Praxis makes perfect
[This is from the March 2006 issue of Socialist Review. It's a slightly ambitious attempt at a joint review of Alex Callinicos's The Resources Of Critique, Slavoj Zizek's The Parallax View, and Alain Badiou's two major works, Being and Event and Logics of Worlds.]
In 1845 the young Karl Marx wrote down a series of short notes to himself summarising the conclusions of his intense engagement with the radical philosophies of his day. They were never intended for publication, but were nevertheless been preserved for posterity after Marx’s death by his lifelong friend and comrade Frederick Engels.
Of these notes – the so called Theses on Feuerbach – the final one is the most famous: “Philosophers have only interpreted the world in various ways, the point is to change it.” For Marx, this statement marked an exit from philosophy and a declaration that philosophy’s interminable problems and contradictions could only be resolved by a kind of radical conscious political activity that he would soon call revolutionary socialism.
Ever since then philosophy and radical politics have been engaged in a curious relationship of simultaneous rivalry and dependence. On the one hand revolutionaries have been deeply suspicious of philosophy, seeing it as a sophisticated mask and justification for the existing political order – ideology, in other words.
But on the other hand, revolutionaries cannot simply ignore philosophy. Radical political practice is inseparable from radical political thought and theory. These theories in turn are both influenced by philosophy and are obliged to hold their own in the court of philosophy.
In recent years these complexities have reemerged into the centre ground of intellectual debate. The ruling class has attempted to impose neoliberalism on the world. This, combined with the new drive to imperialist war has sparked mass resistance.
This resistance on the ground has been accompanied and paralleled by a new strain of radical and explicitly political philosophers such as Tony Negri, Slavoj Zizek and Alain Badiou. In various ways all of these thinkers try to grapple with the abstract aspect of the same problems that political movements face concretely – how can radical change come about? How can the new emerge from the old?
Alex Callinicos’s new book, The Resources of Critique, is a detailed and sustained engagement with these questions and these emerging radical philosophers, as well as with more established leftist and liberal thinkers such as Jürgen Habermas, Pierre Bourdieu and John Rawls. The book operates at several levels, acting as a summary of major current trends in philosophy, a negative critique of those trends, as well as a positive intervention into philosophy and contribution to its ongoing debate.
Ontology matters
The range of authors surveyed in the book is extremely broad, straddling both the “analytic” tradition of social and political theory favoured in British and US academia and the “continental” tradition of speculative philosophy. Much of the book builds on and deepens the philosophical positions developed by Callinicos over the years, especially over moral questions – how, if at all, can a radical left political project be justified? – and problems regarding the nature and origin of scientific knowledge and realism.
But his direct engagement with explicitly ontological issues – roughly speaking, the question of what “being” means at its most general and abstract level – is a new development. Callinicos writes, “Ontology matters. This is the result that has most surprised me personally… [though] I must confess some vestigial wariness about the whole subject.”
Why should ontology matter? The reason is that how we conceptualise being is closely bound up with how we conceptualise how the new can emerge from the old. In the most general sense, if something new can simply be explained by the old, then it isn’t really new in any radical sense of the term, it was “always already there”. Such a static and conservative understanding of the world leads ineluctably to a static and conservative understanding of politics.
But if the new cannot simply be explained by the old, it must in a sense come out of nowhere. Radical innovation – an “event” as Badiou calls it – emerges “from the edge of the void” and ruptures with the current order of being. Yet this too is also politically problematic, as Callinicos notes. It is uncomfortably close to a miraculous and religious conception of the world, and seems to licence all sorts of arbitrary voluntarism and moral relativism.
It follows that radical change, innovations, events, have to be situated somewhere in the dialectical relationship between something and nothing, being and the void. But the structure and nature of this dialectic is anything but obvious. In the latter half of the book, Callinicos lays out his provisional contribution to this problem, drawing on Marx’s understanding of society, Rawls’s theories of justice and the “critical realist” ontological theories of Roy Bhaskar.
The publication of The Resources of Critique coincides with major new works by two of the philosophers most prominently associated with the “ontologies of the void” that Callinicos critically engages with, Zizek and Badiou. In their different ways, they too seek a philosophical understanding of how it can be possible to break with the deadlocks of globalised neoliberal capitalism.
Zizek has declared his latest work, The Parallax View, to be his “magnum opus” and his most philosophically ambitious work to date. As always with Zizek, it is a dizzying mixture of highbrow philosophy and lowbrow cultural analysis, all peppered with psychoanalytic insights, idiosyncratic asides and the odd dirty joke. But underneath this dazzling display of pyrotechnics is a single philosophical theme hammered home relentlessly.
This theme is a concept of “parallax”, which is Zizek’s latest attempt to traverse the paradoxes of the old and new outlined above. Roughly speaking, the idea is that from the perspective of the old, the new appears impossible and miraculous. But from the perspective of the new, the old is radically transfigured and abolished. The trick – and this is where Zizek’s “parallax” metaphor comes into play – is to grasp both these positions simultaneously and identify their truth with their very incompatibility.
All of this sounds very much like the classical dialectics of early 19th century philosopher Hegel reinvented for a materialist and disenchanted age. And indeed Zizek proudly declares himself to be a partisan of “dialectical materialism”, taking on all the connotations of this term for a school of philosophical thought that is often dismissed as hopelessly old fashioned and fatally compromised by Stalinism.
Whether Zizek succeeds in reinventing dialectical materialism is open to question. For my money his approach is a little too overidentified with Stalinism – one gets the impression that the primary reason for Zizek choosing this terminology is to shock the liberal academy. His contrarian audacity in this regard is always charming, but it often acts to paper over his own complicity with the capitalist ideology he so ruthlessly criticises.
An alternative approach is taken in Badiou’s latest book, Logiques des Mondes, which has just been published in French and is currently being translated into English. This work is conceived as a second volume of Badiou’s 1988 masterpiece, Being and Event, which has just come out in English translation – the 18 year gap testifying to both the stupefying parochiality of English language philosophy and the fact that this parochiality has finally had its day.
Logiques des Mondes outlines what Badiou describes as a “materialist dialectic” that plugs some holes in his previous account of how new thinking (“truths” in Badiou’s terminology) can emerge from the sterile and endless circulation of opinion, dogma and academic knowledge. This question is treated in detail in Being and Event through a close reading of mathematical set theory.
Being and Event is certainly an astonishingly original and provocative book, though at times extraordinarily difficult. But as Callinicos notes in his valuable summary and exposition of the work in The Resources of Critique, Badiou’s conception of events and truths suffers from a kind of theoretical ultra-leftism that tends to dismiss questions of objective reality and empirical relations entirely.
Logiques des Mondes is in many ways a response to these criticisms that deploys another aspect of mathematics – the theory of categories – to offer an account of relationality, objectivity and appearance. It also points to a curious shift of tone in Badiou’s work and a break with a certain political pessimism that marked his previous work, written at the height of the intellectual backlash against the radicalism of May 1968.
In the preface to the English language version of his book Metapolitics, also recently published, Badiou writes: “The demonstrations in London against the war in Iraq bore witness to a confidence far greater than in Paris… This is what one might call the French paradox: intellectuals there are capable of great radicalism, but they are also fickle and highly dependent on prevailing phenomena… I am happy that [my work] is appearing in English, for I have found there to be, in the countries which speak this language, perhaps less certitude and audacity, but more tenacity.”
The political implications of Zizek and Badiou’s philosophical interventions will no doubt be worked out over the coming years, and will no doubt be marked by all sorts of mediations, corrections and contradictions.
But the fact that this strain of radical thought is alive and kicking – and tentatively entering into conversation with the new political movements against war and neoliberalism – is itself a beacon of hope and a signal that cracks are beginning to widen in the stultifying order of Blairite “common sense” ideology.
Alex Callinicos, The Resources Of Critique, Polity Press
Slavoj Zizek, The Parallax View, MIT Press
Alain Badiou, Being and Event, Continuum; Logiques des Mondes, Editions du Seuil
Review of Badiou’s The Meaning of Sarkozy
[Updating my blog with a couple of book reviews I wrote for Socialist Review. This first one of Alain Badiou's The Meaning of Sarkozy and was published in the March 2009 issue.]
Philosophers, it is well known, only interpret the world, when the point is to change it. France’s Alain Badiou is a rare exception to this rule – a philosopher who tries to do both. Published in France in 2007, this book was conceived as a polemical response to the election of Nicolas Sarkozy as the country’s president in May that year. It proved to be a surprise hit.
Alain Badiou’s politics are unrepentantly left wing. He was swept up by the May 1968 uprising, when he joined a revolutionary organisation. Ever since then he has remained politically active, focusing in particular on organising migrant workers and defending France’s minority communities. He was, for instance, one of the few French intellectuals to denounce the ban on the Muslim headscarf.
Needless to say, these positions have hardly made him popular among the French establishment. The unlikely mainstream success of his book has enraged the right, who responded with a furious campaign accusing Badiou of anti-Semitism – a baseless charge that Badiou takes great pleasure in ridiculing.
Part of the reason Badiou gained such popularity was that, unlike much of the left, he refused to be disheartened by Sarkozy’s victory over Ségolène Royal, the Socialist Party’s hopeless Blairite candidate. The book argues that real political change comes from the collective actions of ordinary people. He insists that it is both possible and necessary to open up what he calls a “new sequence” of radical egalitarian politics that starts from a thorough rejection of the limits that capitalism tries to impose.
Badiou argues that Sarkozy’s election is ultimately the result of fear. The right wing turned to Sarkozy out of fear of immigrants, workers and the youth of the suburbs. Much of the left turned to Royal out of fear of Sarkozy. In the face of this fear, Badiou makes the case for political courage.
His principles are at times brilliant and simple: “assume that all workers labouring here belong here, and must be treated on the basis of equality” and “any sick person who asks for a doctor should be examined and treated as well as possible, unconditionally with respect to age, nationality or financial resources”. At others they are dizzyingly abstract: “any process intended to serve as a fragment of emancipatory politics must be held superior to any managerial necessity” or “there is only one world”.
Starting from these principles, Badiou constructs a detailed and provocative comparison of Sarkozy’s politics with those of Philippe Pétain, the reactionary French general and head of the Vichy regime that collaborated with the Nazis. He ends with a call for a return to communist principles, in particular the kind of radical equality he sees at work in the early phases of the French Revolution, during the Paris Commune, and in the initial period of Bolshevik rule in Russia.
Badiou has a curious knack for combining speculative conceptual arguments with brawling polemic, and his book is a joy to read. Unfortunately it ends on a somewhat weak note, and one that underlines some of the problems with his fascinating but idiosyncratic political ideas. He is too uncritical of the Stalinist and Maoist politics that dominated the left during the 20th century, and too dismissive of the existing left’s potential.
But these weaknesses are minor compared to the strengths. Badiou is insightful and funny, especially when he gleefully castigates France’s corrupt political elites and idiotic business classes. These are the qualities that made his book a bestseller in France, and they shine forth for British readers too.
Banning the EDL is ineffective, counter-productive and demobilising
[I wrote this article for an internal SWP publication in October 2010 arguing against the tactic of calling for state bans against fascist organisations. I thought I'd dig it out and republish it in the light of current events. At the time of writing the EDL are still intent on rallying in Tower Hamlets this Saturday, and anti-racists still intend to turn out on the streets to oppose them.]
Anti-fascist strategy and tactics are a constant focus of debate for the left, and rightly so. Different political traditions have different analyses of the far right and different approaches to tackling them. But at the same time there is a palpable desire among broad layers of the working class for unity against the Nazis.
This is why, even when anti-fascist groups vehemently disagree on tactics to the extent that unity in action is impossible, there is often an unspoken agreement that each group pursue its own course without making public attacks on the efforts of others.
The widespread acceptance of this tacit truce is one reason why so many on the left have been shocked by the recent conduct of the Hope Not Hate campaign run by Searchlight, the anti-fascist magazine. First in Bradford, and then again in Leicester, Searchlight has actively attempted to dissuade people from attending counter demonstrations against the EDL. Instead, it proposed an anti-fascist strategy that relies exclusively on appeals to the state authorities for a ban on the EDL protest.
Nick Lowles, Searchlight’s editor and chief ideologue, wrote prior to the EDL’s Bradford rally: “We are putting all our efforts into stopping the EDL protest taking place at all… A delegation of leading Bradford figures is going to see the Home Secretary and a legal case is being drawn up to challenge the EDL’s right to protest. This, in our view, is our only option and sole focus.” Counter demonstrations against the EDL – in fact, any alternative anti-fascist tactic that risked confrontation or controversy – should be actively discouraged lest they interfere with the project of marshalling the “hearts and minds of local people” behind calls for a state ban.
