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Frederiek Depoortere

Badiou and Theology

Frederiek Depoortere,Badiou and Theology, Continuum, 2009, 158pp., $2.95 !p"k#, %B&9'805('0)2(21.

*e+ieed "y Clayton Cro-kett, ni+er/ity o Central rkan/a/

Despite Badiou's professed atheism, there are a number of ways that his philosophy can berelated to theology. The value of Depoortere's book is that it is not simply a survey but aconstructive engagement with Badiou's thought, centered on his set-theoretic ontology. Thisvalue, however, is also a limitation, because Depoortere's overall engagement is somewhatidiosyncratic and incoherent, as I will discuss below. fter an introduction that provides helpfulconte!t for reading Badiou in terms of "hristian theology, the rest of the book consists of threefascinating but uneven chapters. The body of the book represents an attempt to articulate, #ustifyand defend a proof of $od's e!istence in both traditional Thomistic and modern set-theoreticalterms, over against Badiou's atheistic interpretation of set-theoretic ontology.

In the introduction, Depoortere defines modernity as %a passion for the new% that has beencompromised by the failure of political utopian pro#ects &(. "hristianity, particularly as seenthrough contemporary accounts of )aul by *i+ek, Badiou and others, offers %the prospect of anew kind of revolutionary sub#ect% &(. Badiou's thought is important because it %offers us cluesfor 'saving' the &"hristian( passion for the new in our post-revolutionary age% &(. But this

passion for the new and this renewed "hristian sub#ectivity are drawn up into a new proof for thee!istence of $od that takes place in very traditional terms. Depoortere argues that the way fortheology to take seriously Badiou's philosophy is to e!plore its usefulness for clarifying ourconcept of $od, %which no longer has any clearly circumscribed meaning,% so he defaults to the%historical consensus of classical theism% &-/(.

Badiou claims in his book Saint Paulthat )aul gives us a new form of universal sub#ectivity, andthis takes the form of an event. Badiou's master-work,Being and Event, develops a mathematicalontology of being 0ua being in order to articulate how an event subtracts from being in a waythat cannot be strictly formali1ed. If the event is what offers the promise for a revolutionarysub#ectivity, why doesBadiou and Theologyignore the event in favor of a sustained e!position

of Badiou's set-theoretic ontology2 Depoortere intervenes into and upon Badiou's ontology inorder to shift the terms of the debate from a decision for atheism to a decision for theism, andthis is a striking and significant intervention. But the idea of the event completely drops out ofthe purview of Depoortere's discussion, which is also significant. The ma#ority of this bookconsists of a constructive philosophical-theological-analytic pro#ect3 what is newis adopting theperspective of set-theoretic ontology to update ristotelian and Thomistic arguments for $od'sessence and e!istence. 4et theory as elaborated by "antor replaces ristotelianism in supplying aphilosophical ontology to ground a neo-Thomistic theology. This constructive pro#ect is also

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problematic, however, because it still relies on fundamentally ristotelian oppositions, mainlythat of actual vs. potential, and because it ultimately depends on a leap of faith from thepossibility of $od as absolutely infinite to the actuality of this absolute infinite's e!istence.

Before e!plaining what is at stake in Depoortere's intervention, and why I think it is ultimately

incoherent, I will briefly survey the three chapters that follow the introduction. "hapter , %5aithand the 6!istence of $od,% lays out definitions and %terminological clarifications% thatpredetermine the encounter with Badiou's work. Depoortere argues, against many modernhumanist understandings, that faith has a supernatural origin and depends on the e!istence of$od to be faith. Depoortere relies strongly on the Summa Theologiaeof 0uinas, the statementof 7atican I onDei Filius, and contemporary 8oman "atholic theologians such as very Dullesfor this conclusion. Depoortere wants to resist the possibility of any faith that does not re0uirebelief in the e!istence of a traditional theistic $od, and here he agrees with Badiou3 %I want toside with Badiou and hold on to a strong understanding of both religion and faith, anunderstanding which implies that neither can be trueif $od does not e!ist% &9(. Badiou claimsthat $od does not e!ist, and therefore religion and faith are impossible. Depoortere takes this

challenge seriously, sharpening the edge of the either:or, but he offers an alternative argumentthat $od does e!ist. Depoortere understands the hermeneutical nature of faith, but he says thatthis circle is a closed circle, and %the only way to escape from this closed circle is to prove thee!istence of $od withoutpresupposing faith% &;(. This attempt to prove the e!istence of $od bymeans of set theory without presupposing sub#ective faith is the implicit thesis of the book, andthe payoff of theology's encounter with Badiou.

"hapter , %Badiou on Being,% carefully and clearly lays out the mathematical basis of set theorythat informs Badiou'sBeing and Event. This chapter is e!tremely valuable, because manythinkers concerned with themes of religion and theology avoid the intimidating mathematicalformali1ation that predominates in Badiou's masterwork. Depoortere gives us an impressive,

sensitive and difficult reading of set theory in general, and Badiou's mathematical ontology inparticular.

