Pascal: mathematics, miracles and ‘infinite thought’

Here Badiou follows his usual practice of developing some cen-tral philosophic themes – event, situation, inclusion, belonging, intervention and the supernumerary – while also devoting some

detailed analytic commentary to an earlier thinker whose work may be shown to have prefigured certain aspects of his own. In this case the figure concerned is Blaise Pascal, the seventeenth-century mathematician, moralist, theologian, aphorist and spec-ulative thinker whose extraordinary range of interests has created considerable problems for – and divisions among – his commen-tators.¹ That he figures so importantly in Being and Event is a striking example of the way that Badiou is able to discover revealing affinities or terms for comparison even in thinkers with whom one would expect him to be sharply at odds on ethical, political, philosophic and (not least) religious grounds.

In this context it is worth recalling the distinction Badiou draws between, on the one hand, latter-day ‘sophists’ such as Wittgenstein and Richard Rorty whose attitude to philosophy is mainly one of indifference, rejection or a wish to have done with such pointless concerns and, on the other, ‘anti-philoso-phers’ who brace themselves against the philosophic challenge and against whom philosophy is likewise compelled to test its own claims as a putative discourse of reason and truth.² Badiou makes the point by contrasting Descartes and Pascal, the one a thinker for whom (purportedly at least) everything proceeded from the application of rational methods and deci-sion-procedures, the other a believer for whom his own achieve-ments in mathematics, logic and natural science were as nothing compared with the leap of faith – the supposed aban-donment of all such rational criteria – that opened the way to authentic religious belief.³ His intention is not for one moment to endorse Pascal’s doctrinal stance or the claim that reason should know its proper limits and thereby make room for that existential foray into the realm of supra-rational paradox and inward, revealed or spiritual truth. Rather it is to emphasize his point with regard to an age-old, conflictual yet productive relationship – that between reason and faith – which finds one of its most striking expressions in St. Paul’s (albeit for the most part mutually baffling) exchanges with the Greek philos-ophers and which has since then re-surfaced in manifold forms wherever there is a question of reason encountering some real or presumptive limit to its proper scope.⁴ Thus the ‘anti-phi-losopher’ – unlike the sophist – is perpetually engaged in a pro-cess of essaying that limit, provoking the philosopher who will

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typically resist any such claim, but also – most importantly as Badiou sees it – showing how the powers of reason may them-selves be refined and extended precisely through the challenge from a sharply opposed though at times strangely intimate quarter.

Indeed this conflict may sometimes exist within the work of a single thinker, as for instance with Cantor, who (as we have seen) continued to hold out for a ‘virtual’ conception of the infinite that would render it compatible with Christian belief – insofar as it surpassed the finite character of human intellectual or cal-culative grasp – even while he was laying the foundations for a thoroughly secularized transfinite conception that would render the existence of God an otiose hypothesis.⁵ What Badiou finds exemplary about Pascal is not so much the doctrinal content of his Christian faith but rather his having staked everything on that hypothesis as one that could be verified only through some future, as yet inconceivable event that would retroactively confer a determinate truth-value on those hitherto strictly undecidable conjectures. And so we come back to the question posed at the end of my last chapter: what is it that marks out the genuine event as a singular and – in its own time and place – unclassifi-able occurrence which none the less exerts (or is capunclassifi-able of exert-ing) a likewise singular demand for allegiance among those who are responsive to it? Badiou cites Lacan’s cryptic remark to the effect that ‘if no religion were true, Christianity, nevertheless, was the religion that came closest to the question of truth’ (p. 212).

He goes on to gloss this saying very much in his own terms, and in a way that shows why Pascal figures so importantly here. Thus,

‘in Christianity and in it alone it is said that the essence of truth supposes the evental ultra-one, and that relating to truth is not a matter of contemplation – or immobile knowledge – but of intervention’ (p. 212).

