What is the problem of which metaphysics is the enquiry?
If we pass by Heidegger’s imagistic allusions to soil, themselves extrapolated from Descartes’s letter to Picot outlining the arborescence of philosophy – a metaphor as we know Deleuze turned on its side – perhaps it was the great rival to Heraclitus, Parmenides who, eschewing organic metaphor altogether, truly expressed it best: the same is to think as to be.
The gap, indistinction or indiscernibility between ‘thought’ or thinking and ‘what is’, by no means necessarily a ‘separation’ to be resolved, is what metaphysics names, and as we have seen in the preceding lessons working out the places and operations implies and entails a lot of to-ing and fro-ing, of back and forth, of what Freud termed fort/da.
Parmenides’ injunction or possibly declaration is in no way an answer; rather it is the task for philosophy to take up, the consequences philosophy draws each and every time it exists. Every time it is made or unmade, this declaration marks the recommencement of philosophy, and it provokes, every time, the question: ‘what is the form of the discourse by which being lets itself be said?’
The answer, evident in the developed orientations to it – analytical, phenomenological, existential, formal, deconstructive etc. – will in turn position being and thought with regard to each other. It will decide: what of being can be thought, and thus what (is) not. In other words, it establishes being to thought – whether as potential, limit, chaos, imaginary, whole, indeterminate, inconsistency and so on. Parmenides’ declaration – which was even a declaration of war or polemos against Heraclitus, the type of declaration the latter would have to respect – separates the thought of being from the imperative of nature, insofar as insisting on the indifference of being and thought is to unify them only in terms of the void – the nothing that is.
What makes them indifferent cannot be something or other, some third thing relative to them. There is literally nothing to tell them apart. In other words, it is by no means necessary to the thought of being that being and nature be conflated as phusis, or in any other fashion, hidden or vital, driven or willed. As such, it becomes possible to say that if being can be thought outside the varieties of adequation, then nature does not exist.
Being can be thought not only as not nature per se, but by a form of thought that is absolutely un-natural and absolutely rational — right up to the point of demonstrating as consistent the inconsistency at its own heart. Thus, by existing, this discourse – being the thought of being qua being – refutes natural being by being what it is not. To jump ahead, this means that the thought of being as such can be the thought also of real change: thinking what is in exception to it. Metaphysics is not constrained to be either the impossibility of change, as in Parmenides, or the all of change, as in Heraclitus. Metaphysics is the site of a war on two fronts.
The declaration of Parmenides, under all its possible interpretations, remains the recognisable core of all metaphysics. It is audible for instance in the famous ‘know thyself,’ which for Plato can only be a task: not because being is ineffable, but because it already contains a division; which is to say, it insists on a thought of the void as what must be traversed. The knowing of the self is the knowing of the division at the core of thought as the impetus to thought. The problem evoked here is of the in-discerning of inside/outside, finite/infinite, mediation/immediacy etc., all relays of the initial decision on being being thought. A distinct strategy since Nietzsche, broadly agreed to by a coterie of seemingly diverse and opposed thinkers in the twentieth century, has been to deny the problem as such. For if, as a problem of metaphysics it is ‘metaphysical,’ and if metaphysics is what must end for the thought of being to truly be, then the question, in Wittgenstein’s terms, is outside the sayable as such.
The upshot of this strategy is that to say that ‘the same is to think as to be’ is itself propositionally unsayable, and so shouldn’t be said if one wants to make sense. Even if Heidegger did re-open the question of being qua being as an anti-platonic gesture and so in terms of being, being said, he did so under the injunction of language or of the poem. This re-opening is in a certain sense to comply with Wittgenstein’s injunctions about the co-incidence of the limit of thought and world as only thinkable to language. What is without language is nonsense for Wittgenstein, while for Heidegger the poem speaks being such as it is free of what annuls it: precisely, Plato’s idea, the inaugural and mathematically conditioned gesture of metaphysics.
Hegel already pointed out when thinking through this problem vis-a-vis the eudemonists and their realisations in Kant, that those who claim to abandon metaphysics can often be seen to do so on metaphysical grounds. It is always, for them, Hegel says, the question of identity – or of a unity in some way. Today’s version of this identity is surely the market as imagined in the Hayekian sense as at once beyond our reason yet amenable to it in some way – in fact, as that to which human being naturally tends. It is reasonable, the refrain goes, that we do not know what the market knows – such knowledge being virtually absolute and so beyond our capacities.