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In order to 'save' $od, Depoortere reverts back to "antor's original presentation of set theory, andhis development of the idea of transfinite numbers. "antor relies on the idea of %well-orderedsets% to suggest that we can count numbers higher than infinity, such as infinity plus one, infinityplus two, etc. &;/(. The mathematical manipulation of numbers greater than infinity, ortransfinite numbers, involves an understanding of numbers as ordinal &ordering, consecutive(

rather than as cardinal &that is, as representing some ob#ective real measurement(. Then the0uestion arises about the real status of these transfinite numbers3 are they actual infinities or #ustpossible infinities2 Do they point toward and are they limited by an absolute infinity, or are they#ust endless2 "antor accepts the a!iom of infinity, which %declares that a limit ordinal e!ists,% orthat such transfinite numbers themselves eventually come to an end &;;(. Badiou, on the otherhand, re#ects both the a!iom of infinity and the continuum hypothesis that is often associatedwith it. The continuum hypothesis suggests that numbers are really related in a well-orderedhierarchy, but this hypothesis cannot be proven true or false within the conte!t of the standard>ermelo-5raenken a!iomatici1ation of set theory. 4o this fundamental undecidability provokes adecision3 from Badiou, for the void and against the one as absolute infinity? from "antor, for theabsolutely infinite as actually e!isting, which according to Depoortere means the mathematical

form of a theological re-instantiation of $od.The final chapter, %Theological 6valuation of Badiou's @ntology,% draws out this distinctionbetween "antor and Badiou and provides a perspective from which to make such a decisionconcerning the actually e!isting infinite. 5or "antor, inconsistent multiplicity

comes at the end, so to speak, at the limitof his mathematical endeavors. There, wherethe count-as-one fails, one bumps into the absolute. 5or Badiou, in contrast, inconsistencyis primary? it is %the nothing that precedes the count-as-one &=(.

Inconsistent multiplicity in mathematical terms means the limit of our understanding, for "antor.

"antor decides for $od as the limit of this inconsistent multiplicity based on his assumption thatthere can be no potential absolutely infinite without it being actual. Badiou cuts off thisassumption by beginning with inconsistent multiplicity and claiming that there is no limit.ccording to Depoortere, there is no mathematical solution to this dispute. Aathematics canthink a potentially e!isting absolute infinity, but %there is no place for an actually e!istingabsolute in mathematics% &;(. Depoortere is correct to point out that Badiou's claim that settheory necessarily e!cludes the absolute infinite goes too far? it is an interpretation or decision bywhich Badiou opts for the void as opposed to the absolute infinite. 5urthermore, Depoorterediscusses an essay by enneth 8eynhout, which argues that one can read Badiou's theory of thevoid in terms of negative theology, where the null set is the sign of Badiou's %hidden $od.%But this negative theological understanding of set theory and Badiou is not sufficient forDepoortere's aims. Depoortere concludes the book with a very condensed argument for atraditional $od understood in set theoretical terms as absolutely infinite by referring to a book by8udy 8ucker,Infinity and the Mind. 8ucker suggests, by means of the %reflection principle,% thatthere is a positive connection between transfinite numbers and the absolute infinite. Thisconnection provides Depoortere an opening to declare that we can preserve the traditionalknowability and unknowability of $od in modern mathematical terms, and therefore %it remainspossible to break out of the closed circle of faith presupposing faith% &9(.

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There are at least two problems with Depoortere's conclusion. Ce is too smart not to 0ualify thesituation of set theory about the infinite and he stresses its indeterminacy. The fact that Badiouopts for the void and for atheism means that it is possible to go back and follow "antor'spreference for $od as actually e!isting infinite. The fact that this situation forces a decision,however, is not only problematic in terms of Badiou's ontology? it means that Depoortere is

forced back into the closed circle that he was hoping to avoid by offering a proof of $od'se!istence. The decision for $od is at the same time a faithful&l( decision, which means that thereis no way out of the hermeneutical circle, at least in terms of how Depoortere constructs it in hisbook. 4econd, Depoortere relies strongly on the Thomistic and ultimately ristotelian distinctionbetween actual and potential to decide for $od, whereas this traditional opposition may not makeas much sense in terms of modern set theory or contemporary philosophy and theology. Themost Depoortere is able to gain from his "antorian mathematical set theory is thepossibilityofan absolute infinite. Ce then falls back on ristotle and 0uinas, as very briefly presentedthrough 8ucker, to argue that the possibility of an absolute infinite implies an actual absoluteinfinite, and to suggest that the e!istence of transfinite numbers gives us positive knowledge ofthis actual infinite. But it is clearly a leap of faith to presume that the absolute infinite is reflected

in transfinite numbers. 5inally, Depoortere is forced to e0uivocate in terms of this possibility ofan absolute infinite, because he needs the absolute infinite to be possible in order to counterBadiou's atheism, but he needs to overcome the limit of this possibility in order to achieve hispurpose, which is to prove the actual e!istence of $od, which is the only way to avoid the closedcircle of faith.

The fact that this book is flawed and cannot achieve what it sets out to do does not diminish itsvalue as a work of theological engagement and theoretical reflection. It does not e!haust thepossible or actual relations between theology and Badiou's philosophy, but it is a serious andprovocative encounter that is worth much more than the countless surveys and superficialappropriations that generally constitute the genre.