosophy ultimately reclaims the power of the negative from the positivity and pure productiveness of Deleuze’s system, thereby freeing thought from the limits set by experience.

Aan deze beschrijving van de uitgever voeg ik gaarne toe het informatieve review van Andrew Ascherl in Umbr(a): A Journal of the Unconscious: Utopia (2008): 150-153. Dit jaartal was niet te vinden in books.google, waaruit ik dit review kon opdiepen, maar trof ik aan in zijn cv die Ascherl op academia.edu plaatste.

Er bestaat ook een review van het boek door Benjamin Noys: 'The Powers of the Negative: The Mathematics of Novelty’ in: Journal of the Circle for Lacanian Ideology Critique, Vol. 2 (2009), 102-108 [cf. academia.edu of ook op de site van het Journal, waar overigens foutief staat dat het van Benjamin Bishop zou zijn (maar die schreef het artikel vóór het review).

Voor ik aan het eind het tweede hoofdstuk van Sam Gillespie's The Mathematics of Novelty: Badiou's Minimalist Metaphysics binnenhaal, hier dus eerst het review ervan door Andrew Ascherl in UMBR(A) Utopia (2008):

 

The Mathematics of Novelty: Badiou Minimalist Metaphysics represents the culmination of Sam Gillespie's pathbreaking work on the philosophy of Alain Badiou. "One of the most gifted and promising philosophers of his generation." as Joan Copjec put it in her tribute to him in the 2004 issue of Umbr(a), Gillespie was largely responsible for introducing Badiou's writing to the English-speaking world through the 1996 issue of the journal, which he co-edited with Sigi Jöttkandt. This special issue was the first of any English-language journal devoted entirely to Badiou's work, and it included translations of four essays by Badiou as well as two introductory essays written by Gillespie himself. Since Gillespie's death, a number of books and essays about Badiou have been devoted to his memory. Among the friends and colleagues who commemorated him and his work in pioneering Badiou's Anglophone reception are Ray Brassier, Joan Copjec, Peter Hallward, Sigi Jöttkandt, and Alberto Toscano — scholars who. like Sam Gillespie himself, are some of Badlou's most astute and tireless critics, interpreters. and Interlocutors.

The primary concern of The Mathematics of Novelty is to investigate the connections between Badiou's theory of novelty and the notion of truth. That Is, what are the conditions under which the new can occur, and to what extent is truth enabled by such conditions? Gillesple's book opens with a sustained, albeit rudimentary, interrogation of the materialist approaches to the concept of novelty found in the philosophies of Badiou and Deleuze. lie does this, not in order to simply argue for the superiority of one philosophical system over another but rather to delimit a path on which one can question and qualify Badiou's theory of the new. He asks, firstly, to what extent is Badiou's ontology adequate to (1) the criteria of multiplicity and (2) the possible occurrence of an event and its subsequent truth procedure? Secondly, how does Badiou reinvigorate the category of truth from its classical strictures as unchanging and thus antithetical to novelty? Finally, how are the previously mentioned sets of problems related?

The subsequent chapters confront these questions clearly and carefully, presenting a rigorous exposition of the core of Badiou's ontology. Beginning with an analysis of the implications of the claim that set theory is ontology through Badiou's reading of Spinoza, Gillespie argues that the acknowledgement of the void — the nothingness outside of ontology which Spinoza foreclosed from his system — is the minimal condition under which thought can think being. Such an equation between thought and being is the crucial support for Badiou's meta-ontological assertion that set-theoretical mathematics is ontology. Moreover, Gillespie claims, because the void (the proper name of being) is the necessary precondition for thought itself, it is also the necessary precondition for thinking the multiplicity that exists in excess to what is presented in a situation. It is from the inconsistency of the void, Gillespie argues, that "subjective action re-decides the consistency of any situation," extending from “a local decision that an event has occurred" (40). Without such a thinking of being as multiplicity, one is left with "a philosophy that can only take recourse in a descriptive affirmation of what always already is" (42).

However, we should not infer from this that being is derived from thought. As Gillespie reminds us, for Badiou "being is not purely generated in and by thinking itself” (47). Rather, being is axiomatically posited from the initial point of departure of zero, the point from which mathematical thought formalizes and enables the thinking of being itself. But how is it that the positing of zero — strictly speaking, nothing — could enable thought? Gillespie provides three preliminary responses. Firstly, he contends that "the new" must not be conflated with mere change. This is concomitant with Badiou's assertion that, despite historical variation and the development and evolution that take place within science and the arts, that which is philosophically new is rare. The void provides for the minimal assertions of the power of thought to think the new through the axiom of the void itself ("the void exists"), the event (located on the edge of the void of the situation) as the encounter of thought with its own limits, and truth as the minimal immanence of thought to itself, free from any positive content. Secondly, Gillespie cautions that the void should not be considered a measurement of a state of affairs "but rather as the local site of a situation from which an event can be extracted" (68). The measurement of change is a representative function, and the void eludes any and all such representation, remaining distinctly indeterminate. Lastly, Gillespie explains, we must be able to think the possibility for the new in and through the concept of truth. Following Badiou, truth is that which occurs in a situation insofar as the situation itself is fundamentally transformed by whatever consequences issue from that truth. Furthermore, "truth is the proper activity of thought, above and beyond its ability to think being" (bid).

