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DRAFT ONLY Platonism as Praxis: The Ancients & the Moderns My philosophy [is] an inverted Platonism: the further removed from true being, the purer, the more beautiful, the better it is. Living in appearance [schein] as goal. —Friedrich Nietzsche, draft for The Birth of Tragedy out of the Spirit of Music When man embarks on the investigation of the nature of things, he realizes at length that he cannot arrive at that nature by any means, for he does not have within himself the elements from which composite things are constituted. ...Man then turns this fault of the mind to good use, and creates two things for himself through what is called “abstraction:” the point that can be drawn, and the unit that can be multiplied. But these are fictions: the point, if you draw it, is no longer a point; the unit, if you multiply it, is not entirely a unit. Moreover man arrogates to himself the right to proceed from these fictions to infinity….By this device, he creates a kind of world of shapes and numbers which he can embrace entirely within himself. ….When the mind gathers the truths of the things it contemplates, it cannot do so except by making the truths it knows. Of course, the physicist cannot define the things themselves[;] …that is God’s right but is unlawful for man. So he defines the names themselves, and creates the point, the line, the surface following the model of God, without any substrate and as though from nothing [tamquam ex nihilo]—as if they were things. … Therefore…the most certain sciences are those which, redressing the defects of their origin, resemble divine knowledge in their operation, inasmuch as in them the true is convertible with what is made. …[But] the mind does not make itself as it gets to know itself. —Giambattista Vico, On the Most Ancient Wisdom of the Italians I.2 The one who is conscious of himself as an individual has his vision trained to look upon everything as inverted. —Søren Kierkegaard, Purity of Heart is to Will One Thing Ch. 13 1
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Platonism as Praxis: The Ancients & the Moderns

My philosophy [is] an inverted Platonism: the further removed from true being, the purer, the more beautiful, the better it is. Living in appearance [schein] as goal.

—Friedrich Nietzsche, draft for The Birth of Tragedy out of the Spirit of Music

When man embarks on the investigation of the nature of things, he realizes at length that he cannot arrive at that nature by any means, for he does not have within himself the elements from which composite things are constituted. ...Man then turns this fault of the mind to good use, and creates two things for himself through what is called “abstraction:” the point that can be drawn, and the unit that can be multiplied. But these are fictions: the point, if you draw it, is no longer a point; the unit, if you multiply it, is not entirely a unit. Moreover man arrogates to himself the right to proceed from these fictions to infinity….By this device, he creates a kind of world of shapes and numbers which he can embrace entirely within himself. ….When the mind gathers the truths of the things it contemplates, it cannot do so except by making the truths it knows. Of course, the physicist cannot define the things themselves[;] …that is God’s right but is unlawful for man. So he defines the names themselves, and creates the point, the line, the surface following the model of God, without any substrate and as though from nothing [tamquam ex nihilo]—as if they were things. … Therefore…the most certain sciences are those which, redressing the defects of their origin, resemble divine knowledge in their operation, inasmuch as in them the true is convertible with what is made. …[But] the mind does not make itself as it gets to know itself.

—Giambattista Vico, On the Most Ancient Wisdom of the Italians I.2

The one who is conscious of himself as an individual has his vision trained to look upon everything as inverted.

—Søren Kierkegaard, Purity of Heart is to Will One Thing Ch. 13

In the Discourse on Method, Descartes relates the story of his own self-education. In particular, he reports that

…above all I delighted in mathematics, because of the certainty and self-evidence of its reasonings. But I did not yet notice its real use; and ... I was surprised that nothing more exalted had been built upon such firm and solid foundations.1

Descartes decided to so build, attempting to duplicate the certainty attendant upon mathematical conclusions in other cases, including the reliability of the senses, the dynamics of physical bodies in motion, and the existence of God; but his starting-place is the famous “Cartesian doubt” which refuses to grant anything as known unless it is utterly certain either in itself (the cogito) or grounded upon such a certainty by reliable chains of inference.

1 Discourse on Method, ch. 11

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In his lectures on Kant's first critique, translated as What is a Thing?, Heidegger summarizes his account of Cartesian dubiety like this:

Descartes does not doubt because he is a skeptic; rather, he must become a doubter because he posits the mathematical as the absolute ground and seeks for all knowledge a foundation that will accord with it.2