Of course there is a risk of serious misunderstanding at this point, given Badiou’s clear attraction to just those elements in Pascal’s thought that will probably strike a non-believer as most open to question on moral as well as on philosophic grounds.

Thus it might seem that he is adopting something like the doc-trine of ‘eschatological verificationism’ advanced by some theo-logians as a counter to the logical-positivist claim that the only meaningful statements were those that were either verifiable/

falsifiable through methods of empirical (e.g. scientific) testing or else self-evidently true (hence tautologous and empirically vacuous) in virtue of their logical form.⁶ To this the theologians sometimes respond that the postulates of Christian faith are such as will eventually be verified or falsified although under evidential conditions that at present cannot be clearly envisaged or specified with great accuracy.⁷ However there is all the dif-ference in the world – so to speak – between, on the one hand, a realist ontology (Badiou’s) that locates the truth-makers for truth-apt but as-yet unverified conjectures or hypotheses in a realm of future discovery that is strictly intra-mundane even if it extends to abstract entities such as numbers, sets and classes and, on the other, a theological position that goes so far beyond anything that counts (on empirically or logically adequate grounds) as proof, knowledge or evidence. That is to say, there is nothing in the least eschatological about Badiou’s conception of truth – be it in mathematics, the natural sciences or politics – as requiring an attitude of future-oriented openness to that which may always turn out to have surpassed our best current means of proof or ascertainment. On the contrary, what distinguishes the genuine (epochal) event from the run of more-or-less significant occurrences or happenings is the fact of its standing in a certain retroactively transformative relationship to previous episodes by which it was obscurely pre-figured, and also – as follows nec-essarily from this – in a proleptic relationship to later events whereby its truth-content will be further revealed or progres-sively unfolded. For that content has everything to do with real developments, whether of a natural-scientific, socio-political, or formal-conceptual kind, and nothing whatsoever to do with hypotheses that by their very nature – pace the above-mentioned theologians – lie beyond the utmost reach of verification.

It is important to be clear about this since it bears on one objection that is sometimes raised to Badiou’s closely related ideas of the event as that which disrupts any given situation and of the subject as existing – indeed as quite literally brought into being – through his or her ‘militant’ fidelity to the event. Again there is a risk, not least on account of his taking St. Paul as an exemplary character in this regard, that Badiou will be interpreted as some kind of crypto-theological or (perhaps more to the point) crypto-Kierkegaardian thinker whose professions of religious

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unbelief are not to be taken at face value.⁸ Thus he might be understood as endorsing something very like Pascal’s famous wager, that is, his purported proof on probabilistic grounds that we had better place our faith in an omniscient, omnipotent and omni-benevolent deity since even if the chances of his actually existing are close to zero still we are better off believing in him than not since the prospect of eternal salvation is infinitely bet-ter than the prospect of ebet-ternal damnation.⁹ It strikes me that nobody who has read very far into Badiou’s work could suppose him to have any sympathy with this line of argument, at least as regards its moral, religious and (not least) its socio-political implications. After all, it goes clean against two main precepts of Badiou’s work, namely his commitment to a thoroughly secular-ized, materialist ontology – one that most emphatically leaves no room for the Christian God or any other deity – and also his insistence on the absolute necessity of thinking things through with the maximum degree of conceptual and logical rigour.

From this point of view he would doubtless be in sympathy with atheists-on-principle like Mill and Russell who have offered the best, intellectually and morally most decisive answer to Pascal:

that there is a plain obligation not to acquiesce in any holy para-dox that requires belief in an executive god whose supposed attributes (as listed above) cannot be reconciled one with another or jointly with the facts of human experience.¹⁰ On the other hand Badiou is enough of a ‘continental’ rationalist to judge that there is much to be learned from a thinker like Pascal if one takes due stock of his great mathematical advances and translates his other (theological) statements into ethico-political terms.¹¹ What then emerges is a way of conceiving Christianity as some-thing like a figural or even allegorical substitute for that which could not be expressed more directly owing to the pressures of doctrinal adherence or social-political prudence. Thus, in Pascal’s conception, ‘[a]ll the parameters of the doctrine of the event are disposed within Christianity: amidst, however, the remains of an ontology of presence – with respect to which I have shown, in particular, that it diminishes the concept of infinity’ (BE, p. 212).