This article argues against the Searchlight strategy on three grounds. First, I argue that the state cannot be relied upon to effectively contain racist and fascist groups: bans don’t work. Second, I argue that such appeals to the state can easily slip into calls to strengthen the state’s repressive apparatus – an apparatus that is routinely deployed against the workers’ movement. Third, and most importantly, I argue that Searchlight’s calls for a state ban necessarily go hand-in-hand with a concerted effort to demobilise and disarm the movement – not just the anti-fascist movement, but the working class more generally.
That is why Searchlight’s current trajectory is not merely misguided. It is dangerous, and it needs to be challenged vigorously and robustly across the working class movement.
Effectiveness
Despite all the hype about bans from the home secretary, in both Bradford and Leicester the EDL protests went ahead as so-called “static” demos. All that was banned were proposed marches that the EDL had applied for permission to hold.
In fact, the banning orders made no specific reference to the EDL, instead banning all marches in the city – including any anti-racist ones. So the EDL got to hold their static demos as they had done on every other occasion, including Stoke-on-Trent where they ran riot. In fact, it is common practice for the police to “escort” the EDL to their assembly point – thus creating a de facto march even when the protest is officially a static one.
Moreover, once the EDL has assembled for its rally, police efforts to contain them have been patchy to say the least. On almost every occasion groups of EDL have broken out of their pen and attempted to go on the rampage – in Stoke, Dudley, Bradford and Leicester.
Anti-fascists, in contrast, are policed far more vigorously. In Bolton and Leicester the police went out of their way to prevent Asian youths from joining the Unite Against Fascism counter demo. In terms of their public statements, the police typically pay lip service to being “neutral”. Yet in practice they routinely endorse the EDL’s ridiculous claims to be “peacefully protesting against militant Islam” while smearing anti-fascists as “the real troublemakers”.
None of this should be remotely surprising to anyone versed in the history of anti-fascist and anti-racist struggles. From Cable Street in the 1930s to the present day, the police have always been keen to “facilitate” the fascists and reluctant to crack down on them. The police force’s deep seated and ineradicable racism – at times blending into sympathy and even outright collusion with the far right – means they cannot be relied upon to check the growth of fascists. The same analysis applies to state bans against racists and fascists more generally. Their enforcement is lacklustre and their effectiveness minimal.
Repression
Many people recognise the weaknesses of state bans as outlined above. Even Searchlight were forced to admit this on the day of the Bradford demonstration. Lowles wrote: “800-1,000 EDL came into Bradford, acted appallingly and largely got away with it. They chanted disgusting anti-Muslim abuse, threw bottles and other missiles whenever they could, repeatedly attacked the police lines and then, when a group did break out, were able to run around the city without being picked up. The police were soft on the EDL and this only encouraged them to get even more rowdy and obnoxious.”
Searchlight did not seem to let these observations get in the way of continuing with their strategy of talking up bans and opposing counter demonstrations. But others on the left have reacted by calling for the state’s powers to be beefed up in order to enable effective bans on the EDL’s “static” protests.
While this position is more consistent than Searchlight’s, it is not one that revolutionaries can endorse. The past two decades have seen a huge increase in the powers, equipment and resources available to the police for “public order” purposes.
In particular, the “war on terror” has been used as an excuse to clamp down on civil liberties and ramp up the repressive powers of the police. This has led to brutal police methods being routinely deployed against left wing protesters – the Unite Against Fascism counter demo in Bolton and last year’s G20 protests in the City being particularly glaring examples. We should be calling for these powers to be dismantled, not strengthened.
Moreover, when legislation is passed giving the state powers to control protests, it is invariably framed in terms of “public order” rather than being deployed against racist or fascist groups. These supposedly “neutral” formulations are then used to crack down on the left and the right, or on the left rather than the right.
We can see this logic at work in the bans on marches mentioned earlier. We can also see it in historical examples. The 1936 Public Order Act banned political uniforms and required police consent for political marches – measures ostensibly directed against the Blackshirts. In practice these measures were deployed primarily against the left, striking workers and Irish Republicans. We can expect an identical pattern today.
Demobilisation
But there is a deeper problem with the strategy of calling for state bans, above and beyond the documented ineffectiveness of such tactics and the risks of strengthening the state’s repressive apparatus.
The problem lies in the very gesture of appealing to the authorities to “do something”, rather than looking to our class’s own power. Capitalist society tries to structure our lives as powerless individuals, and capitalist ideology encourages us to think of ourselves as powerless individuals. Revolutionaries face a constant uphill struggle to counter these processes and instil collective self-confidence into the working class.
This is why the “common sense” position adopted by much of the left – that of supporting both counter demos and state bans – is problematic. In practice, the first of these works to mobilise a mass movement, while the second demobilises it. That is why those who formally adopt the “common sense” position in practice always tip one way or the other.
Searchlight’s latest policy shift moves from implicit to explicit demobilisation. They are now openly trying to dissuade people from attending counter demonstrations and undermine those who attempt to organise such protests. And Searchlight’s allies in Bradford and Leicester have gone further, branding anti-fascist counter demonstrators as an equivalent threat to the EDL.
The administrator of Hope Not Hate’s Facebook page for Bradford sent out a message on the eve of the demo declaring that “the UAF are just as dangerous” as the EDL. In Leicester, a councillor working with Hope Not Hate told the local paper: “People will have heard about the EDL’s plans to protest in Leicester on Saturday, and about the counter-protest planned by UAF. There is nothing we can do to prevent these demonstrations, but what we can do is to make it clear that any organisation that promotes hatred and fear is not welcome here.”
In fact Searchlight has for some time now been arguing against any anti-fascist tactic that involves mobilising large numbers of people. It opposes anti-racist music carnivals, claiming that such activity “drains and diverts activism away from local campaigning”. It opposes “rallies, marches and pickets” against the fascists on similar grounds – they are, allegedly, “a distraction from the real work required in the communities”. The nature of this “real work” is never very clear. In Bradford it involved getting people to sign a statement against the EDL that did not even mention the word “racism”.
But as the October 2010 issue of Searchlight makes clear, this strategy of demobilisation is not intended to be restricted to anti-fascism. Nick Lowles and Paul Meszaros write: “This debate over strategy reflects a wider debate in the trade union movement over direction and tactics. At the TUC conference there were clear lines of disagreement between those who preferred a strike-based approach to opposing the cuts and those who believed the focus needed to be on winning the hearts and minds of union members and then taking the campaign out into the community.” The tactics being used by Searchlight to demobilise anti-fascist activism are a test case. The intention is to use the same tactics to choke off militant action against cuts and job losses. “Winning hearts and minds” in a nebulous “community” becomes the excuse for scuppering strike action by actual workers.
This strategy of demobilising people in the face of the fascist right would be worrying enough at the best of times. Given the current context of dark clouds gathering it is positively dangerous. We are witnessing an upsurge in anti-immigrant sentiment and unprecedented levels paranoid hostility towards Muslims not just here in Britain but across the Western world.
All this takes place in the context of cuts and austerity measures that risk plunging us into a 1930s style depression. And we know exactly what a similar conjuncture produced in the 1930s: the triumph of fascism in Germany, six years of savage world war, and the near extermination of Europe’s Jewish population.
Our urgent task is to create an anti-fascist, anti-racist mass movement that can head off the EDL and BNP while feeding into and strengthening wider working class struggles. Challenging and defeating these dismal calls for demobilisation will be an integral part of that task.
The one and the multiple in Badiou’s ontology
Hegel argued that a philosophical system could not, in the final analysis, be conceived entirely separately from the method by which it was presented. If this judgement still holds today, it must surely apply to Badiou, one of the few contemporary philosophers to declare that systematic ontology is both possible and necessary, and whose major work Being & Event is devoted to laying out just such a systematic ontology.
So we can be sure that Badiou’s ontology is oriented by the fact that its opening meditation sets out from the question of the one versus the multiple. The question – explored in this short essay – is over the nature of this orientation. I argue that the decision affects Badiou’s system on two distinct levels: there are effects arising from the specific manner in which he privileges the multiple over the one, and there are effects arising from the very fact he starts with the problem of multiplicity.
The first of these levels is more superficial than the second – in other words, one can concoct mathematicised ontologies that broadly resemble Badiou’s but which diverge on specific questions such as the existence of the Whole or the status of Atoms.
However, it is harder to see how Badiou could have produced a set theory based ontology that did not have to resolve the metaphysical problems surrounding multiplicity fairly early on. If Badiou had started from a radically different question, his system would look and feel very different.
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Before getting into the detail of Badiou’s ontology as laid out in B&E, I’ll start with a brief look at the some of the context surrounding the question of multiplicity. The first thing to note is that Badiou’s decision to start from this issue was by no means unusual or unprecedented in late 20th century French philosophy.
The rise of structuralism in the 1960s inevitably raised questions over the ontological status of its systems of signs. These questions became more pressing as it became clear that individual signs were being almost entirely absorbed into those systems, their positive identity replaced by a collection of differential relationships with other signs.
Derrida embarked on his critique of the metaphysics of identity, while Deleuze put forward his own concept of pure multiplicity. The notion of a multiple conceptualised without any prior reference to a one was already well established in France by the time Badiou wrote B&E in the mid-1980s.
The question of the multiple had a political and scientific context too. Liberal ideology in all its variations tended to privilege sovereign individuals over groups or classes. Socialists tended to make the opposite choice, emphasising collective subjectivity over individual rationality. And meanwhile mathematicians had developed and honed their own theory of multiplicity – set theory – in response to paradoxes they had encountered during the previous few decades.
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Badiou’s distinctive approach to the problem of multiplicity arose, roughly speaking, from combining these three currents. But it was his use of set theory that marked him off both from other contemporary approaches to the issue and from those found in the philosophical tradition.
That tradition stretches back a fair way, as Badiou makes clear in the opening paragraph of B&E’s first meditation. He quotes a formulation from Leibniz that seemingly chains being to the one and downgrades the multiple: “Ce qui n’est pas un être n’est pas un être.” (“What is not a being is not a being.”) He mentions Plato’s Parmenides dialogue, whose latter half is devoted to a bewildering series of paradoxical arguments over the ontological rivalry between ones and multiples (a dialogue examined in more detail in the second meditation).
Badiou even offers his own summary of the metaphysical chicken-and-egg problem at hand: “What presents itself is essentially multiple; what presents itself is essentially one.” A thing might initially seem to present itself as a unitary one, but in the very act of presenting itself it unravels, so to speak, into a multiple: my dinner resolves into {fish, chips, peas} for example.
Having set out the problem, Badiou proceeds to make a sudden and controversial move. He cuts through the ontological Gordian knot by announcing a decision: the one is not. From now on he is going to privilege the multiple over the one in terms of ontological priority, and proceed to systematically examine the consequences of this decision for ontology.
Badiou rapidly supplements his declaration with a slightly more mysterious one: “il y a de l’Un” (“there is Oneness”). We will examine what this means shortly. But before that there are two important points to note about the decision that the one is not.
The first is that Badiou is not suggesting that everyone who came before him was simply wrong on this question, or stupid. His position is rather that the advent of modern mathematics – and set theory in particular – makes it possible for the first time to develop a systematic ontology based around the multiple rather than the one.
This is set out more clearly in the introduction: “The science of being qua being has existed since the Greeks – such is the sense and status of mathematics. However, it is only today we have the means to know this.” (B&E, p3)
In Badiou’s terminology, there has been a scientific event, organised around the names Cantor-Gödel-Cohen, that has fundamentally transformed the way we understand the ontological situation. Following the consequences of this new insight is part of Badiou’s subjective fidelity to that event.
The second point is that even within the broad parameters of a set theory based ontology, Badiou could have made a different decision. To understand this we need to think a little bit more about how sets are structured.
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In the third meditation of B&E, Badiou notes how the paradoxes of naïve set theory forced mathematicians to adopt an axiomatic approach to set theory based around undefined abstract signs: “It is necessary to abandon all hope of explicitly defining the notion of a set. Neither intuition nor language are capable of supporting the pure multiple – such as founded by the sole relation ‘belonging to’, written ∈ – being counted-as-one in a universal concept.” (B&E, p43).
The ∈ symbol is the fundamental undefined relation of set theory. It is asymmetric, in that x ∈ y does not imply that y ∈ x. In fact in a phrase like x ∈ y, the multiple x is usually thought of as an ‘element’ and the multiple y is thought of as a ‘collection’. But these determinations are relative to the statement x ∈ y, they say nothing about the nature of x and y themselves.
One of the key features of Zermelo-Fraenkel (ZF) set theory – the axiomatisation of sets favoured by Badiou and by most mathematicians – is that every entity is a pure multiple, ie a set that can in principle appear on either side of the ∈ sign. But there are alternative axiomatisations where this is not the case.
For instance, we could allow certain entities to appear on the left of ∈ but not the right. This would correspond to things that could be members of sets but not have any members themselves – what mathematicians call atoms. Conversely, we could allow entities that can appear on the right but not the left. These would be so-called classes – collections of sets (or atoms) that could not, however, themselves be members of sets or classes.
In a sense both atoms and classes represent deviations from the notion of a pure consistent multiple, metaphysically speaking. An atom corresponds to the “little one” you get when you examine the elements that comprise a multiple. A class corresponds to the “inconsistent multiple” you get when a multiple is considered without the implicit gathering-together that makes a multiple of it.
The variations on ZF that include atoms or classes (or both) are perfectly legitimate from a mathematical point of view. One can in fact prove that if ZF is consistent, so are they (and vice versa). So Badiou could have chosen a variant ontology that included atoms or classes. But this would not be an ontology based on pure multiples of multiples. It would be imply that a different path had been taken to resolve the question of the one versus the multiple.
Such a course of action would have two drawbacks from a philosophical point of view, however. For starters it would not accord so well with mathematical practice among set theorists, who tend to treat ZF as their ‘plain vanilla’ axiomatisation.
More seriously, perhaps, such variant systems would break Occam’s Razor by “needlessly” introducing different types of entities. They would typically involve a much messier and larger collection of axioms (the axiom of extensionality can’t easily distinguish between atoms and the void, for instance, since both have no members). And this in turn would contradict Aristotle’s dictum, quoted approvingly by Badiou on p60 of B&E, that the first principles should be “are as few as they are crucial”.
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Returning to Badiou’s decision to grant sole ontological credentials to the multiple – what does this mean for the one? Does it simply disappear entirely? Not quite. We have already seen in our discussion of atoms and classes above that pure multiples can take on the ‘role’ of ones. For instance, the multiple x ‘acts’ as a one in the statement x ∈ y – it becomes an element of y, as Leibniz might put it.
It is this ‘virtual’ one that Badiou is referring to when he says “il y a de l’Un”. It does not exist as such (that privilege belongs solely to the multiple-that-is-presented), but is rather an ‘operational effect’ of the count-as-one that invariably accompanies presentation.
This count-as-one underpins a subtle but important distinction between consistent and inconsistent multiplicity. The multiples that are presented to us are consistent (in the etymological sense: they con-sist, stand together). But given a presented consistent multiple, one can retroactively posit what the multiple would have been prior to being counted-as-one, prior to becoming con-sistent.
This is the inconsistent multiplicity that is never directly presented but can always be postulated as what-must-have-been before the count-as-one. To return to an earlier example, I can imagine what the inconsistent multiple that became {fish, chips, peas} would look like – I just mentally ‘take the brackets off’.
Note that the paradoxes of naïve set theory tell us that not every multiple can be counted as one. For instance, the so-called Russell set that comprises every set that is not an element of itself cannot be made to con-sist – it is a fundamentally inconsistent multiple. Different axiomatisations of set theory will involve different multiples becoming unpresentable in this manner.
Finally, one can apply this distinction between consistent and inconsistent multiplicity to the multiple-of-nothing, ie the void. The consistent multiple is usually written ∅ and corresponds to what Badiou sometimes calls ‘the name of the void’. The inconsistent multiple is the void proper and is harder to visualise – one can perhaps consider { } with the brackets taken off…
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We have seen how certain variants of ZF set theory – ones involving atoms or classes – introduce changes to Badiou’s ontology that correspond to slightly different ontological decisions concerning the one and the multiple. These changes are, however, relatively superficial, in that any ontological theorem developed in one system can easily be adapted to the others.
The question remains as to whether or not Badiou’s focus on the question of the one and the multiple determines or shapes his system at a deeper level, or whether one can produce significantly different ontologies that nevertheless start out from that question.
One approach would be to consider axioms that correspond to a very different type of set theory to ZF, rather than a minor variant. One such system is New Foundations (NF), proposed by WVO Quine in 1937. NF has several unusual features that seem positively pathological to anyone used to ZF. You can prove that the Whole, the set of all sets, exists. The axioms of foundation and choice are provably false in NF, while the axiom of infinity can be proved without recourse to a new axiom. One could surmise that an NF-based ontology would correspond to a fully theological and idealist universe, where Spinoza’s God as Totality actually exists!
A cousin of NF known as NFU provides a natural setting for ‘mereology’ – the metaphysics of wholes and parts. An NFU-based ontology would arguably preserve Badiou’s basic ideas but take whole/parts as its fundamental metaphysical opposition rather than one/multiple (see Parts of Classes by David Lewis for more on this). Nevertheless, both these ontologies would still be based on a version set theory, so one suspects that the aporias of the one and the multiple that have been around since Plato would soon resurface, albeit in altered form.
The more intriguing question is whether one can remain faithful to Badiou’s “mathematics = ontology” injunction but not start from set theory (which is, after all, only a small region of mathematics and a relative backwater at that). Badiou has himself done this to a certain extent in Logics of Worlds, which deploys category theory rather than set theory. But Badiou insists that this ‘logic’ supplements his set-based fundamental ontology rather than replaces it.
Other mathematicians are more radical. FW Lawvere, for instance, has spent decades arguing that categories suffice as a foundation for mathematics and that set theory can be safely junked (or rather rewritten on categorical lines). If such projects are feasible – and they are still the subject of fierce debate among mathematicians – it opens the prospect of a radically different mathematical ontology that corresponds more to what he calls the ‘constructivist’ orientation in thought. One suspects Badiou would not be best pleased by such a development should it transpire.
Ultimately this speculation underlines an important philosophical point: for all his advocacy of particular ontological decisions, Badiou’s system is in the final analysis a “meta-ontological” one that is open to transformation by mathematical events. The ontology of Being & Event corresponds to the maths of 1960s, that of Logics of Worlds to that of the 1980s. Future scientific revolutions will impact on it further – and in ways that by definition cannot be foreseen in advance.
Force and understanding in Hegel’s Phenomenology of Spirit
The Phenomenology of Spirit charts the development of consciousness as it rises from lowly common sense to the heights of what Hegel calls ‘absolute knowing’ – the unconditioned form of thinking proper to philosophy itself. This development passes through a series of transitions, and this short essay takes a close look at just one of them: the chapter entitled ‘Force and the Understanding’ at the end of the ‘Consciousness’ section.
We start by briefly surveying this chapter’s position and role within the overall schema of the Phenomenology. We then move on to examine in some detail the nature of the object as outlined in the previous chapter on perception – an object whose contradictions will continue to unfold in the chapter on understanding that is the focus of our enquiry.
There then follows an exposition of how this object develops through the consecutive phases of ‘force’, the ‘realm of laws’ and the ‘inverted world’, before culminating in the ‘infinity’ that prepares the transition to self-consciousness. At each stage we move further away from a commonsense conception of the object. This process reaches a climax at the end the chapter where Hegel overturns our naive notion of ‘appearance’ in favour of a more dialectical conception.
The mysterious ‘inverted world’ is, I argue, an unstable and transitory phenomenon thrown up by the passage from one conception of appearance to the other. I end with a few remarks on how the paradoxical structure of ‘infinity’ overcomes object-oriented consciousness and prepares the ground for the subsequent shift to self-consciousness.
Understanding and consciousness
Hegel divided the Phenomenology into three overarching sections: ‘Consciousness’, ‘Self-Consciousness’ and a third much larger unnamed section that traverses chapters on ‘reason’, ‘spirit’ and ‘religion’ before ending on ‘absolute knowing’. The first section examines forms of consciousness directed towards objects that are conceived of as external to consciousness. The second involves consciousness turned towards itself, or towards another consciousness. These two moments are brought together in the third section, which concerns forms of experience that are aware of themselves and of the wider world in both its natural and social aspects.
The ‘Consciousness’ section is itself broken down into three chapters covering ‘sense-certainty’, ‘perception’ and ‘understanding’, three progressively more complex forms of object-oriented consciousness. Sense-certainty and perception correspond to the standpoints of naive and critical empiricism respectively. They both try to pinpoint the essence of the object in its sensuous presence. It is only after the failure of these efforts that we move to the third stage of understanding (Verstand), which moves beyond sensibility and instead attempts to grasp the object intellectually.
Despite this shifting standpoint (and the corresponding shift in the nature of the object, from ‘this’ to ‘thing’ to ‘force’), each stage of consciousness tries to position the object’s essence in the object and therefore outside itself. Consciousness is reluctant to assume responsibility for the object and abides by the tacit maxim: “Don’t mind me, I’m not here.”
It is only at the end of the chapter on understanding, after the deconstruction of appearance, that the boundary between consciousness and its object is finally dissolved. We discover that “behind the so-called curtain which is supposed to conceal the inner world, there is nothing to be seen unless we go behind it ourselves” (PS, §165). The chapter on understanding thus represents the traumatic last stand of object-oriented consciousness as it gives way to the birth of self-consciousness.
The object of perception
Before we start working through the chapter on understanding it is worth taking a preliminary look at the object as outlined in the previous chapter on perception, in paragraphs §113 to §115. Many of the twists and turns of the dialectic in the third chapter are prefigured in the construction of this object. A sound grasp of it therefore makes it much easier to see what is going on in later stages.
Perception arises from sense-certainty when the universality implicit in that sense-certainty is brought to the fore. That universality is expressed in the object of perception, transforming it from a brute ‘this’ into “the thing with many properties” (PS, §112). Unlike sense-certainty, “perception contains negation, that is, difference or manifoldness, within its own essence” (PS, §112).
The implicit tension between the unity of the thing and the plurality of its properties is what animates the development of this object in this chapter and the next. The irruption of universality into the ‘this’ means that “many such properties are established simultaneously, one being the negative of another” (PS, §113). The question is how this multitude of properties can be related to the one thing, and Hegel offers two contrasting models of how this could be.
The first of these models is set out in paragraph §113. It is characterised by passivity and indifference. The many properties are “indifferent to one another, each is on its own and free from the others”. They “interpenetrate, but without coming into contact with one another”. Hegel uses the word ‘also’ (auch) to describe this indifferent togetherness: a grain of salt “is white and also tart, also cubical in shape”, and moreover “the whiteness does not affect the cubical shape, and neither affects the tart taste” (PS, §113).
What does this indifferent ‘also’ of properties define? Not a thing exactly, but rather ‘thinghood’ (Dingheit): a medium for the properties, or a location where they can be together. Moreover, since the properties are not properties of some thing, strictly speaking they are not quite yet properties either, but rather ‘determinacies’ (Bestimmtheiten) or ‘matters’ (Materien).
However, there is a deeper level to the thing than this indifferent ‘also’, and this makes up the Hegel’s second model of the perceptual object – the excluding ‘one’. Rather than the properties merely lying together indifferently, they start to actively distinguish themselves from one other, and even oppose one another: white not tart, tart not cubical.
As the ‘matters’ start to exert their distinctiveness and pull apart from each other, the thing must start to exert its distinctive unity in order to hold them (and it) together. In this manner the ‘also’ becomes a ‘one’ and “thinghood is determined as a thing” (PS, §114).
Hegel brings together these two models in paragraph §115. The object of perception, considered in toto, is dynamic, comprising the movement from the indifferent ‘also’ to the excluding ‘one’ and back again. The object is “the point of singular individuality in the medium of subsistence radiating forth into plurality” (PS, §115).
But this is an insight for us, the philosophically experienced readers that the Phenomenology is implicitly addressed to. Consciousness at the stage of perception is still wedded to sensuous being, albeit critically. It cannot therefore grasp the entire dynamic cycle of the object, but only one of its moments, in snapshot as it were.
The remainder of the chapter traces the futile attempts of perception to posit one of these sensual moments as the truth and essence of the object. These attempts fail and lead to despair and deception. Consciousness is forced to step beyond the sensuous and posit the essence of the object at a higher level – that of understanding.
The play of forces
The chapter on ‘Force and the Understanding’ starts with a brief discussion of the ‘unconditioned’ (unbedingt) universal. ‘Unconditioned’ here means unconditioned by the sensuous, an ‘un-thinged’ object if we take the German term literally.