What the market knows and we never can attain, is precisely, the ends of our reason nevertheless. It is our limit and our destiny. Its potential is what we act out, thus making known to us our true nature. This non-knowledge at the heart of our knowledge which is thus the very knowledge of our being, the very thing we cannot know, is a sophistic convenience, which is to say it is an ideology at the level of practice. Ideology should not be understood as a negative term here; it just marks a function. What is negative about ideology is its use as a negative by those who practice it necessarily and deny it actually – in fact, denial and occlusion are the positivist essence of ideology.
For Hayek et al., and there are many in this et al. as we know – known to it and unknown to themselves both – the market is not an ideology and not, thus, a metaphysics. It is supposedly a fact of our existence, and the fact or pragmatics of our existence is to naturally fall short of knowing by nature: thus we cannot know; better we submit to this nature than attempt to scale the mountain of what we are capable of. If we reconcile ourselves to this finite framework, empirically attested or, as the self-styled anti-metaphysicians like to say, ‘evidence-based’ (so long as we agree the parameters), what we are capable of will be revealed in good order as in accord with such a nature.
But clearly this is the assumption that consists in metaphysics: the assumption of the true nature of our nature or what we might call subject as subjection. It’s one option but, as always, relies on a prioris off limits to creatures like us. So these conclude with what they contend, and thought, in the sense of an intervention on this construction itself, becomes an annoyance best disavowed, just as Plato’s Socrates was disavowed by the panoply of ‘patrons of the flux’ and thinkers of the state contemporary to him. Thus thought in the sense that aims at what we are capable of, must be precisely exceptional to facts of existence, not being this creature of the limit, thus, not being the subject of this constraint regulated by the rule of language, world, sense, nature or horizon, and so on. In other words, thought requires a subject-figure that does not by the necessity of its nature return to the rule.
What, then, does it means to hold that nature does not exist? If such can be thought, thought that interrupts the adequation between nature and language, Being and beings, then a whole swathe of metaphysical and anti-metaphysical traps might be sprung – given that, on either side, some sort of natural ineffability serves to unify their opposition.
Alain Badiou’s ontological intervention is to show that the rule as such, which is always some assumption of what it is to be – phusis/market/fact etc. – posits itself as incomplete, thus leaving open the space precisely for: first, some form of thought that can think incompleteness as such, in other words ‘actual infinity’; and second, some subject which is not at all reducible to some rule. Thus, something else can be thought. Certainly the theme of the impasse is explored constantly in Plato and in Plato the geometric paradigm, as the ‘Platonist’ Gregory Vlastos labels it, serves as that which forces the impasse to which all the Athenian language games concede, with great shows of satisfaction. If, on the contrary, this impasse can be thought, we avoid precisely the circularity inherent to classical metaphysics and to its supposed contraries: in this sense both metaphysics and anti-metaphysics succumb to the same circle. It would then be this same/difference, rather than metaphysics as such, that needs to be terminated altogether.
In his first Manifesto for Philosophy, Alain Badiou announces his project under a double Platonic disposition: as a ‘Platonic gesture’ correlated to a ‘Platonism of the multiple’. The latter phrase marks the renewed necessity of an ontological project in the wake of and contra Heidegger; the former the formal arrangement for the thinking of truth or truths. Since a truth is what is truly new, this makes truth (once again) ‘a new word in Europe.’ This double dispensation is necessary if philosophy — a term Badiou happily interchanges with metaphysics — is to ‘return to itself’ and not submit to the incessant calls for its end: that its ends be circumscribed, that it end or that it has come to its end. Against this tendency toward ends, philosophy, Badiou argues, is possible: ‘the crux of the matter is to know what the following means: taking one more step. A step within the modern configuration, the one that since Descartes has bound the three nodal concepts of being, truth and the subject to the conditions of philosophy.’