This latter qualification is crucial since it sets Badiou’s argument firmly apart from any strain of theological thought, however

‘negative’, that would conserve some remnant of divine being beyond all the multiplied denials that God could ever be defined

or conceptualized in humanly available terms. It also serves to make his point, once again, that the operative concept of infinity that entered the discourse of mathematics with Cantor had noth-ing in common with that earlier ‘romantic’, mystical, religious and (purportedly) supra-rational idea of infinity that still left its mark on Cantor’s more backward-looking pronouncements.¹² Where Pascal stands apart from that strain of thought – despite his seeming dedication to it as a matter of overt faith – is in vir-tue of his having pressed further than anyone up to that time in striving to think the paradoxical relationship between the exer-cise of reason conceived as subject to the limits of human under-standing and the requirements of faith conceived as inherently surpassing or transcending those limits.

Thus, on Badiou’s account, the rational content of Pascal’s avowedly anti-rationalist (Christian-fideist) thought is the idea that any decisive advance toward truth will be ‘decisive’ not only in the sense that it marks a clear stage of progress in the growth of human knowledge but also in the sense that it bears witness to a choice and thereafter to a deep-laid intellectual and/or ethi-cal commitment on the part of its early advocates and subse-quent upholders. This is why Badiou finds something altogether exemplary in Pascal’s famous ‘leap of faith’, that is, his convic-tion that ‘the heart had reasons of which reason knew nothing’, or that logic was a poor thing in comparison to the promise of redemption – no matter how groundless in rational or probabi-listic terms – held out by Christian belief. Such was Pascal’s motive in declaring the futility of all endeavours to prove the existence or define the attributes of God through scholastic, logic-based, metaphysical or onto-theological modes of thought.

For it was only through faith – and moreover through faith in the occurrence of miracles as that which stretched rational cre-dence to the limit and beyond – that Christian belief could pos-sibly be justified, witnessed or defended against the encroachments of a new mathematico-natural-scientific rationality to which, ironically, Pascal himself was a leading contributor. So if his thought still retains its ‘disconcerting’ or ‘provocative’ power even today then it has to do with the vexing question of ‘why does this open-minded scientist, this entirely modern mind, abso-lutely insist upon justifying Christianity by what would appear to be its weakest point for post-Galilean rationality, that is, the

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doctrine of miracles?’ (p. 215). Moreover, what ‘madness’ – or perverse desire to maximize the odds against his own persuasive success – could have led Pascal to make faith in miracles the basis of his efforts to convert a fictive partner in dialogue, a self-professed ‘libertine’ and materialist disciple of Epicurus, Lucre-tius and Gassendi, to embrace the truths of revealed religion?

Badiou’s answer is quite straightforward: that ‘miracle’ for Pascal, like ‘chance’ for Mallarmé, is the name of whatever tran-scends or eludes definition according to the norms of some exist-ing situation, state of knowledge, conceptual scheme or received ontological framework. In this sense it is ‘the emblem of the pure event as resource of truth’, one whose very character is always ‘to be in excess of proof’ and which therefore serves – to Pascal’s fideist way of thinking – as a failsafe guarantee of God’s