Nevertheless the ‘unconditioned universal’ remains an object for understanding, conceived of as external to and independent of consciousness. Understanding “shrinks away from what has emerged” (PS, §132) and does not yet fully acknowledge its own role in generating the unconditioned universal.
Hegel moves on to note a “positive significance” to the failure of perception: it collapsed because it could not grasp the unity of the excluding ‘one’ and the indifferent ‘also’ (PS, §134). This unity now takes centre stage. Understanding can see in the mind’s eye what perception cannot: both moments in “their transition into one another” (PS, §135). Hegel names this transition ‘force’.
The term ‘force’ (Kraft) is a curious one and clearly meant to evoke the similarly named concept from Newtonian physics. But it would be a mistake to read the term too literally and see this chapter as primarily a commentary on physics. Hegel’s concerns are always in the last instance philosophical ones, and the ‘force’ he talks about is ultimately his own philosophical concept, not one borrowed from another discipline. The relationship to physics in this chapter is indirect, apart from in the later stages of the chapter that I discuss below.
Hegel initially conceives of force asymmetrically: the movement from the ‘one’ to the ‘also’ is the ‘expression of force’, while the movement from the ‘also’ back into the ‘one’ is ‘force proper’ (PS, §136). But this conception is rapidly supplanted by a symmetric one in which the two movements are conceived of as two forces, each ‘soliciting’ and ‘being solicited’ by the other (PS, §138).
Moreover, this stately dance of forces reciprocally summoning one another (perhaps best pictured as a double helix) begins to take priority over the forces themselves. As Hyppolite puts it in his commentary on this chapter: “When the two forces are posed in their independence, their interplay reveals their interdependence.” (Hyppolite, p124).
Two points should be noted about this play of forces that prepare the way for what follows. First, the two forces are the same insofar as they are both forces and different insofar as there are two of them. They exhibit a paradoxical combination of sameness and difference – “the absolute antithesis is posited as a self-identical essence” (PS, §134) – that prefigures the ‘infinity’ that arrives at the chapter’s end.
Second, Hegel notes that while the concept of force “becomes actual through its duplication” (PS, §141), the two forces only exist in terms of each other, and hence “their being really has the significance of a sheer vanishing”. This simultaneous combination of manifestation and vanishing is the hallmark of appearance, to which we now turn.
Appearance and the supersensible world
This ‘vanishing’ triggers a shift in the understanding’s object: where once it looked at the play of forces, now it looks through that mediating play “into the true background of things” (PS, §143): “There now opens up above the sensuous world, which is the world of appearance, a supersensible world which henceforth is the true world, above the vanishing present there opens up a permanent beyond.” (PS, §144).
This supersensible world is thus initially conceived of as a ‘beyond’ of appearance, with appearance as a medium or the ‘middle term’ of a syllogism (PS, §145). It is as if consciousness is a three-stage rocket fired into the stratosphere: sense-certainty takes us so far, perception a step further, but both finally give way to understanding that penetrates the furthest reaches of the beyond.
But this picture of appearance is misleading in certain respects. As Heidegger notes in his lectures on the Phenomenology: “Appearance, taken as appearance, is the appearing of something other than itself.” (Heidegger, p107). What did Van Gogh paint? A picture, to be sure, but he did not just paint that; he also painted a vase of sunflowers, which was not a picture. Similarly appearing is not just about the passing away of appearance, but also the manifestation of that appearance’s other.
This leads to a second, properly dialectical, model of appearance that combines the two moments of vanishing and manifestation. Strictly speaking appearance can no longer be thought of as a medium through which we access a beyond, nor can we counterpose appearance to its beyond. The two are rather identified, not straightforwardly, but in terms of their mutual vanishing into each other.
Hegel flags up this transformation in paragraph §147: “The supersensible is the sensuous and perceived posited as it is in truth; but the truth of the sensuous and the perceived is to be appearance. The supersensible is therefore appearance qua appearance… It is often said that the supersensible world is not appearance; but what is here understood by appearance is not appearance, but rather the sensuous world as itself the really actual.”
It will nevertheless take some time for understanding to work through this transition from the first conception of appearance to the second. This passage takes us from the ‘realm of laws’ to ‘infinity’, a journey that takes us through the strange terrain of the ‘inverted world’.
The realm of laws
We start with appearance as a medium through which we grasp the beyond. The appearance is the play of forces whereby they arise and vanish into each other in ‘absolute flux’ (PS, §148). The truth of this flux is ‘universal difference’ expressed as a law, the “stable image of unstable appearance” (PS, §149). Initially, therefore, the supersensible beyond presents itself as “an inert realm of laws” that stands in contrast to the incessant change of the perceived world.
This picture is, however, problematically one-sided. If the supersensible world is one of static laws and the phenomenal world one of incessant change, then “form and content remain inadequate” (Hyppolite, p127). An essential aspect of the world – change, dynamism, multiplicity – remains marooned at the level of appearance and fails to be sublated into the supersensible. The dialectic that follows aims to introduce dynamism to the static law and thus bring understanding to life.
While Hegel’s aims might be clear, his arguments in what follows are, to my eyes, the most obscure and least satisfactory of this chapter. The bulk of this passage is devoted to a critique of mathematical physics that draws heavily on arguments from Hegel’s Jena lectures on logic and metaphysics. Hegel charges physical laws with being unable to provide an adequate account of their own necessity, thereby lapsing into “merely verbal” (PS, §154) and ultimately tautological ‘explanations’ that repeat the world rather than actually explain anything (PS, §155).
It is difficult not to discern in all this what Badiou calls the “Romantic gesture” in Hegel: setting up philosophy in rivalry to mathematical science then treating the latter as “no more than a crude, dispensable stage on the way to the former… everything which has been sieved and sublated is henceforth dead for thought” (Badiou, p35).
Certainly Hegel never returns to the question of physics in order to supplement it with the necessity he claims it lacks. The natural science that crops up in the later chapters of the Phenomenology is noticeably purged of troublesome mathematical content, and is instead content to paddle in the shallow waters of biological classification.
The inverted world
Details aside, the aim of the dialectic above is to introduce change into the supersensible world. The paradoxical combination of sameness and difference we discovered in the play of forces now becomes a ‘second law’ of appearance, one based on the “permanence of impermanence”. Hegel describes this new law in terms that nod towards electromagnetism: “what is selfsame repels itself from itself” and “what is not selfsame is self-attractive” (PS, §156).
The introduction of this foreign principle has a dramatic effect on the “tranquil kingdom of laws” – it is “changed into its opposite”, a “second supersensible world” that is “the inversion of the first” (PS, §157). There then follows one of the most bizarre passages in the Phenomenology, where Hegel describes this topsy-turvy world where sweet becomes sour, white becomes black and north becomes south. The inversions cover moral laws as well as natural ones: honour becomes contempt and punishment becomes pardon (PS, §158).
What is going on here? Hyppolite argues that the inverted world should be seen as a radicalisation of the commonsense view of appearance and supersensible beyond as opposites: “The difference between essence and appearance has become an absolute difference, with the result that we say anything in itself is the opposite of what it appears for another. We could indeed agree with common sense that appearances are not to be trusted; that they must, on the contrary, be negated if their true essence is to be discovered.” (Hyppolite, p136).
The inverted world is thereby an unstable phenomenon brought about by an incomplete transition from the naive to the dialectical conception of appearance. The problem arises from introducing the principle of dynamic contradiction into the realm of laws without altering that realm’s qualitative status as an ‘inner world’ or a ‘beyond’ of appearance.
Another way of looking at this involves highlighting a problem with the ‘three-stage rocket’ model of appearance outlined above. This picture conceives the ‘beyond’ of appearance as if it were somehow lurking over the horizon – and not as something qualitatively different to appearance. The beyond is rather conceived of as an appearance that just happens not to appear. And the inverted world simply pushes this logic to breaking point: it is quite literally the appearance that does not appear: sweet things are ‘inwardly’ sour, white things are ‘inwardly’ black.
There is a fallacy in all this, as Hegel explains. If we are to import a principle of dynamic contradiction into the supersensible world, we cannot let the inner-outer distinction remain untouched: “But such antithesis of inner and outer, of appearance and the supersensible, as of two different kinds of actuality, we no longer find here.” (PS, §159). Conceiving things in this way in fact sends us back from understanding to the level of perception complemented by an imaginary inner world “thought of as sensuous”.
Instead we have to find the inverted world in this world, as possibilities operating within it, and think the two together. The inverted world “has at the same time overarched the other world and has it within it… it is itself and its opposite in one unity” (PS, §160). Hegel calls this unity of opposites – “the bond of the bond and the non-bond” as he put it in his early writings – infinity.
Infinity and self-consciousness
Infinity is the paradoxical truth of the object that holds together unity and difference in a higher unity. Hegel calls it “the simple essence of life, the soul of the world, the universal blood… it pulsates within itself but does not move, inwardly vibrates, yet is at rest” (PS, §162). Its structure was there from the start of consciousness, animating the dialectical progressions of sense-certainty and perception. But it is only at the culmination of the dialectic of understanding that it has “freely and clearly shown itself” (PS, §163).
Infinity is the truth of the object, but it is not quite itself an object. For a consciousness that grasps infinity grasps its unity with infinity as well as its difference. The ‘object’ no longer stand opposed to consciousness, and so consciousness transforms into self-consciousness: “I distinguish myself from myself, and in so doing I am directly aware that what is distinguished from myself is not different.” (PS, §164)
Appearance as a curtain hanging before the inner world, or the middle term of a syllogism, has thus dissolved. Instead the two former extremes – the inner being of consciousness and the inner being of the object – are united (PS, §165). The stage is set for the next phase of the phenomenological journey: that of self-consciousness.
Bibliography
The primary text used is GWF Hegel, Phenomenology of Spirit, translated by AV Miller (Oxford University Press, 1977). I have also consulted Jean Hyppolite’s French translation, Phénoménologie d’Esprit (Éditions Montaigne, 1941). Secondary texts cited include: Jean Hyppolite, Genesis and Structure of Hegel’s Phenomenology of Spirit (Northwestern University Press, 1974); Martin Heidegger, Hegel’s Phenomenology of Spirit (Indiana University Press, 1988); Alain Badiou, Theoretical Writings (Continuum, 2004).
Giorgio Agamben: What is a commandment?
notes from CRMEP seminar delivered at Kingston University on 28 March 2011 – audio – draft transcript
ARCHE v ARCHE
The Greek term arche means both origin (hence “archeology”) and command (hence “oligarchy”). This is not so strange; to be the first to do something is in a sense to be its chief. We could say that the origin is always already the commandment, that which rules. In this sense the origin never ceases beginning, it never goes away but persists as a governing principle: continuous creation.
We get this sense in Heidegger’s understanding of history as Geschichte, a period that is “sent” or “destined” by a hidden origin. This in turn has inspired two contrasting responses: the “anarchical Heidegger” of Reiner Schürmann that maintains the hidden origin but neutralises its commanding function; or the “democratic Heidegger” of Jacques Derrida, which neutralises the origin but maintains a commandment without origin.
ARISTOTLE & APOPHANSIS
There is surprisingly little on commandment as such in the philosophical literature. Obedience is frequently analysed, eg by Hobbes, but not commandment as an activity in itself, indifferent as to whether or not the command is effective, obeyed or understood. When it does appear in its own right it is typically treated as a moral category related to the will.
Aristotle’s logic is concerned solely with apophantic discourse, that which manifests truth or falsity (eg indicative sentences about a state of affairs). All non-apophantic discourse, such as commandment, threat or prayer, is relegated to being a matter of rhetorics or poetics. But he doesn’t say much about commandment in his writings on these topics either.
IS v OUGHT
If commandment is not apophantic and does not describe or refer to a state of affairs, its meaning must lie in the act of utterance rather than the act of execution. It concerns an “ought” rather than an “is”, a Sollen rather than a Sein.
In this vein Émile Benveniste described the imperative as lacking denotation, as the “naked semantic core of a verb”. Antoine Meillet also noted that imperatives in European languages are typically the morphological root of the verb, and hypothesised that the imperative was the primitive form of a verb: “walk!” precedes “to walk” or “he walks”.
This opens up the possibility of an alternative ontology, or pre-ontology, based on commandment rather than assertion, on “be!” rather than “is”. While philosophical or scientific statements would fall under the ordinary “is”-based ontology, fields like law, religion or magic would operate in the imperative mode: “let there be…”
See also Paul’s letter to the Hebrews: “Faith is the substance of things hoped for, the evidence of things not seen.” (Hebrews 11:1), or JL Austin’s distinction between the locutionary (“is”) and illocutionary (“ought”) dimensions of a speech act. In modern life we are surrounded by commandments all the time: we are governed by the non-apophantic logos.
WILL v CAN
When the philosophical tradition does tackle commandment directly it conceives it as an act of will. But this is unsatisfactory as an explication, since the will is an even more obscure referent than commandment itself. Only crazy people try to give a definition of will! Nietzsche had a better idea when he tried to grasp will through commandment, will as that-which-commands. Moreover, the concept of will is missing from early classical philosophy – it is only introduced later, in Roman historicism and Christian theology.
As a verb “to will” is always closely associated with “to can”. [NB The verb “can” doesn’t have an infinitive form exist in English – Agamben seems to be inventing one here, deliberately or otherwise.] Both are empty modal verbs that need a non-modal supplement: “I will X”, “she can Y”.
Philosophy’s concern is precisely with the meaning of these empty modal verbs. Consider Kant’s drastic and almost insane injunction: “Man muß wollen können…” [“One must be able to will…” or “One must can will…” (that a maxim of our action become a universal law), from Groundwork of the Metaphysic of Morals, §2.] This strange commandment points to the impossibility of Kantian ethics.
VOLITION & POTENTIALITY
In Christian theology will is seen as that which checks potentiality, especially the paradoxical omnipotence of God. Early Christian theologists were obsessed with these paradoxes: God could undo the past, and so a raped virgin could recover her virginity! God could act arbitrarily, and so suddenly start running for no reason whatsoever!
These paradoxes point to a dark side of potentiality, and the need to qualify God’s absolute omnipotence (potentia absoluta) as an ordinary omnipotence (potentia ordinata). In the abstract God can indeed do anything, but in practice he only does what he wants to.
Will thus commands potentiality, thereby bounding it and domesticating it. Nietzsche’s hypothesis was therefore correct: to will is to command, or specifically, to command potentiality. And against this generalised and omnipresent commandment, we would invoke Bartleby’s response: “I would prefer not to.”
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Rough notes from the Q&A session follow. As is the nature of these things, the discussion was often confused and I can’t assure people of the accuracy of what follows. I’ve only picked up on some of the questions asked and grouped together ones on a similar theme.
• Andrew McGettigan asked about the difference between the imperative and the subjunctive. He wondered whether many of Agamben’s examples of commandments were in fact subjunctive rather than imperative. Agamben replied (I think) by saying that the subjunctive is a minor or derived mode of the imperative, so both are forms of commandment. However, in response to a later question he implied that the imperative and subjunctive were quite separate, and that the subjunctive was not a commandment strictly speaking.
• Anindya Bhattacharyya asked where mathematics fitted in to the distinction between “is” ontology and “be!” ontology. Mathematical discourse is full of statements like “Let G be a group…” that conjure up abstract and hypothetical entities. Even its formal axioms are best understood as commandments or laws invoking a mathematical realm as opposed to descriptions of a preëxisting mathematical reality.
Agamben replied by mentioning Émile Meyerson’s argument that the mathematical equality sign had an asymmetric commandment dimension to it. He added that maths straddled the distinction between the two ontologies, or perhaps formed a third ontology lying outside that distinction. He later returned to this possiblity of a third ontology – see below.
• Peter Hallward asked whether it was possible to conceive of commandment entirely independently of its execution. Isn’t a commander whose troops routinely ignore his orders no longer a truly commander? He also questioned the role of Bartleby – surely his “passive preference” was even more obscure than the commands he was assailed with? Stella Sanford also asked about the role of being-commanded-by, citing Emmanuel Levinas. Didn’t this indicate a different approach to commandment, one that went beyond ontology?
Agamben replied that he invoked Bartleby as a rejoinder to the predominance of commandments, and not as a solution to our problems. He also reiterated (rather tetchily) that he was not interested in the “obeying” aspects of commandment and viewed such aspects as an evasion of the question of command-in-itself. The issues of execution or being-commanded-by involve apophantic reference, and thus fall under the sphere of the indicative rather than the imperative proper.
Another question also asked about the links between commandment and the problematic of free will, resistance, authority etc. Agamben responded by citing Hannah Arendt. The notion of political authority derives from the Roman senate; but the senate never commands in the imperative, it always suggests in the subjunctive. Hence authority had nothing to do with commandment. As noted above, this answer seemed to contradict the one given to Andrew McGettigan earlier.
• There were several questions that tried to tease out the ethical and political implications of Agamben’s position. If he was opposed to ontologies of commandment, did that mean he favoured the apophantic ontologies? Agamben replied no, he wanted to neutralise both in favour of a third superior ontology. Could his formulation perhaps supply solutions to longstanding ethical conundrums about the relationship between “is” and “ought”, and thereby save Kantian ethics? Agamben replied that he “never had solutions” and did not think Kantian ethics could be saved. He said Kantian ethics was a “terrible mistake” and that ethics cannot have the form of a command.
• I couldn’t quite hear what sounded like a fascinating question about the role of commandment in Islam, citing how commandment and law are laid out in the Iranian constitution. I couldn’t catch Agamben’s reply either, but he stated that Islam had “a stronger notion of commandment” than Judaism or Christianity. He also noted links between commandment and the form of ancient Roman law – “if X, do Y!” – as well as links between commandment and nomination, citing Genesis 2:19-20 where God creates the animals and Adam names them.
Download this document as a PDF: Agamben on Commandment 2011-03
Badiou on the revolutions in Egypt and Tunisia
Alain Badiou wrote a short piece for Le Monde last month on the revolutions in Egypt and Tunisia. It’s already been translated into English a couple of times (on the Verso blog and over at lacan.com) but I’m not sure either quite captures Badiou’s pithy style and peculiar post-Maoist politics. So here’s a third translation, one I cobbled together with my limited French language skills and then sent over to Alberto to clean up (though blame me for any errors that remain).
Three quick critical comments before the main course:
• The major weakness of the piece is Badiou’s exclusive focus on Tahrir Square, a focus that ironically echoes the limited framing provided by Western TV cameras. He doesn’t seem to register the huge uprisings in towns and cities across Egypt, not least Alexandria, Mahalla and Suez (where protesting workers systematically burnt down every state security building and ran the police out of town). Most frustrating of all, there’s no mention of the strike wave that was instrumental in finally dislodging Mubarak and will remain the crucial site of struggle over the coming months. This is particularly odd given a very brief conversation I had with Badiou in 2007 regarding the Middle East: he insisted that Egypt was the key to the situation precisely because of the huge number of workers concentrated there…
• Despite these limitations the piece beautifully captures a certain utopian moment that is bound up with Badiou’s notion of the generic – which pops up here under the name “movement communism” (communisme de mouvement). But this utopian moment is a fleeting one. Recent weeks have seen reactionary forces regroup in Egypt. An International Women’s Day rally in Tahrir Square was physically attacked by obscure forces. Sectarian fighting between Muslims and Copts has recently flared up again. All of this lends a certain poignancy to Badiou’s lyrical description of generic solidarity.
• The most contentious (and to my mind most interesting) aspect of the piece is the critique of Western democracy. It raises a sharp question over to whether a truly egalitarian distribution of power involves an extension of democracy as we currently understand it, or a radical break with such conceptions. Badiou is on the latter side of this argument, and puts his case forcefully. But to my mind he is a little too fast in writing off the term “democracy” as irredeemably associated with parliamentary stupidity. Is there not a “movement democracy” that accompanies the “movement communism” he speaks of, a democracy that is antagonistic to its parliamentary simulacrum?
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Tunisia, Egypt: When an east wind sweeps away the arrogance of the West
Alain Badiou in Le Monde, 18 February 2011
The east wind prevails over the west wind. How long will the West, the fading and idle “international community” of those who consider themselves masters of the world, continue to give lessons in good management and proper behaviour to the rest of the planet? Isn’t it laughable to see these dutiful intellectuals, these soldiers dispatched from the capitalist-parliamentary system which we treat as some kind of moth-eaten paradise, offer themselves to the magnificent people of Tunisia and Egypt to teach these savages the ABCs of “democracy”?
What appallingly enduring colonial arrogance! Given the situation of political misery that we’ve been in for the past 30 years, isn’t it obvious that it is we who have everything to learn from the current popular uprisings? That it is we who need to urgently and closely study everything that over there has made it possible to overthrow by collective action governments that were oligarchic, corrupt, and moreover – perhaps above all – in a situation of humiliating vassalage vis-à-vis Western states?
Yes, we must be the pupils of these movements, not their stupid teachers. Because, in the unique brilliance of their inventions, they bring to life certain political principles which for a long time we’ve been told were obsolete. Above all, the principle that Marat ceaselessly declared: when it comes to liberty, equality and emancipation – we owe everything to mass riots.
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It is right to rebel. Just as our states and those who rely on them (parties, trade unions and servile intellectuals) prefer management to politics, so they prefer demands to revolt and “orderly transition” to any rupture. But the Egyptian and Tunisian people remind us that mass uprising is the only action commensurate with a collective feeling of revulsion at those who occupy state power. And in this case, there is only one slogan that links together the disparate elements of the crowd: “You, there, get out!” The exceptional importance of this revolt, its critical power, is that the slogan repeated by millions of people gives the measure of what will be, indubitably and irreversibly, its first victory: the flight of the man who’s been singled out by the slogan. And whatever happens next, this triumph of a popular action – one that was illegal by its very nature – will have forever been victorious.
The fact that a revolt against state power can be absolutely victorious is a teaching of universal significance. Such a victory always indicates the horizon of every collective action withdrawn from the authority of the law, what Marx named “the withering away of the state”. It tells us that one day the people, freely associated through the deployment of their own creative power, will do without the grim coercion of the state. It is this ultimate idea which explains why a revolt bringing down established authority triggers such boundless enthusiasm around the world.
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A single spark can start a prairie fire. Everything started with the self-immolation of a man reduced to unemployment, who was forbidden from exercising the miserable trade that allowed him to survive, who was slapped by a policewoman to make him understand what was real in this vile world. This gesture snowballed over the next few days and weeks, until millions of people were crying with joy in a far-off square and powerful potentates were abruptly forced to flee.
But where does this astounding expansion come from? Is it the spreading of an epidemic of freedom? No. Jean-Marie Gleize put it poetically: “A revolutionary movement does not spread by contamination, but by resonance. Something built here resonates with the shock wave emitted by something built over there.” This resonance is what we call an “event”. The event is the sudden creation, not of a new reality, but of a myriad of new possibilities.
None of them is a repetition of what is already known. That is why it is obscurantist to say “this movement calls for democracy” (meaning, the “democracy” that we enjoy in the West), or “this movement calls for social improvement” (meaning, the average prosperity of our petit bourgeoisie). Starting from almost nothing, but resonating everywhere, the popular uprising has created unknown possibilities for the whole world. The word “democracy” is hardly spoken in Egypt. They speak instead of “a new Egypt”, of “true Egyptian people”, of a constituent assembly, of a total transformation of life, of unprecedented and previously inconceivable possibilities.
This is about a new prairie, no longer the one that the spark of the uprising set aflame. This prairie to come is to be found between the declaration of a reversal of forces and the taking up of new tasks. Between what was said by a young Tunisian: “We, sons of workers and peasants, are stronger than the criminals”, and what was said by a young Egyptian: “Starting today, 25 January, I am taking over the affairs of my country.”
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The people, and the people alone, is the creator of universal history. It is quite striking that in our West, governments and media acknowledge the rebels in a Cairo square as “the Egyptian people”. What’s going on here? The only “people” these powers usually consider as “reasonable” or “legal” are the majorities thrown up by a focus group or an election. How is it that all of a sudden, hundreds of thousands of rebels can represent a nation of 80 million? This is a lesson we should not forget and will not forget.
Beyond a certain threshold of determination, obstinacy and courage, the people can indeed concentrate their existence in a square, an avenue, a few factories, a university… The whole world will witness this courage, and above all the amazing creations that accompany it. These creations are proof that a people has come to be. As one Egyptian protester forcefully put it: “Before, I watched television. Now it’s the television that’s watching me.”
In the wake of an event, the people is composed of those who can resolve the problems posed by the event. For instance, the occupation of a square requires food, sleeping arrangements, guards, flags, prayers, defensive battles. This ensures that the place where all this happens, the symbolic place, is safeguarded for its people, at any price. These are problems that can seem insoluble as hundreds of thousands of people arrive from everywhere, especially since the state has disappeared from the square. To solve insoluble problems without the help of the state – that is the destiny of an event. And that is what makes a people exist, suddenly and for an indefinite time, there where it has decided to gather.