So then what can be said of truth as far as Badiou's ontology is concerned? At first glance, it is tempting to radically divide ontology from the category of truth, based on the perception of an absolute separation between the primary, titular categories of Being and Event: on the one hand, being, proper to ontology, is simply what is; the event, alternatively, is fundamentally undecidable from the perspective of ontology — it can only retroactively come to be through a subjective truth procedure. Gillespie maintains, however, that such an opposition is patently erroneous: “It is impossible to think the category of truth apart from the foundations that mathematical ontology provides [...] The challenge," Gillespie continues, is "to examine the extent to which the appearance of a truth is enabled through the mathematization of being" (72). Thinking through the relation between ontology and truth requires a renewed interrogation of truth as a philosophical category as well as an investigation of what foundations are necessary for such a conception of truth. Moreover, Gillespie contends it is only a sufficient understanding of Paul Cohen's generic set theory that will allow us to comprehend Badiou's category of truth. The Mathematics of Novelty is in large parte detailed and patient study of Badiou's ontology, and the chapter containing the outline of the connection between truth and ontology is certainly the most difficult of this slim volume. Overall, however, Gillespie's exegesis of the mathematical foundations of Badiou's ontology is one of the clearest and most approachable introductions to the meditations of Being and Event ever written — the heroic efforts of Peter Hallward and others notwithstanding. This is particularly true of the sections on the twin theories of the generic and forcing as well as Gillespie's discussion of the relation between the ontology of a situation and the truth that ruptures it.

As Gillespie argues, the necessary connection Badiou must make between ontology and truth "necessitates a subreption of the indiscernible, an imposition of an order to give consistency to what is fundamentally inconsistent" (95). That is, in order for Badiou to avoid a problematic tautology in his theory of the event it is necessary to posit a phenomenology of sorts that would account for what occurs when subjects recognize or are seized by events. Because the category of the event cannot be derived from Badiou's formal ontology, according to Gillespie one must look to an additional, phenomenological framework for an elucidation of the way in which events mobilize subjects to engage in truth procedures. Not surprisingly, Gillespie finds such a supplementary schema in Lacan's teachings on affect and on anxiety in particular. While the set theory of Cantor and Cohen provides the basis for Badiou's ontology, his theory of the event clearly derives from Lacanian psychoanalysis. As Gillespie puts it, °the event is neither a category of presentation nor representation [...) It is an unpresentation" (101). That is, presentation does not directly present the inconsistency of being but rather being in its material instantiation. Thus, the only direct presentation of inconsistency is an event, the eruption of the void into the situation. As clear as Badiou may make this point himself, Gillespie points out that for Badiou's philosophy to move "beyond the sterility of the system put forth in Being and Event” it must be supplemented by two operations that cannot be derived from set-theoretical ontology (ibid). Namely. one must be able to think the categories of being and truth in particular situations without resorting to subtraction. Equally necessary is a phenomenology of subjectivity that would unite particular situations to subjective action. For Gillespie, this comes, as mentioned above, in the form of an isomorphism between Lacan's conceptualization of the relation of the subject of psychoanalysis (the speaking subject) to its own real or indiscernible being and Badiou's theory of a subject seized by the incalculable of an event. In short, Gillespie argues that subjective fidelity toward a particular truth Is propelled by a form of what Lacan theorized as the drive. More specifically, for Lacan the confrontation of the subject with the nothing that is the subject's own being — anxiety, the lack of lack — is the catalyst for subjective action. As Gillespie explains, "a person is compelled to go into analysis less on the basis of a compulsive need or desire for something...as because of an underlying anxiety that makes life unbearable" (119). The process of analysis is thus a way for that subject to give form to the indiscernible being in which such anxiety is rooted, namely jouissance, or that part of it that supports subjective activity: object a. Object a is the correlate of Badiou's event Insofar as both provide a minimal basis for the subject's confrontation with being. While the operation of forcing causes the subjective excess of indeterminate being (the event) to pass from a strictly subjective principle into a universal truth and thus is what distinguishes Badiou's subject from Lacan's subject, Gillespie reminds us that forcing is not possible without the activity of a militant subject whose framework is provided by Lacan through the category of affect, specifically anxiety.

After explicating the central categories of Badiou 's philosophy (being, truth, the event, and the subject), Gillespie confronts the questions of what, in the end, philosophy is for Badiou. That is, what is philosophy capable of? Set theory, from Cantor to Zermelo and Fraenkel, is a scientific innovation that reinvigorates the classical philosophical category of ontology in such a way that it allows philosophy to reflect on and think the compossibifity between the novelties produced in science, art, politics, and love that issues from a shared basis in a common ontology. Badiou's mathematical ontology changes the question “What is thought?" from a determination of thought as substance to a conception of thought as capacity. Gillespie shows that, in opposition to a descriptive affirmation of the world in which, for example, Deleuze's thought places novelty, Badiou's philosophy situates the new in complete exteriorly to the situation (or world) — that is, in the void. “Philosophy is not a description of truth procedures that have occurred, but rather a call to action for truth procedures to occur. Whether or not there has ever been a true event" of novelty, Gillespie argues, "is therefore beside the point: it is simply enough to know that there can be events insofar as we are capable of thinking nothing" (148). It is in this radical separation of itself from the world that "philosophy becomes an imperative to try out through militant activity" (ibid.). The Mathematics of Novelty is in the end an exercise in such philosophical activity, both militant and elegant, at once a clarification and a transformation of Badiou's thought. Gillespie's loss to philosophy is indeed, as Joan Copjec has said, incalculable, and this loss is truly underscored by the brilliance of this long-awaited book.

— Andrew Ascherl

 

Sam Gillespie's The Mathematics of Novelty: Badiou's Minimalist Metaphysics  bevat, zoals ik al zei en ook uit deze bespreking blijkt, een sterk 2^e hoofdstuk over – vooral - Badiou’s Spinoza dat ik via books.google, waar het ook volledig te lezen is, hier binnenhaal: