Plenum and void: why Aristotle hated a vacuum

It is at this stage in the unfolding of his argument that Badiou turns to Aristotle as one of those thinkers with whom he is pro-foundly at odds in relation to some basic metaphysical and onto-logical commitments but whose thinking he typically treats as a challenge to be met so far as possible on shared argumentative ground rather than dismissed out of hand. The main point at issue is Aristotle’s denial that there could possibly exist any such thing as a void or vacuum in nature.²⁰ This was a doctrine – on essentially metaphysical grounds – that continued to enjoy the

authority of something like holy writ throughout the medieval and renaissance periods in European thought, and which began to lose ground only with the rise of early modern science and its rejection of scholastic dogma in favour of experimental methods that involved (in this case) the construction of increasingly effec-tive vacuum pumps. In recent years this received view has itself been subject to challenge from ‘strong’ sociologists of knowledge who reject the idea of scientific progress as a piece of self-serving mythology and who view the issue of experimental physics versus Aristotelian doctrine – or (in the classic encounter of this kind) of the seventeenth-century physicist Robert Boyle versus the philosopher Thomas Hobbes – as a case of two conflicting ideo-logies, rather than a conflict between scientific method and a legacy of outworn metaphysical baggage.²¹ Badiou’s aim is not so much to adjudicate in this quarrel (which has surely been set-tled on physical-scientific terms) but to shift the whole ground of debate and define what precisely Aristotle meant when he wrote of the non-existence of the void as a matter of metaphysi-cally ordained or a priori demonstrable truth. ‘For the Greek’, Badiou writes, ‘the void is not an experimental difference but rather an ontological category, a supposition relative to what naturally proliferates as figures of being’ (p. 71). That is to say, no merely ‘artificial’ creation of a void, such as Boyle was much later to achieve – albeit, on his own admission, to a very imper-fect or partial degree owing to the drastic limitations of available technology – could possibly count as refuting the Aristotelian doctrine, based as that doctrine was on a quite different order of purely ex hypothesi speculative reasoning that brooked no such empirical counter-evidence.

Badiou’s point here is not, of course, to uphold Aristotle’s claim against the massive, strictly unignorable weight of accu-mulated physical-scientific evidence nor indeed – as should be obvious by now – to defend it as a matter of prior metaphysical or ontological commitment. After all, nothing could be further from Badiou’s absolute and principled insistence on the essen-tially subtractive nature of ontology – the primacy of that which eludes specification in positive (‘presentifying’) terms – than the Aristotelian doctrine that ‘nature abhors a vacuum’, or that talk of the void must involve either scientific absurdity or logical self-contradiction. However this is to commit something like a

READING THE TEXT

basic category-mistake since, in Aristotle’s thinking as Badiou understands it, ‘the artificial [i.e. experimental] production of a void is not an adequate response to the question of whether nature allows, according to its own opening forth, “a place where nothing is” to occur, because such is the Aristotelian definition of the void’ (p. 71). He is drawing quite explicitly on Heidegger’s reading of Aristotle here, and this is indeed – so far as I recall – the most markedly Heideggerian passage of commentary anywhere in Badiou’s work. All the same it is not so purely echt-Heideggerian as to conjure a depth-hermeneutic realm of metaphysically unencumbered Being that would constitute both the primordial, long-forgotten source and the concealed ontological ground of all those merely ontical beings that science has taken for its object-domain. On the contrary, what most engages Badiou’s interest is Aristotle’s axiomatic mode of reasoning from first prin-ciples which, although sharply opposed to his own, can none the less be seen to have certain implications that are strikingly germane to much of what Badiou has to say on his three main topics of the void, infinity and the event.

Thus if Aristotle’s theses have not been refuted on their own metaphysical ground by subsequent advances in physical-scientific understanding then this is not because, as Heidegger would have it, the physical sciences (like philosophy) have long been mort-gaged to a technocratic will-to-power and an epochal oblivion of Being but rather because Aristotle’s reasoning places him in the company of those – Badiou included – ‘for whom the void is in truth the name of being, and so can neither be cast into doubt nor established via the effects of an experiment’ (p. 72). That is, any refutation of Aristotle’s doctrine at the level of ontological enquiry here in question – as distinct from the physical-scientific level where its claims can no longer stand up – will have to go by way of a critical engagement with the underlying logic or onto-logic of Aristotelian physics. It will therefore not be required to take sides on the kind of issue nowadays engaged between real-ists who suppose Boyle to have got it right – or at least to have been very much on the right scientific track – in asserting the pos-sibility of a vacuum and those on the opposite (strong-sociological or cultural-constructivist) wing who consider Boyle’s claim and Hobbes’s denial of it to be strictly on a par as regards their truth-content since each was the product of a certain ideological or

socio-cultural mindset. For the record, one can state with a fair degree of assurance that Badiou would lean strongly in the for-mer (scientific-realist and rationalist) direction. However, this is not – or not primarily – where his interests lie. Rather he seeks to demonstrate that Aristotle’s staunch, metaphysically grounded opposition to any idea of the void as existing in nature or as having any legitimate place in the conceptual apparatus of the various physical or human sciences was in fact the result of his perceiving very clearly where such thinking led and the kinds of paradox to which it would surely give rise.

Thus in Aristotle’s case it is a consequence of his basic prem-ise that to entertain a notion of the void as anything other than a sheer impossibility or affront to rational thought is ipso facto to invite all the massive conceptual, metaphysical and ontolo-gical problems that come in its train. Chief among them are the problems of spatio-temporal indifference (since the void admits of no distinctions in this regard), un-measure (since it likewise prevents any meaningful comparison between different dimen-sions, velocities, or other such quantitative attributes), and above all infinity (by reason of its forcing thought to confront that intrinsically disturbing since – for Aristotle and even for Cantor – inherently excessive or paradox-inducing idea). This is why, as Badiou cautions, we should not be ‘led astray’ by physics ‘in the modern sense’, that is, by the otherwise spectacular self-evidence of past and presently continuing progress in the physical sciences.

What Aristotle is asking us to think is something quite different:

namely, that ‘every reference to the void produces an excess over the count-as-one, an irruption of inconsistency, which propa-gates – metaphysically – within the situation at infinite speed’

(p. 75). In which case – he concludes – ‘the void is incompatible with the slow order in which every situation re-ensures, in their place, the multiples that it presents’. It can only be conceived in terms of a potentially subversive or destabilizing threat to the entire onto-metaphysico-epistemological structure of thought that constitutes Aristotelian philosophy in its various specific regions of enquiry. When Aristotle says that ‘the void bears no ratio to the full, such that neither does movement [in the void]’, or again that ‘there is no ratio in which the void is exceeded by bodies, just as there is no ratio between the nothing and num-ber’, Badiou would scarcely take issue with the content of these

READING THE TEXT

statements – bearing out as they do his own central theses with regard to the subtractive nature of ontology – but only with Aristotle’s belief that they constitute a case by reductio ad absur-dum against the possibility of a void.

Thus he fully endorses the reasoning behind this Aristotelian doctrine – ‘to my mind, the ensemble of these remarks is entirely coherent’ (p. 74) – but takes it to demonstrate just the opposite of Aristotle’s intended point, namely that the impossibility in question is that of adequately conceiving the void in terms of a

‘presentifying’ metaphysics and ontology, rather than a concep-tual impossibility tout court. That we can grasp this distinction now where Aristotle couldn’t, despite being carried so far towards it by the rigour and consistency of his own logic, is mainly the result of our coming at the issue from a standpoint informed by set-theoretical concepts and techniques, above all with regard to infinity and transfinite mathematics. Moreover it enables us to read the works of earlier thinkers – among them (most impor-tantly for Badiou) Plato, Aristotle, Leibniz, Spinoza, Rousseau, Hegel and Heidegger – in such a way as to locate the various symptomatic tensions, conflicts and blind-spots of unexamined presupposition that mark their discourse where it touches on themes that involve some dealing with those problematic topoi and is thus forced up against its own conceptual limits.

I should make it clear – lest anything I have said give rise to the contrary impression – that Badiou is as far as possible from implying that his approach to these thinkers could fairly be described as a ‘psychoanalysis of philosophy’. Indeed it is one of his leading claims that philosophy should know its proper place not only in the sense of accepting a strictly ancillary role vis-à-vis the ground-breaking ontological work of mathematics but also in the more positive sense of maintaining its crucial measure of autonomy vis-à-vis those various enabling ‘conditions’ which might otherwise compromise its critical independence or intel-lectual integrity. All the same, as will emerge more explicitly in Part VIII of Being and Event when he turns to Freudian–Lacanian themes, Badiou’s practice of symptomatic reading is one that has much in common with the kinds of critical-philosophic dis-course that resulted from the structuralist-inspired rapproche-ment between Marxism and psychoanalysis from the mid-1960s on. That rapprochement came about very largely through the

intensive theoretical labours of Louis Althusser, and it is thus worth noting that Badiou – despite his express opposition to the linguistic turn in its structuralist as well as its Wittgensteinian and other forms – is among the very few major present-day think-ers who have retained at least a qualified allegiance to the Althus-serian project.²² Indeed this is one striking example of what Badiou means by the fidelity to certain truth-procedures (whether in mathematics, science, politics or art) where the upshot – the prospect of their being carried through to a successful conclu-sion – may be highly uncertain, even subject at times to severe or calamitous setbacks, yet where the stakes are sufficiently high to warrant that kind of long-term commitment. This is why he is so drawn to thinkers, like St. Paul and Pascal, with whom he would appear to have little in common politically, ethically or philosophically. What they share is the distinctive coupling of a well-nigh existentialist conception of truth as a matter of authen-tic individual dedication to the project in hand with a strongly universalist claim to the effect that, should the project at last be vindicated, then its truth or validity conditions will apply across every kind of social, cultural, political, ethnic or other such restrictive boundary.

This conjunction of seemingly opposite doctrines will appear less strained or downright contradictory if one reflects on the way that mathematical discoveries – such as Andrew Wiles’s celebrated recent proof of Fermat’s Last Theorem after more than three centuries of intensive effort by numerous dedicated individuals – may well involve personal commitment on a quite heroic scale of mental and physical endurance and yet, once established, hold good without regard to any such (now) extra-neous facts about their psycho-biographical genesis.²³ Not that Badiou would subscribe unreservedly to the distinction – com-monly advanced or assumed among analytic philosophers of science – between ‘context of discovery’ and ‘context of justifi-cation’, or the various circumstances under which some discov-ery may have come about and the various standards of empirical, logical, inductive, predictive or causal-explanatory justification that led to its widespread acceptance in the scientific community.²⁴ His approach differs from theirs mainly in the much greater weight he attaches to questions of historical development – that is, the genealogy of set-theoretical concepts, techniques and

READING THE TEXT

proof-procedures – and also, consistent with that, his greater emphasis on how such discoveries can be shown to have occurred through certain highly specific procedures of thought on the part of certain mathematicians confronted with certain, likewise specific problems or obstacles to progress. On the one hand this is why he can cross disciplinary boundaries so as to stress the closely analogous relationship between cutting-edge work in mathematics, requiring as it does the highest degree of dedication to a given truth-procedure, and those other chief fields of human endeavour where the demands of rigorous and consequent thought go along with the demand for unswerving fidelity or single-minded commitment. On the other hand, it is why he comes out in such firm opposition to the idea that truth in any of those subject-areas might properly be thought of as ‘relative to’

or ‘constructed by’ the various languages, discourses, cultural communities, more-or-less specialized (e.g. mathematical) ‘forms of life’, and so forth, which supposedly constitute the ultimate horizon of intelligibility for those who inhabit them.