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There is no communism without the communist movement. The popular uprising of which we speak is clearly without a party, without a hegemonic organisation, without a recognised leader. There will be time to assess whether this characteristic is a strength or a weakness. In any case this is the reason why what is happening has all the features of what one should call movement communism – and in a very pure form, perhaps the purest since the Paris Commune.
“Communism” here means the joint creation of a collective destiny. This “common” has two special features. First, it is generic, representing all humanity in one place. In this place, you find all the various sorts of people that make up a people, any kind of speech is listened to, every proposition is examined, every difficulty treated on its own terms. Second, it overcomes all the major contradictions which the state claims only it can manage (without ever finally overcoming them): contradictions between intellectuals and manual workers, men and women, poor and rich, Muslims and Coptic Christians, provincials and city dwellers…
Thousands of new possibilities concerning these contradictions rise up at every moment, ones that the state – any state – is completely blind to. One sees young female doctors who have come from the provinces to treat the wounded sleeping in the midst of a circle of fierce young men, and they sleep more soundly than they have ever done, knowing that nobody will touch a hair on their head. One sees an engineers’ organisation talking to youth from the suburbs, urging them to hold the square, to protect the movement with their fighting spirit. One sees a row of Christians standing watch over Muslims bowed in prayer. One sees traders feed the unemployed and poor. One sees everyone talking to their unknown neighbours. One reads a thousand placards where the life of each seamlessly blends into the great history of all.
Movement communism is the sum of all these situations and inventions. The single political problem for two centuries has been this: how do we permanently establish the inventions of movement communism? And the sole reactionary response has always been this: “It’s impossible, dangerous even. Let us put our trust in the state.” Glory to the Tunisian and Egyptian people for reminding us of the only true political task: to face down the state with organised fidelity to movement communism.
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We do not want war, but we are not afraid. Everywhere you hear talk of the calm and peaceful nature of these huge demonstrations, and that calm is linked to the ideal of electoral democracy that has been ascribed to the movement. Note however that there were hundreds of deaths, and there still are deaths every day. In many cases, the dead were fighters and martyrs who fell while initiating and then protecting the movement. The political and symbolic places of the uprising had to be held at the cost of fierce fighting against the militias and police forces of the threatened regimes.
And who paid there with their lives, if not the young people from the poorest parts of the population? As for the “middle classes”, our hopeless Michèle Alliot-Marie said the democratic outcome of the sequence depended on them and them alone. But these middle classes remember that at the crucial moment, the survival of the uprising was guaranteed only by the wholehearted commitment of popular detachments. Defensive violence is inevitable. It continues to unfold in Tunisia, in difficult conditions, after the young provincial activists have been thrown back on their misery.
Can anyone seriously think these innumerable initiatives and cruel sacrifices had no fundamental goal beyond leading people to a “choice” between Suleiman and El Baradei, just as we do when we pathetically resign ourselves to arbitrating between Messrs Sarkozy and Strauss-Kahn? Would that be the only lesson of this wondrous episode?
No, a thousand times no! The Tunisian and Egyptian people tell us this: rise up, build a public place for movement communism, defend it by all means and invent there the successive stages of action – that is the real of the politics of popular emancipation. It is not only Arab states that are against the people and, elected or otherwise, fundamentally illegitimate. Whatever their fate, the Tunisian and Egyptian uprisings carry a universal meaning. They prescribe new possibilities whose value is international.
Notes on Nietzsche’s eternal recurrence
Somewhat surprisingly given its prominence in the interpretation of Nietzsche’s work, the motif of eternal recurrence occurs explicitly only a few times in his published books: in certain passages and episodes in The Gay Science, Thus Spoke Zarathustra and Beyond Good and Evil, for instance. The consensus on the importance of eternal return for Nietzsche relies rather on his unpublished writings, such as his letters, or the miscellaneous personal notes and unfinished fragments found in The Will to Power and other posthumous editions of his notebooks.
These unpublished writings suggest that Nietzsche accorded great importance to the thought of eternal return in his overall project. In Ecce Homo, Nietzsche describes the Damascene moment when the idea of eternal recurrence first came upon him while walking in the woods near Lake Silvaplana in August 1881 (EH, p69). He insists it came upon him, rather than vice versa.
A letter to Franz Overbeck written a few years later in March 1884 describes the thought of eternal return as having the potential to “break the history of humanity in two” – a formulation that appears repeatedly in Nietzsche’s letters right up to the eve of his insanity. As Joan Stambaugh puts it in her 1972 study of eternal return: “Nietzsche’s own attitude toward this thought is striking. He does not quite seem to know what to do with it, and yet he cannot leave it alone.” (Stambaugh, xi).
Arguably this judgement applies equally to the innumerable commentaries upon and interpretations of Nietzsche’s work. Karl Löwith, Martin Heidegger and Pierre Klossowski are just some of the distinguished names that have seen eternal recurrence as a key that unlocks Nietzsche’s thought, revealing an underlying systematicity lurking beneath the stormy surface of his prose. Heidegger, for instance, devotes an entire volume of his 1940 study of Nietzsche to what he calls “the doctrine of eternal return”, declaring that Nietzsche’s “fundamental metaphysical position” is captured by it. Löwith similarly describes eternal return as “the unifying fundamental idea in Nietzsche’s philosophy” in his 1935 book on the topic.
This essay takes a slightly different approach. Treating eternal recurrence as a systematic doctrine fails to do justice in my eyes to the profoundly anti-systematic and indeed anti-philosophical tenor of Nietzsche’s work. The eternal recurrence of the same is a provocation to thought rather than a mystery underlying it. To adapt an image from Gilles Deleuze’s 1962 book on Nietzsche, the thought of eternal return is “an arrow shot by Nature that another thinker picks up where it has fallen so that he can shoot it somewhere else” (Deleuze, ix).
Stambaugh makes a similar point when she states that any interpretation of eternal return is “forced to ‘go beyond’ Nietzsche’s writings, published or unpublished, on the subject… If one adheres strictly to what Nietzsche wrote about eternal return, it is impossible to ‘solve’ the enormous problems inherent in this thought.” (Stambaugh, p103).
At any rate, such speculative and experimental approaches to eternal return are far more in keeping with Nietzsche’s spirit than rifling through his personal papers in the hope of chancing upon a revelation. Consequently, this essay will examine various interpretations of eternal recurrence with the aim of seeing what can be done with the thought – especially with regards to questions of time and history – rather than what Nietzsche might have ultimately ‘meant’ by it.
Eliade’s myth of eternal return
Perhaps the first point to make about Nietzsche’s thought of the eternal return of the same is that it represents a broadside against our prevailing metaphysical ‘common sense’ about time and history. In fact the suspicion of progressivist historiography and linear accounts of time are present in Nietzsche’s earliest published writings, notably the 1873 essay ‘On the Uses and Disadvantages of History for Life’ in Untimely Meditations. The motif of eternal return in his later work can be seen as a radicalisation of these early insights and positions.
With this in mind, it is worth briefly sketching out one of the most influential accounts of eternal return as an alternative to linear history – that set out by the Romanian philosopher and historian of religion Mircea Eliade in his 1949 book The Myth of Eternal Return. Eliade sets up an opposition between, on the one hand, the “historical man” of modern societies who consciously and voluntarily makes his own history, and on the other, the “traditional man” of agrarian and pre-modern societies that holds a hostile and negative attitude towards history, holding instead to a cyclical conception of time whereby the cosmos periodically abolishes itself only to be reborn again.
Eliade argues that the cyclical time of traditional societies is designed to ward off the “terror of history” by draining historical events of their meaning. A deed in the present is seen not as a historical act, but as the repetition of an archetypical gesture undertaken by the gods in a mythological prehistory. The reality of the deed stems from its status as an echo of this mythic past, and not from the event in itself. And the eventual cyclical return of the gods ensures that the event’s historical irreversibility is also ultimately overcome.
What complicates this picture of simple antagonism between historical and cyclical time is the complicity between them. Pre-modern societies try to ward off history – but their time is nevertheless slowly corrupted by it. This corruption by history only stops when the grand cycle comes to an end – the cosmos is destroyed and created anew, thereby purging history from time.
Eliade makes little effort to conceal his sympathy for these traditional accounts of time and his despair at a “spiritually arid” historicist modernity that inevitably (in his eyes) falls into relativism and nihilism. Hegel and Marx, unsurprisingly, come in for particular criticism. In many respects Eliade’s political outlook, themes and judgements on the question of eternal return are at least superficially very similar to those of Nietzsche.
Nevertheless it should be noted that Eliade’s version of the myth of eternal return does not refer directly to that of Nietzsche. In fact Nietzsche is only mentioned twice in passing throughout the book. The first reference is a positive one, with Nietzsche’s eternal return cited approvingly as part of a recent traditionalist backlash against rampant historicism. The second, however, is negative: Nietzsche is described as a thinker of “destiny” – and is thus consigned to the modern historicist camp that Eliade bitterly opposes.
This ambivalence gives us a clue as to how profoundly Nietzsche’s thought of eternal return differs from that of Eliade, despite the many thematic and political resemblances. For starters we should note that Eliade’s “archaic ontology” consigns the reality of apparent world to a mythical plane. This gesture is precisely what Nietzsche identifies as “Platonism” and polemicises against – see for instance the passage “How the ‘True World’ finally became a fable” in Twilight of the Idols.
Moreover, Eliade’s insistence on “warding off” the terror of history is a profoundly reactive stance to take with respect to modernity – especially when his purported justification for that stance are the horrors meted out by history against the suffering and powerless masses. Nietzsche, for all his nostalgia for aristocratic values, is never interested in simply restoring a past golden age. For him the past is important only insofar as it can detonate the present and thus induce the extraordinary rupture necessary for the overcoming of nihilism. Far from warding off history, eternal recurrence for Nietzsche is, paradoxically, a necessary condition if we are to take but a single step forwards.
Cyclicity, the Same and Poincaré recurrence
A third point of divergence between Eliade’s version of eternal return and Nietzsche’s concerns the question of what exactly returns and how. For Eliade it is a matter of the entire cosmos repeating itself perfectly, in precise cycles divided into subcycles. For instance, he carefully recounts how the 12,000 year long mahayuga cycle in Hindu mythology is broken down into four smaller (and diminishing) yugas, each in turn preceded by a “dawn” and “twilight” stage.
Can we discern an analogous perfect cyclicity in Nietzsche’s thought of the eternal return? There are certainly unpublished notes where he toys with the idea. For instance, note 1066 in The Will to Power (dated 1888) deploys a combinatoric argument in an attempt to prove that the world must repeat itself precisely after a finite amount of time: “A circular movement of absolutely identical series is thus demonstrated: the world is a circular movement that has already repeated itself infinitely often and plays its game in infinitum.”
In fact this argument is fallacious, even if we accept Nietzsche’s premises of a finite number of “forces” and infinite time, as Georg Simmel pointed out as early as 1907 (Kaufmann, p329). Simplifying Simmel’s example slightly: imagine a clock dial with two hands, the first making one rotation each hour and the second making √2 rotations each hour. No two configurations of this clock could repeat precisely without contradicting the fact that √2 is an irrational number.
We can however, demonstrate that any particular clock state repeats itself approximately (to any desired degree of precision). This is a phenomenon mathematicians call ‘Poincaré recurrence’ and is a common feature of closed dynamic systems. (Note however that some physicists, notably Ilya Prigogine, argue that Poincaré recurrence does not ever actually occur in reality – and that this non-recurrence undergirds and ensures the irreversibility of time.)
The ‘On the Vision and the Riddle’ section of Thus Spoke Zarathustra provides further evidence that Nietzsche’s thought of eternal return should not be understood in terms of perfectly repeating cycles. Zarathustra is climbing a mountain burdened by the Spirit of Gravity, a dwarf that rides on his back, mocking and discouraging him. They come across a gateway called “Moment” (Augenblick) with two infinite paths leading from it representing the future and the past.
Zarathustra asks the dwarf if the paths would remain in “eternal opposition” if one were to “follow them further and ever further and further”. The dwarf responds glibly that “time itself is a circle” – prompting an angry response from Zarathustra who chides him for taking the thought of eternal return “too lightly”. The dwarf vanishes shortly thereafter, presumably vanquished by Zarathustra.