‘not being reducible to this pure object of knowledge with which the deist satisfies himself’ (p. 216). However, once again, it would be wrong to conclude either that Badiou’s reading of Pascal itself has certain fideist or crypto-theological undertones, or indeed that Pascal’s treatment of these issues – the radical dis-junction he proposes between reason and faith, or mere ‘correct-ness’ and truth – is capable of valid interpretation solely on its self-avowed, Christian-theological terms. For it is Badiou’s main purpose in this section to demonstrate that, on the contrary, Pascal’s professed aim of subjugating reason to the claims of faith is placed in doubt – despite and against his intent – by a precocious grasp of certain mathematical truths that went far beyond what had yet been discovered, proved or even conjec-tured at the time. If his thoughts about the infinite are known to most people mainly through his famous confession of terror when confronting the ‘eternal silence of the infinite spaces’, it is not so much this aspect of existential dread that Badiou has in mind but rather Pascal’s having been the first thinker to explore what might be the consequences (mathematical and scientific as well as theological) of adopting a perspective whereby the finite became a special case or limiting instance of the infinite, rather than the other way around. ‘In a spectacular reversal of the ori-entation of antiquity, he clearly states that it is the finite which results – an imaginary cut-out in which man reassures himself – and that it is the infinite which structures presentation’ (p. 220).

And again, ‘Pascal thus simultaneously thinks natural infinity,

the “unfixable” relativity of the finite, and the multiple-hierar-chy of orders of infinity’ (p. 220).

This he achieves, moreover, through a mode of thought that combines the utmost degree of formal and conceptual precision with a willingness – indeed, a religiously motivated compulsion – to pursue the antinomies of speculative reason (those inherent liabilities of human thought that Kant would later place under strict rules of confinement) to the point where they acquire an altogether new creative-productive power.¹³ That is to say, the rigour of his thinking about issues of mathematics and logic should not be conceived as opposed to, incompatible with or compromised by his insistence on the prior claim of faith over reason. Rather it depends crucially on that claim – on the idea that truth might always transcend the utmost capacities of pres-ent-best knowledge, proof or ascertainment – in order to conceive how such formal procedures can sometimes produce decisive advances and, more rarely, full-scale revolutions in thought. This in turn has to do with what Badiou defines as the axiological dimension of Pascal’s project, that is, his ‘formal doctrine of inter-vention’ whereby the event – whether Christ’s birth and death, a revolution in moral or political thought, a mathematical or sci-entific breakthrough or even a subjectively life-transformative episode – acquires the kind of paradigmatic force that thereafter compels the choice between fidelity and rejection. Thus ‘beyond Christianity, what is at stake here is the militant apparatus of truth: the assurance that it is in the interpretative intervention that it finds its support, that its origin is found in the event; and the will to draw out its dialectic and to propose to humans that they consecrate the best of themselves to the essential’ (p. 222).

Here again it needs stressing – as against the objection that is likely to be raised by analytic philosophers – that Badiou’s use of a voluntarist language (‘assurance’, ‘will’, ‘consecrate the best of themselves’) is not just an instance of gross confusion between

‘context of discovery’ and ‘context of justification’.¹⁴ This would be the error – currently widespread among constructivists’, descriptivists, cultural relativists and ‘strong’ sociologists of knowledge – which in effect makes a full-scale programme of refusing to distinguish whatever belongs to the subjective sphere of motivational psychology and whatever pertains to the norma-tive dimension wherein scientific and other truth-claims are held

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accountable to the strictest standards of rational accountability.¹⁵ Instead it is a question of acknowledging how difficult it is to disentangle the distinct yet closely imbricated concepts of truth-fulness and truth, or how the latter becomes void of substantive (genuinely rational) content if decoupled from any reconstruc-tive account of the processes of thought by which those who have pursued various kinds of truth have typically set about bringing them to light and defending them against sceptical attack.¹⁶ This is another way of saying that Badiou is one of the few philosophers not merely to face both ways across the analytic/

continental divide as need or inclination dictate but rather to situate his thinking on alternative ground beyond that stereo-typical binary conception. Such, to repeat, is the central thesis of Being and Event: that while a mathematically informed (i.e. set-theoretically based) ontology offers the closest approach to truth within some existing, currently most advanced state of know-ledge still there is always an appeal open to speculative claims whose truth-content can be fixed – or whose truth-value can be borne out – only through the work of thinkers or ‘militants’

committed to just that presently unfinished task.

committed to just that presently unfinished task.