We are now better placed to take stock of his comments con-cerning Aristotelian physics (or metaphysics) and the mistake of supposing that Aristotle’s denial of the void has been – or could in principle be – refuted by modern science. This is not to place Badiou in the company of those above-mentioned ‘strong’ socio-logists who would insist that the principle of ‘parity of esteem’

be carried so far that we refrain from judgement as regards the (notional) truth of the issue between Boyle and Hobbes and instead seek an explanation for both of their conflicting views in the particular socio-cultural-political context wherein those views took rise. Rather – and contrary to any such flat-out rela-tivist approach – what Badiou wants us to see is that when Aristotle asserted the non-existence of the void with such (as it turned out) misplaced confidence and vigour he did so for rea-sons that had nothing to do with empirical or experimental proof and everything to do with his clear understanding that its exis-tence, or mere possibility, would utterly wreck his entire concep-tion of the cosmic and natural order of things. That Aristotle got it wrong in physical-scientific terms Badiou would not for one moment deny. That his denial of the void on metaphysical grounds was also an error – and one with negative repercussions for the history of thought right down to Hobbes and beyond – is

likewise a conclusion that Badiou could scarcely wish to chal-lenge, given his own ontological commitments. However, this is just his point: that what Aristotle grasped was the range of (to him) deeply disturbing or downright absurd consequences that would follow necessarily from any proposition asserting the actual or possible existence of a void. That is to say, Aristotle’s logically precise and philosophically acute (though scientifically fallacious) arguments against the existence of a vacuum bear witness to his grasp of just how destructive were the implica-tions of the contrary thesis with regard to his own cosmological, metaphysical, natural-scientific and even – by close analogy – ethico-political precepts. What they threatened and what Aris-totle needed to keep very firmly at bay was also what Badiou sees as the liberating effect of set-theoretical thought not only in mathematics and the formal sciences but in every discipline, field of research, or project of discovery – politics included – where the issue can be stated with conceptual precision in terms of belonging, inclusion, membership and the count-as-one along with their negative (exclusionary) counterparts. In short,

‘[t]he void is in-numerable, hence the movement which is sup-posed therein does not have a thinkable nature, possessing no reason on the basis of which its comparison to other move-ments could be assured’ (p. 75). It is here that Aristotle’s think-ing encounters its own ‘point of impossibility’, the point at which its whole co-implicated structure of metaphysical, onto-logical and epistemoonto-logical (not to mention ethical and politi-cal) assumptions comes up against the kind of aporetic challenge that would shake that structure to its very foundations if allowed to proliferate throughout its various regions in the way that Badiou describes.

So far our voyage of commentary through Being and Event has taken us from Plato to Aristotle, that is, from Badiou’s medi-tations on a thinker with whom he feels a strong (if qualified) intellectual kinship to his diagnostic reading of a thinker with whose central claims he is profoundly at odds yet whose reason-ing he finds both consequent and all the more revealreason-ing for its blind-spots of questionable presupposition. Having ‘placed’ his thought in relation to theirs and having used the resultant three-sided comparison as a means to draw out some of Badiou’s most important and distinctive themes we can now proceed to engage

READING THE TEXT

more directly with the intricate sequence of mathematical and other arguments that constitute Part II of Being and Event.

Discussion points

Badiou’s strong universalist stance in ethics and politics goes sharply against the present-day emphasis, among cultural and critical theorists, on the need to show maximum possible respect for differences of creed, tradition, cultural background, value priority or gender orientation. Are you persuaded by his argu-ments in support of this position

What exactly is the relationship between mathematics, onto logy and political thought as Badiou conceives them?

PART II. BEING: EXCESS, STATE OF THE SITUATION, ONE/MULTIPLE, WHOLE/PARTS OR ∈/⊂?’