Heidegger draws the following lesson from this passage: “So the dwarf has not really grasped the riddle; he has made the solution too easy. Accordingly, the thought of eternal recurrence of the same is not yet thought when one merely imagines ‘everything turning in a circle’… That is precisely the thought of circling as the dwarf thinks it, the dwarf who, in Zarathustra’s words, makes things too easy – inasmuch as he absolutely refuses to think Nietzsche’s stupendous thought.” (Heidegger, p42).
One finds similar judgements against the cycle interpretation of sameness in Deleuze: “Every time we understand the eternal return as the return of a particular arrangement of things after all the other arrangements have been realised, every time we interpret the eternal return as the return of the identical or the same, we replace Nietzsche’s thought with childish hypotheses. No one extended the critique of all forms of identity further than Nietzsche.” (Deleuze, xi).
And Stambaugh notes that Nietzsche’s expression das Gleiche “does not express simple identity and therefore does not, strictly speaking, mean the Same. It lies somewhere between the Same and the Similar, but means neither exactly.” She uses the example of two women wearing two hats that resemble each other so closely that one could mistake them for the same hat. The hats would be the ‘same’ in the sense of gleich: “This more than similarity, but it is not identity.” (Stambaugh, p31). The resemblance here to Poincaré recurrence is striking: the same recurs eternally, but always with a glitch that stops just short of perfect identity and cyclicity.
Subjectivity and time
So far our survey of the thought of eternal return has focused on what might be called the “objective” side of the question – the recurrence of all things, or of arrangements of the world. But Nietzsche’s writing on the eternal return typically involves a “subjective” side as well, fusing together the grandest cosmic vistas with the most intimate personal experience. The following famous passage from The Gay Science involves just such a juxtaposition:
What if some day or night a demon were to steal into your loneliest loneliness and say to you: ‘This life as you now live it and have lived it you will have to live once again and innumerable times again; and there will be nothing new in it, but every pain and every joy and every thought and every sigh and everything unspeakably small or great in your life must return to you, all in the same succession and sequence – even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned over again and again, and you with it, speck of dust!’ (GS, §341)
What, in this passage, is the glitch between recurrences that makes this scene much more than mere endless and trivial cyclical repetitions? It is the uncertainty over how the reader reacts to the demon: one can either be crushed by the thought of eternal return, “throw yourself down and gnash your teeth and curse the demon who spoke thus”, or one can affirm the eternal return and “long for nothing more fervently than for this ultimate eternal confirmation and seal”. The glitch, in other words, is the space of subjective decision.
We see here how the eternal return in Nietzsche’s hands ties together the objective and subjective – or more accurately, creates a basis for a subjectivity in terms of an infinitesimal crack in the objective order of being. Similar themes can be found in Sartre’s Being and Nothingness, where Sartre bases subjective freedom on the nothingness that separates each moment from the next.
It is perhaps no surprise that several commentators have interpreted the eternal return (and this passage from The Gay Science in particular) in ‘ethical’ terms, arguing that it offers a kind of purely immanent equivalent of Kant’s categorical imperative. Deleuze puts it as follows: “The eternal return gives the will a rule as rigorous as the Kantian one… As an ethical thought the eternal return is the new formulation of the practical synthesis: whatever you will, will it in such a way that you also will its eternal return.” (Deleuze, p68).
A similar quasi-ethical question of subjective attitudes to the past animates Nietzsche’s early ‘History for Life’ essay mentioned above. The bulk of the essay is a broadside against a certain positivist vision of history that sees it as a science that accumulates facts about the past. Such an attitude to history, Nietzsche argues, in fact paralyses us with knowledge and prevents us from truly acting. In contrast to this historical attitude, he puts forward a ‘suprahistorical man’ with a capacity to actively and wilfully forget, thereby overcoming this paralysis.
Both the historical and suprahistorical attitudes are contrasted with the unhistorical life of animals that “live in the present, like a number without any awkward fractions left over” – suggesting, perhaps that animals live in purely cyclical time and cannot think the eternal return proper (UM, p61). On this note, see also the curious animal chorus in the ‘Convalescent’ section of Thus Spoke Zarathustra (TSZ, p232) – Zarathustra treats the animals with kindness, yet it is clear from his “buffoons and barrel organs” remarks that they do not quite ‘get’ the teaching of the eternal return.
We have remarked already on the spatial juxtaposition of the cosmic and the intimate in the eternal return – this is paralleled by a temporal superposition of eternity on an instant, which leads us to another variation on this theme of time and subjectivity. Stambaugh picks up on the idea of eternal return as a relation of the instant to eternity in order to construct a phenomenology of time that can overcome the nihilism of historicism (though as noted above, she is careful to situate her interpretation as one that deliberately ‘goes beyond’ Nietzsche’s actual writings).
Stambaugh argues that Nietzsche’s Moment is radically opposed to traditional notions of time as duration or flux. The ‘horizontal’ flow of time is at each instant punctuated by a ‘vertical’ drop that corresponds to Zarathustra’s experience of ‘no time’: “Well of eternity! Serene and terrible noontide abyss! When will you drink my soul back into yourself?” (TSZ, p289). Moments arise and perish into this vertical abyss, Stambaugh argues, rather than being strung together horizontally. The past and future become dimensions of the present, and eternity becomes the absolution of time (Stambaugh, p126).
Benjamin, history and now-time
Stambaugh’s interpretation of the eternal return of the same seizes upon one of its many potentialities – the implicit phenomenological critique of the metaphysics of time – and develops this potential doggedly and systematically. Yet for all its strengths, certain aspects of Nietzsche’s thought drop out of Stambaugh’s reading, notably the historical dimension of eternal recurrence and the asymmetry between past and future that this involves.
I’ll end with a few words on Walter Benjamin’s Theses on the Concept of History, a text deeply influenced by Nietzsche’s approach to history and his thought of eternal return, and one that restores the lost dimensions mentioned above. To my mind it is the single most powerful example of a productive approach to Nietzsche’s eternal return, one that uses the thought rather than comments upon it or attempts to decode it.
Benjamin wrote the Theses in 1940, shortly before his death and in circumstances of almost unthinkable historical catastrophe: the total victory of fascism in Germany over the forces of the left. He tears into progressivist and empathetic approaches to history – which invariably end up sympathising with the ruling class while lulling workers into a false sense of security and dulling their ability to fight – and instead calls for a historical materialism that recognises its task is to “brush history against the grain” (Thesis 7).
Nietzsche’s suspicions of a nihilism lurking at work within history are transformed into the chilling image of the Angel of History being hurled into the future, watching over its shoulder as the corpses pile up behind him (Thesis 9). Benjamin also adopts and radicalises Nietzsche’s insistence that the road to the future lies through the past, declaring that the working class struggle is “nourished by the image of enslaved ancestors rather than by the ideal of liberated grandchildren” (Thesis 12).
But perhaps the most striking Nietzschean themes appear in theses 14 and 15. “History is the subject of a construction whose site is not homogenous, empty time but time filled full of now-time (Jetztzeit).” He calls for a “tiger’s leap into the past” that reactivates lost possibilities in the present and detonates them into the future. “What characterises revolutionary classes at their moment of action is their awareness that they are about to make the continuum of history explode.” The harbingers of a new dawn in history shoot their rifles at clock-faces – bringing time to a standstill.
Bibliography
Texts by Nietzsche
Untimely Meditations, edited by Daniel Breazeale, Cambridge University Press 1997
The Gay Science, edited by Bernard Williams, Cambridge University Press 2001
Thus Spoke Zarathustra, translated by RJ Hollingdale, Penguin 1969
Ecce Homo, translated by RJ Hollingdale, Penguin 1992
The Will to Power, edited by Walter Kaufmann, Vintage 1968
Secondary texts
Gilles Deleuze, Nietzsche and Philosophy, Athlone 1983
Mircea Eliade, The Myth of Eternal Return, Routledge & Kegan Paul, 1955
Martin Heidegger, Nietzsche volume II: The Eternal Recurrence of the Same, Harper & Row 1984
Walter Kaufmann, Nietzsche: Philosopher, Psychologist, Antichrist, Princeton 1974
Joan Stambaugh, Nietzsche’s Thought of Eternal Return, John Hopkins 1972
Benjamin translations taken from Fire Alarm by Michael Löwy, Verso 2005
Review of Badiou’s Number and Numbers
[first published in Radical Philosophy 156, July/August 2009]
One of the more astonishing aspects of Alain Badiou’s philosophical position is that the key to what is most distinctive about it can be summarised in just three words: mathematics is ontology. His major work, Being and Event, kicks off with this stark assertion, and proceeds to derive a series of bold conclusions – the wresting of ontology from Heidegger’s embrace, the construction of a rigorous and rationalist metaphysics, and a wholesale refoundation of the relationship between philosophy and science, the latter henceforth being conceived as one of philosophy’s ‘conditions’.
It should be noted, however, that while Badiou identifies ontology with mathematics in its most general sense, Being and Event by and large concerns itself with a very specific field of mathematics, namely set theory. Badiou recasts this as the theory of ‘pure multiplicity’, a reference to the fact that sets do nothing more than gather together their multiple elements and count them as one. There are reasons for this choice, of course, not least of which is the role that set theory plays within mathematics. Set theory acts as a kind of internal ontology of mathematics, certainly in the weak sense that any mathematical entity can be thought of as a kind of set, and arguably in the strong sense that mathematical entities actually are sets. For example, the mathematical concept of an ordered pair <a, b> is distinct from that of the set {a, b}. The former has an ordering that makes a its first element and b its second. The latter, in contrast, is a pure multiple without any kind of order inscribed upon it. But although ordered pairs are conceptually distinct from sets, they can be implemented as sets by defining the ordered pair <a, b> as the set {{a}, {a, b}}. The reader can check that given any set of this form, one can extract the first and second elements from it. Ordered pairs can thus be simulated through the intricate weaving together of pure multiplicities. The same, arguably, is true of any other entity used in mathematics.
But while set theory plays an important foundational role in mathematics, that is almost all it does. The concepts and techniques it deploys are of little interest to the ‘working mathematician’, most of whom get by with only a smattering of knowledge of the field. Only occasionally does a problem in general mathematics turn out to revolve around set-theoretic considerations – though such occasions can and do arise, which is why set theory cannot simply be dismissed a province for pedants and philosophers.
All this opens up an intriguing problem: what is the ontological significance of the rest of mathematics, the overwhelming bulk of mathematics, once one moves beyond the limited terrain of pure set theory? Far from being the final word on the question of being, Badiou’s identification of mathematics with ontology opens the door to a vast ‘meta-ontological’ research programme, one that scours the entirety of contemporary mathematical thought, elucidating its concepts and thinking through their metaphysical implications. Indeed, Badiou’s own work occasionally hints at this larger research programme. In his essay ‘Group, Category, Subject’, he argues that the mathematical theory of groups can act as a grounding framework for the psychoanalytic notions of subjectivity found in Lacan and Freud. In ‘One, Multiple, Multiplicities’, his rejoinder to Deleuzean critics, Badiou argues that notions of the ‘open’ and the ‘closed’ should ultimately refer back to the way these concepts are deployed in topology.
The most systematic exploration of a region of mathematics outside its foundational core comes in Badiou’s short book Number and Numbers. It was published in 1990, a couple of years after Being and Event, and has now been expertly translated into English by Robin Mackay. In it Badiou examines what mathematicians call the ‘surreal numbers’ – a class of number-like entities that incorporate familiar species of number, such as the integers, the rationals and the reals, but also encompass less familiar ones such as transfinite ordinals and infinitesimals (ie infinitely small quantities). The surreal numbers were introduced by the mathematician John Horton Conway as a byproduct of his investigations into Go, the ancient Japanese board game. Conway simply called his creations Numbers – the term ‘surreal numbers’ was coined by Donald Knuth in his peculiar 1974 booklet of the same name, the text that introduced Conway’s creations to the wider public. Knuth’s terminology has since stuck. Significantly Badiou reverts to calling them Numbers, despite the fact that in other respects his approach is diametrically opposed to Conway’s recursive and constructivist presentation.
Badiou sets out his stall in the polemical opening pages of Number and Numbers – a chapter numbered zero and entitled “Number must be thought”. In it he notes the profusion of different types of numbers, both within mathematics and in culture at large, and contrasts this empirical extravagance with the stubborn absence of any unifying concept of number. It is to remedy this deficiency that Badiou turns to the surreals and presses them into service. He notes that the class of surreals subsumes all the heterogeneous entities we ordinarily like to think of as numbers, and a whole lot more besides. Yet as a class they can be defined in a uniform and relatively straightforward manner. They are both comprehensive and simple – and for Badiou the simultaneous presence of these two virtues is the calling card of the properly ontological. The surreal numbers are thus more than a curiosity or a neat trick: they capture the essence of number itself. The Numbers tell us what number is.