In several works Badiou gives shape and form to what such a re-newed philosophy must traverse and pass through; it is, as we know, to this adversary that he gives the catch-all term ‘anti-Platonism.’ ‘… that constellation of multiple and heteroclite ‘philsophies and anti-philosophies that taken together, makes ‘their anti-Platonism incoherent’ but, as we know, what unites them is that each ostensibly accuses Plato of being ignorant of something essential to philosophy and ‘this something is identified with the real itself’: as we have seen; change for the vitalists, language for the analytics, concrete social relations for the Marxists, negation for the existentialists, thought in as much as it is other than understanding for Heidegger, democracy for the political philosophers. And for Badiou, ‘Platonism’ is the great fallacious construction of modernity and post-modernity alike. It serves as a type of general negative prop: it only exists to legitimate the new under the heading of anti-Platonism.
To recall: there are three predominant ‘philosophical’ tendencies of this anti-Platonist collective: 1) the hermeneutic tendency, whose central concept is interpretation; 2) the analytic, whose concept is the ‘rule’; and 3) the post-modern, concerned with the deconstruction of totalities in favour of the diverse and the multiple. In common they have: a commitment to language, its capacities, rules and diversity such that language is the ‘great transcendental of our times’. A and this is the content so to speak of the commitment to the end of metaphysics and thus philosophy since Plato. Hence the modality of a reversal whose procedure ‘puts the category of truth on trial’.
Nonetheless, Badiou agrees with two allegedly anti-Platonic claims that arise from the contemporary critiques: Being is indeed essentially multiple; and Plato does indeed mark a singular and decisive point in the history of thought. Here Heidegger as much as Deleuze is a central figure of reference.
However, in regard to the first point of agreement, to say being is multiple today is to say that it falls under the regime of mathematics qua ontology and not ‘language’. Badiou’s position is thus to invert this accusation and argue that it is precisely Plato’s conception of what there is that matters and what there is are truths whose ontological status is at once undecidable and generic and whose presentation is evental, thus exceptional, and subjective.
In regard to the second point, Plato is to be understood as the incitement to thought, through whom thought is given ‘the means to refer to itself as philosophical’ and thus ‘independently of any total contemplation of the universe or any intuition of the virtual’. Plato is decidedly not the moment at which thought turns to despair. For Badiou, the rejection of the linguistic (re)turn is predicated on the existence ‘of a regime of the thinkable that is inaccessible to this total jurisdiction of language.’ What is required therefore is a ‘Platonic gesture’ whose condition is a ‘Platonism of the multiple’.
So, what form of discourse can think being, such that the void of being’s relation to thought is at its core, yet can think the what is-not-being-qua-being as rational for it? For Badiou, following and extending Plato, mathematics alone is capable of such a thinking. It is, he says, the ‘science of being qua being’ or mathematics (qua discourse) is ontology. The entirety of Being and Event is the demonstration of the veracity of the consequences of this philosophical decision. Invoking all necessary qualifications and precautions against the over excitable, both analytic and continental, this has been the most misunderstood decision of Badiou’s philosophy: mathematics thinks or is the discourse of or the science of being qua being.
In the first instance, then, philosophy is divorced from ontology. Extrapolating on his own interrogation of this decision via set-theory – which couples to it a theory of the event, the generic form of a truth and thus its ‘subject’ – Badiou will argue that mathematics has always been ontology. Not that mathematicians are decidedly ontologists, but, given that what they work on is literally nothing, not being as object, as substance, or as an ‘empirical given,’ it is being itself which they inscribe in the numbers and letters which make up their discourse.
Out of the void, then, which, as Badiou establishes, is the ‘name of being’ – the name of what is un-presented in presentation as such, pure multiplicity and not One – ontology constructs an entirely consistent and infinitely extensive system of thought. Thus mathematics thinks of being what of being can be thought. Philosophy, then, as Descartes made allusion to, is under condition yet thinks in its own terms, thus relative to the concepts and categories it renders thinkable, the thought of being as such. This makes of mathematics itself a thought, something philosophy after Plato has always been less than willing to grant. Even when it has shown mathematics all due respect, philosophy has almost always assumed that it can go one better when it comes to thinking what is to be. Philosophy has considered its operators conceptually superior to the technical (or aesthetic) specificities of mathematics, even when it is plainly number which is at stake – the one and the many, parts and wholes, the finite and infinite.
If mathematics is integral to philosophy as a condition it is also crucial in that it both demonstrates that the thought of being is possible and consistent, thus rational and not indeterminate, senseless or theological. Mathematics is a discourse which is not reducible to or subsumable within the framework of language: neither the well-made language of logical positivism and its heirs in the analytic tradition, nor the poetic, fragmentary form it takes in post-Heideggerian post-modernisms, nor, finally — though this constitutes an entirely distinct relation in Badiou’s thought — the place assigned to language in psychoanalysis.
But this introduction of mathematics here is to get ahead of the game as it were, given that in the essay whose analysis forms the bulk of this lesson, Badiou posits this rational interruption of metaphysics only at the end and under the signification of what he calls a Platonic gesture.
In the essay ‘Metaphysics and the Critique of Metaphysics’ – which we will essentially follow from here on in – Badiou names this Platonic project, noting the paradoxical form of the utterance, as a ‘metaphysics without metaphysics’: a metaphysics that in its first indication cleaves itself as dialectical from a pre-Kantian ‘classical metaphysics’ and from its post-Kantian (but not simply Kantian) modern negative variant, ‘archi-metaphysics’.
However, this Hegelian dialectical metaphysics must itself give way to the second Platonic gesture, to a mathematical and thus ontological reconsideration of ‘the links between finitude, infinity and existence’: This second gesture is to ensure that being and truth remain thinkable in their division and, moreover, that this division not be characterised or over-determined by any extrinsic knowledge as to their coupling: not by a theory of correspondence, adequation, transcendence or language.
As so often in Badiou’s work a negation provides the impetus of interrogation (like Stalin!). So he moves from the rejection of anti-platonism to an analysis of the impossibility of the void as what marks the history of ontology from Aristotle to Heidegger – passing through Spinoza, Leibniz and Hegel – to disprove the positive assertion of ‘democratic materialism’: that no exception exists to its double remit concerning the existence only of bodies and languages.
Conversely, we also often see the affirmation of an impossibility, contrary to what particular philosophies conceive as their rational kernel: in reading Hegel, we find Badiou’s counter-affirmation of the inexistence of the whole; in Deleuze, the affirmation of the impossibility of the eventum tantum (or even that multiplicity drives the Deleuzian metaphysics); in Aristotle or Spinoza, the affirmation that the void insists for thought.
These interrogations have in common the axiomatic that organises Badiou’s philosophy: that the One is not, and, if the One is not, then the nothing is. This axiomatic, which contemporary post-Cantorian mathematics provides, is the basis for Badiou both of a reinterrogation of philosophy tout court, and a point of orientation of and for the present of philosophy. The critique of prior metaphysics, then, begins in this same way: claims to ‘the end of metaphysics’ organise the entire contemporary system of reference, from Kant to the present. For such post-Kantians, metaphysics is either obsolete or in crisis. That it’s dying, it should die; that it’s in crisis, that it be radically overhauled such that the means of its confinement attest to the rightful antipathy of contemporary ‘rationality’.
The productions of this ‘opera of the end’, as Badiou calls it, vary. He delineates 4 ‘librettos’:
1. Critique: Kant’s critical limitation of the reaches of dogmatic metaphysics (as we’ll see, the metaphysics which accounts for or even counts the indeterminacy of God in its systematics) as too ambitious or categorically promiscuous; the intellectual, political and historical exhaustion of what metaphysics was supposed to provide as the virtue of knowledge or its guarantee.
2. Positivism. A rational positivism, as ‘mathematized experimentation’ based in the empirical sciences – or in a knowledge of them – substitutes its virtues for the exhausted guarantees of an indeterminable God. Comte, Wittgenstein and Carnap serve to name the arbiters of this paradigm for Badiou here.
3. Dialectics. The dialectical refusal of any metaphysics of the one in the sense of eternal, stable entities supported by ‘fixed categories’, ‘which metaphysics’, Badiou declares, being the ‘mutilation of thought’, allows ‘something like a submission to death to prosper’. Hegel, Marx, Nietzsche, Freud and Lacan name this deposition of the ‘principle of identities’ in the name of the real of contradictions and ‘concrete becomings’.
4. Hermenuetics. Referring to Heidegger without naming him, the epochal nature of the return of the dead Gods: ‘that which discerns under the name of metaphysics the nihilistic disposition of the entire history of the West.’ This is what must be reversed and thus metaphysics itself must, via a patient hermeneutics, come to nothing. Its origin, as it were, must be unfounded such that the history of the present be revoked. Natural being, phusis, ‘holds sway’ against the Idea (174-5).
These four operas, Badiou avers with all seriousness, do violence to philosophy as cry, insult and mockery. Eschewing a more extended account of Badiou’s somewhat ironical review of the charges – including Kantian hubris, Comtean physical and political pathology, and Heideggerean global terrorism – what we need to note is that their general consensus turns on the impossibility of metaphysics to think the new.
For Kant, nothing new is achieved in all the ‘chatter and bustle’ of metaphysics, which has effectively remained unchanged since Aristotle; for Comte, metaphysics is not only a sickness (‘but is it so different for Kant? And will it be so different for Wittgenstein, or Heidegger?’), but also the ideological apparatus of a certain formation of power. In both cases, it blocks ‘a strategic passage: the passage between philosophy [Comte’s] and social order’ or ‘the “social installation” of anti-metaphysical philosophy.’
As for Heidegger, the reign of metaphysics as Idea suppressing the nature of being as coming forth, culminates in the enframing of the entire earth qua technology. Thus, while referring to Nietzsche as the last metaphysician via his ‘will to power’, Heidegger finds the ‘the truth of Being … replaced by machination’s erection of ‘goals” (values). As with the Platonism of the anti-Platonists, the metaphysics of the anti-metaphysicians is what it is because it leaves something out: ‘the true nature of what is’. And thus ‘what is to be feared in [metaphysics] is precisely the apparent weakness of its content’ (177-8).
Ultimately, then, what is left out is thought itself, given it must name what addresses itself to this ‘what is’ under the mode of a formal clarity – whether that be of the critical, positivist, hermeneutical or clearing type. But we might venture, it is thought as a peculiar form of salvation – not just for Heidegger, clearing space for the Gods, but for Kant too, so as to save man himself as author of subjective reason; for Comte as access to the world as such devoid of ‘vaguery’ and ‘equivocity’ (179).
What remains over in each of these thinkers is the supposition that metaphysics stripped bare reveals the extant truth of being as such. One is reminded here of Nietzsche’s comment regarding truth being a woman and philosophers being ‘clumsy’ and ‘unskilled.’
Badiou says: ‘What makes metaphysics fearsome is that it ignores the discipline of the true questions in favour of an indeterminacy that any signifier of mastery whatsoever can come to inhabit’ (178). Metaphysics thus is fiction: the search for (the) truth (of being) in name only – hiding in fact a true indifference to it. Thus the anti-metaphysician (so, physicians of the cure) are the true champions of truth. After Heidegger, putting into play the adage that the cure is often worse than the disease, Badiou avers that much of contemporary philosophy, in a strange parody of this claim against the indifference of metaphysics, simply excises truth from all consideration – other than, perhaps, as virtual adjunct to an affective knowledge: the logical rule in analytic philosophies or the transcendental ground for the equality of opinions or perspectives in post-modernisms.
So this is the horn of the dilemma for the varia of anti-metaphysician – the proper approach to being is occluded as metaphysics, which posits an in-determinacy at the heart of its rationality. Anti-metaphysics counts indeterminacy qua indeterminate in what can be thought. It not only holds off from interrogation of the indeterminate as indeterminate, but occludes the necessity for the indeterminate in the very form of its rationality. Hence anti-metaphysics is a dogmatic metaphysics, asserting as reasoned the full place of the indeterminate – God as we know it, but as Badiou says, any ‘master signifier’ whatever – and thus feeding off of its ‘own inability to attain knowledge’.
Badiou notes that Kant had already spotted what Heidegger makes palpable as the necessity of its end: ‘that of the indifference of non-knowledge’ qua the question of Being (178-9). Because Badiou’s interrogation of the anti-metaphysicians as the proponents of an ‘archi-metaphysics’ allegedly subversive of and directed towards power ‘dogmatics’ shows how they maintain being in the place of being undecided, this master signifier must be dealt with. The surprise is how they go about it.
Badiou is able to weave together under this designation of an archi-metaphysics – a designation none of its proponents aspire to – its critical, positivist and hermeneutic strands. He shows how the delimitations of each, real in their operational form, nonetheless conform in the orientation and structure of their address: annunciation (indifference), determination (of the indeterminate) and desire (end). Badiou is thus able to argue for how certain utterances and determinations of Heidegger resonate back into Kant (e.g., the analysis of the power of metaphysics as occlusion), and that Comte pre-empts Heidegger’s claims for the onto-theological destination of metaphysics, the famous ‘forgetting of forgetting’. Badiou cites Comte: “‘Metaphysics is in fact nothing but a form of theology gradually enervated by dissolving simplifications’” (179).
These remarks highlight what each archi-metaphysician in their own defense would no doubt seek to occlude. So Badiou demonstrates the negative nature of their conceptual alliance. Indifference, simplification, abstraction, separation, dissolution: such are the operations through which, under the accepted name of metaphysics, the power of a neutral thought, or of the object-less argument, establishes itself. The power of the undecided and the undetermined as such (179).
I cite this to pre-empt: for what everything archi-metaphysics opposes of dogmatic metaphysics, Badiou, in slightly different terms and by subtractive rather than strictly negative operations, will affirm. But in affirming that thought must affirm the existence of the indeterminate as thinkable, Badiou will, via the contemporary mathematics of set-theory, break also with the dogmatist schematic, such that the infinite or indeterminate is not potential, and so off limits to thought as such, but actual. And so, contra archi-metaphysics – and the latter distinction draws many more contemporary thinkers into the archi-metaphysics remit – what is, the infinite, is actually thinkable as such: it is not the known or determined un-thought of all thought.
The infinite is neither ineffable nor determined. After Cantor, the infinite is not off-limits to thought. The saving grace of archi-metaphysics, that it knows the infinite qua indeterminate, whereas the dogmatists treated it as resource for knowledge, saves only the indeterminate whose thought it was to have deposed. The indeterminate – on the basis of the say-so of dialectics but not as a dialectics – must therefore be thought again. Hence the indeterminate becomes actual not virtual: thinkable, but outside the constrictions of language (critical, positivist, hermeneutic).
Just as Plato was wont to do with Homer, Hesiod, Heraclitus, and Protagoras, Badiou will ally these hermeneuts and critical reasoners with the contemporary positivists or ‘partisans of linguistic empiricism’ for whom metaphysics, by its utterances, makes no sense – the holy grail of logical positivism. Citing Wittgenstein and Carnap, but following the former through the chicanes of the final propositions of the Tractatus (from 6.40), in which Wittgenstein imposes, by turns subtly and in sledgehammer style, the limits of our world as being the limits of our knowledge (language): beyond this being said is what is mystical. Hemmed in by this tautology, of sense making, reminiscent of the great Protagoras, we are condemned to say as subjects of metaphysics, only what can be said.
Such a trajectory is of course proper to philosophy, Wittgenstein says. To take the propositions of natural science – i.e. something that has nothing to do with philosophy – and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions. Although it would not be satisfying to the other person – he would not have the feeling that we were teaching him philosophy – this method would be the only strictly correct one.
It is curious that the motif of a certain stealth must appear in this archi-metaphysics, that thought itself is too much for us to bear. So we must outsource what is right and to a logic of sense that remains apart from and exceeds that of which we are capable. Yet this stealth and this mysticism claims to be rationally deduced. Once again we see the unconscious at work: ‘For Wittgenstein, metaphysics denotes the void in signification, just like for Heidegger it denotes the void in the problematic or the question, and for Comte the void in scientific denotation’ (180).
Something is missing, the fact of the question – whether as statement or law or as the presence in thought of being itself. Yet, as Badiou mischievously points out, when it came to love for Comte, an unsayable remains in play. As for Wittgenstein, the mystical, as noted, is given its place relative to sense: the ‘facts ma’am’, it seems, don’t after all ‘exhaust our experience’. And, completing the trilogy, Heidegger’s ever-returning saving God marks this same ‘void’ place. Thus archi-metaphysics sets itself a task in contradiction to its original target of critique: to ‘over determine the undetermined’ (180), which is to say, for archi-metaphysics ‘the last recourse to the metaphysically undetermined, poses itself with a certain intensity’ (181).