Much attention has been paid to the political gloss Badiou puts on his project here. The book’s back cover blurb presents his attempt to construct a rigorous concept of Number as a broadside against ‘the political regime of global capitalism’ and its reliance on a concept-less and ramified numerosity. Despite my sympathies with Badiou’s leftist politics, I find this claim overblown. While it is certainly true that capitalism presses numbers into its ideological service, it is not clear how a rigorous concept of Number would per se challenge such abuses. And surely the problem with opinion polls, stock market prices, econometric models and so on resides not in the maths as such, but in their tenuous relationship to reality. The now-discredited formulae used to price financial derivatives are still perfectly effective and compelling when used by physicists to model Brownian motion.
These caveats aside, Badiou is right to point out that contemporary thought has a blind spot when it comes to number, and right to attempt to remedy this deficiency. The next half dozen chapters proceed to survey earlier attempts to think number by Frege, Dedekind, Peano and Cantor in the late nineteenth and early twentieth centuries. This is the most accessible section of the book and is valuable in its own right as a thorough introduction for non-specialists to the philosophical and mathematical issues at work here.
The treatment of Frege gives an insight into Badiou’s approach. We start with a firm focus on the metaphysical stakes of Frege’s project – the conviction that numbers can be engendered from pure thought. We are then guided through Frege’s construction of number, its demolition and partial repair at the hands of Russell and Zermelo, before coming to Badiou’s materialist critique. Frege ultimately fails because one cannot derive the existence of objects from pure thought. The existence of something rather than nothing is an ontological axiom, not a logical necessity. Yet there is a twist in the tail – Frege’s masterstroke of starting his consideration of number from zero rather than one turns out to lay the foundations for a materialist ontology capable of providing a framework for the thinking of Number. All this is achieved in nineteen terse, numbered paragraphs.
Having completed his historical survey, Badiou moves on to recapitulate certain aspects of set theory and ontology – material that will be familiar to those who have read Being and Event and that acts as a useful companion to that work. He then proceeds to use this set-theoretic machinery to define Numbers, demonstrate that they have a natural linear order, and prove a variety of theorems about them. The book culminates in the definition of basic arithmetical operations such as addition and multiplication, and the verification that these operations obey the standard algebraic laws one would expect. As is often the case in Badiou’s work, the mathematics he presents is standard, though the presentation of it is tweaked to reflect his philosophical agenda. For instance, Badiou defines a Number to be a specified subset of a specified ordinal. This is not a standard definition, though it can be shown to be equivalent to those found in mathematical literature.
The merit of Badiou’s approach here is its low ontological overhead. Number is defined more or less directly in terms of the basic set-theoretical relationships of belonging and inclusion. In particular, the definition goes through without reference to any prior notion of order, seriality or counting. Number is thus sundered from any kind of intuition or empiricism and rendered purely as a ‘form of Being’. It is also worth noting that Badiou’s approach to Numbers makes them appear ‘all at once’, so to speak. The entire field of surreal numbers is defined in one fell swoop – the weirdest and wildest Numbers born simultaneously and alongside familiar entities such as 2, –17 and ¼. This is in sharp contrast to Conway’s generative approach that starts from the integers and progressively creates ever more complex surreals. The contrast is even sharper with Knuth’s take on Conway, which is framed in explicitly theological terms as a creation parable involving God and a pair of maths-besotted hippies.
These and other fascinating technical intricacies aside, the big question is whether any of this works. Does Badiou supply a coherent, unifying concept of number that is consistent with his wider ontological project? Does he manage to succeed where others have failed in ‘thinking Number’? In my judgement the answer is a provisional and cautious ‘yes’. Badiou’s metaphysical take on the surreals is bold and startling, but it does provide an answer to the question ‘what is number?’, albeit one that is most persuasive to those already partial to Badiou’s views on these matters.
Nevertheless, some warnings are in order, most of which revolve around the mathematics of surreal numbers. Despite the astonishing beauty of the surreals, attempts to make use of them in wider mathematics have so far foundered (at least so far as I am aware). For instance, while the surreals admit particularly neat definitions of addition and multiplication, exponentiation proves to be significantly more awkward. Moreover, these definitions do not easily yield a practical algorithm for calculating arithmetic sums and products, as one might have hoped. And while the surreals include all manner of infinitesimal quantities, it has proved exceptionally difficult to develop calculus using these infinitesimals. The surreals promise much, but have so far delivered little.
But is it just a coincidence that the surreal numbers, like set theory, turn out to be of little practical use for the working mathematician? Perhaps there is a necessary disjunction between ontological importance and practical utility. Perhaps the ‘use’ of these regions of mathematics is precisely to act as an ontological foundation for the rest of mathematics, and we shouldn’t expect anything more of them. Perhaps ontology is the discourse that picks up precisely at the point where practicality has nothing left to say. This would be a surprisingly Heideggerian conclusion to draw from Badiou’s austerely rationalist vision, but one that would be in keeping with his distrust of the dimly empirical.
Kant’s notion of ‘critique’ in the Critique of Pure Reason
The publication of Kant’s Critique of Pure Reason in 1781 is widely seen as inaugurating the era of modern philosophy. It is the first of Kant’s three great critiques. Together these works systematised a new conception of subjectivity that gave birth to the German Idealist movement. They remain profoundly influential over two centuries later.
Kant’s notion of “critique” undergoes revisions during this period, although the basic themes are there from the outset. In particular, the concept is reworked between the CPR’s first and second edition, published in 1787. Kant responded to debates sparked by the first edition by rewriting the book’s opening chapters to defend and elaborate his stance. These changes include the famous characterisation of the critical project as a “Copernican revolution” in philosophy (CPR, Bxvi).
The two editions of the CPR have inspired different interpretive traditions. The first edition lies behind the dominant German reading, which focuses on the faculty of imagination and culminates in phenomenology. The French and English language readings, in contrast, tend to focus on epistemological concerns and take their cue from the second edition.
This short essay examines the concept of critique as outlined in the ‘Preface’ and ‘Introduction’ to the CPR, and the shifts that take place between the two editions. I look at how an initial judicial version of the critique is elaborated into a scientific project and an ethico-political one. Kant’s concern is to found both projects securely, in a single gesture, through the precise demarcation of the borderline between them.
Preface A: critique as tribunal
The preface to the first edition of the CPR (‘Preface A’) is a short polemical work – a philosophical manifesto that situates Kant’s new critical project with respect to its rivals and outlines its basic duties, standards and aims.
It opens with a celebrated description of the parlous state of contemporary metaphysics as a “battlefield of endless controversies” (CPR, Aviii). Kant draws out this metaphor, in a somewhat convoluted manner, to describe his main philosophical opponents: dogmatism, scepticism, empiricism and indifferentism. Critique, it will transpire, is opposed to all four schools.
The dogmatists are the dominant rationalist metaphysics of Leibniz, especially as interpreted by Wolff and Baumgarten. They are described as a despotic “queen” that was once revered but is now despised and besieged by the “nomads” of anarchist scepticism – a reference to Hume’s devastating attack on the metaphysics of causality.
Locke’s empiricists try to save the day, but their attempts fail. Metaphysics to fall back into “indifferentism” – the pop philosophy of Kant’s day that supported the pieties of dogmatism with glib common sense. Kant scarcely conceals his contempt for this latter school of thought.
To resolve this chaos Kant institutes a “court of justice” that will be “none other that the critique of pure reason itself” (CPR, Axii). Critique is thus introduced as a kind of tribunal that passes judgement on warring metaphysical parties and draws up a just settlement that all must abide by.
The spirit of Enlightenment political thought is palpable here. In a footnote, Kant claims that “ours is the genuine age of criticism, to which everything must submit” – even religion. Reason only grants “unfeigned respect” to that which can “withstand its free and public examination”, and religion’s majesty offers it no exemption from this interrogation.
Critique at this point is characterised by its reflexive nature. Reason turns its gaze upon itself and embarks on the difficult but necessary task of self-knowledge. This will allow it to secure its rightful claims, not by mere decree, but through its own legislative capacity.
Kant ends the ‘Preface A’ by stressing the preparatory character of critique. It is an arduous task, but one that clears the ground for a truly scientific metaphysics. It is this promise of future scientificity that dominates the rewritten preface found in the CPR’s second edition.
Preface B: critique as revolution
The ‘Preface B’ is differs from its predecessor not just in length and detail, but also in terms of its tone and concerns. The breezy self-confidence of the earlier preface is replaced by a furrowed brow, determined, laborious and at times defensive.
It opens with a question that returns insistently over the next few pages. Can reason in general and metaphysics in particular be set on “the secure course of a science”? Or is it condemned forever to “merely groping about” in the dark and at random?
Kant begins his answer with a historical survey of scientific reason to date. He considers logic, mathematics and physics, highlighting aspects of each form of thought that enabled it to successfully attain scientific status.
From logic – a discipline Kant views as essentially complete – we draw a simple but vital lesson. The power of logic, Kant argues, is intimately connected to its sharply delimited boundaries. Attempts to “improve” logic by enlarging its scope end up merely disfiguring it. The freedom of science is thus founded upon restraint in its sphere of application.
From mathematics and physics, Kant points to the active role of reason, revisiting the judicial metaphor of ‘Preface A’. Reason approaches nature with principles in one hand and experiments in the other. It does so to learn from nature, not as a pupil learns from a teacher, but as a “judge who compels witnesses to answer the questions he puts to them” (CPR, Bxiii).
Kant distils the lessons of this survey into his call for a “Copernican revolution” in metaphysics. The scientificity of mathematics and physics arise through a revolutionary break whose essential element is the inversion in the roles of object and subject. Rather than cognition conforming to objects, objects must conform to our cognition. We are the mobile and active element, not the stars that we gaze upon – hence the reference to Copernicus.
The precise procedure of this new scientific metaphysics is set out in a footnote on page Bxviii. Kant says his method is “experimental” in the sense that it posits distinctions. If these distinctions succeed in removing an otherwise intractable contradiction, the “experiment” is considered a success, and the scientific status of the distinction confirmed. This description concisely captures Kant’s actual method of argumentation throughout the CPR.
The second half of ‘Preface B’ is concerned with spelling out some consequences and benefits of this Copernican revolution in philosophy. In particular, Kant returns to the theme of how rigorously specifying the limits of pure reason can secure its scientific foundations.
This delimitation has a negative function – it debunks the “pretension to extravagant insight” of dogmatic metaphysics, and neutralises contradictions between metaphysical principles and those of Newtonian science. But critique also has a positive ethico-political role to play in terms of grounding the possibility of human freedom.
For instance, distinguishing objects of experience from things-in-themselves, and restricting the domain of causality to the former, prevents us from binding the soul with the same rigid laws that operate among phenomena (CPR, Bxxvii). Similarly, pure reason’s inability to provide proofs of the existence of God opens up a space for practical reason to operate – we “deny knowledge in order to make room for faith” (CPR, Bxxx).
The critique of pure reason thus lays the groundwork for the reconciliation of scientific and ethico-political forms of thought that were previously at loggerheads. It does so through the rigorous specification of its own limits – and it is to that specification that Kant turns to next.
The Introduction: critique as a special science
The ‘Introduction’ to the CPR does not undergo quite the same drastic rewrite between editions as the ‘Preface’. But Kant does expands the text significantly, adding sections that parallel the shift of emphasis between the two prefaces. These lay out a detailed discussion of mathematics and physics to justify and motivate analogous but more controversial metaphysical claims.
The ‘Introduction’ proceeds by setting forth distinctions that rapidly narrow down pure reason’s field of cognition. First we set aside empirical cognitions in favour of those that are purely a priori. Then we distinguish analytic judgements that merely clarify what has already been thought from synthetic ones that are truly creative. Pure reason is concerned with these synthetic a priori judgements, which Kant claims can be found in maths, physics and metaphysics.
The “general problem of pure reason” is recast in terms of asking how synthetic a priori judgements are possible. The critique of pure reason – conceived once more in reflexive terms as reason examining its own presuppositions – is thus presented as a “special science” that acts as the key to unlocking the more general question of scientific metaphysics.
Kant wraps up the introduction by reprising his argument about the autonomy of practical reason, though this sphere is now more rigorously specified as that of cognitions that are a priori but cannot be entirely separated from empirical experiences of desire and pleasure (CPR, B29). He ends by setting up the distinction between passive sensibility and active understanding – at which point the Critique of Pure Reason proper begins.
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