For Heidegger, the skepticism which founds the modern moment of philosophy is thus intimately connected to a particular conception of being. It is well known that Heidegger believes this conception to be a distraction from the real question of Being; that he sees the mathematical, conceived as the numerical, as a distraction, a decisive moment in the “forgetting of Being.” I want here to spell out some speculative consequences of thinking through the “remembering” of Being Heidegger wants to call us to, which arise when we consider it in conjunction with re-engaging with Plato’s conception of mathematics. I will do this by arranging a series of conjunctions between the thought of Alain Badiou and that a number of other thinkers, who besides Heidegger include Stanley Rosen, Alexander Kojève, Emmanuel Levinas, Ludwig Wittgenstein, and Badiou’s onetime student Quentin Meillassoux. I have chosen Badiou not only because his thinking is characterized by an admirable breadth, systematicity, and rigor3, but because the terms of his thinking are avowedly both “Platonist” and “mathematical.” I will wind up questioning his right to both adjectives, mainly by recourse to the way in which Plato’s mathematics has been reconstructed in the work of Ernest McClain4. But before we get to McClain, there will be others to engage in order to show what is at stake. I can only apologize for the inadequacy of my elucidation of each of these thinkers’ work, which I have relied upon rather piecemeal; a more sufficient exposition of them would have turned this paper into a library. Nonetheless, there is some unavoidable preliminary exegetical work to be done to present the outlines of Badiou’s philosophy, which is not yet as familiar to American readers as earlier French thinkers like Bergson, Sartre, or Derrida.

Alain Badiou: Mathematics as Ontology

Badiou has made an emphatic, even militant, point of reclaiming the Platonic mantle for philosophy after a century in which the most vehement and prolific developments in philosophy were explicitly anti-platonic. This goes for the analytic philosophy of the Vienna Circle, the various existentialisms taking their lead from Sartre (or Nietzsche), the “ordinary language” work inspired by one reading of late Wittgenstein, Popperian philosophy of science, and post-structuralism. As Badiou notes, not the least of these anti-Platonic forces has been the thinking of Heidegger himself, who identified “platonism” with the

2 Heidegger, What is a Thing?, tr. Barton & Deutsch, p 103

3 There is every sign that Badiou is already the “next French import” to American universities, as those who like to grumble about such things have been saying for some time now. Such a complaint about the industry of publishing and the trends of academia can be comprehended, perhaps with sympathy; but to substitute a dismissal (whether breezy or grouchy) for a philosophical engagement is beneath contempt.

4 Although I have not made frequent references to it here, the mostly unpublished work of John Holthouse on ancient philosophy and music has also been decisive for this effort. Holthouse is able to demonstrate an isomorphism, sometimes indisputably close and always very provocative, between the categories of ancient music and ancient philosophy, from the presocratics through the neoplatonists. The collection and publication of this work is a great desideratum.

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genesis of onto-theological “forgetting of Being.” Badiou’s counter-move is to regard Heidegger “as commonplace.”5 Badiou does indeed seek to think through the “question of Being,” but in a very different key than does Heidegger: specifically, he wants to demystify this question, to scrub it free of any aura of magic or summons such as one can easily think adheres to it, at least when reading Heidegger. For Badiou, there is no mystery about Being, and one need not speak of it in hushed tones or with any “piety of thinking;” but at the same time, one need not capitulate to the flattening of logical positivism which tried to laugh Heidegger out of court. In a sense, indeed, Badiou regards not only Heidegger but also Carnap “as commonplace.” He does this first by stipulating, and then by very patient spelling out the consequences of, a remarkably simple and audacious equation: ontology is mathematics; and Being is the mathematical.

This (all too?) elegant formula means that insofar as anything is, its structure is in principle completely delimitable in the language of mathematics. It is the task of mathematics—not philosophy—to elaborate that language. What is, is simply the multiple as such; mathematics is ontology, and ontology is mathematics. An entity is always an ensemble, and its orderedness (what makes it an entity rather than merely scattered random things) is, in the language of mathematics, its status as a set. Yes: for Badiou, the formulations of set theory provide the best language for ontology available.6 In his application of set theory, Badiou carefully takes its axioms and shows how each one unpacks into a clear and applicable philosophical procedure. The axiom of extensionality, for instance, states that two sets are equivalent if and only if their elements are the same. It is clear, says Badiou, that this axiom pertains directly to the old problematic of the same and the other, or identity and difference; it not only states the terms of the problematic, but also give a precise formula for resolving it. The axiom of extensionality is thus revealed as a proposition about Being. The same is shown in Being and Event for each of the axioms of set theory.

Badiou’s recourse to mathematics has an overtly philosophical motivation: it is his express desire to rehabilitate the notion of Truth. Truth, like Plato, had a hard time of it philosophically in the 20th century, and on the contemporary scene one might be excused for thinking that its critique was pretty well finally established. About the world, human beings, and the way to live, the widespread and unstated public consensus is that Nietzsche got it right: there are no truths, only interpretations. One may fairly quickly lay out the problem with this easy and unthinking relativism, ostensibly revolutionary (according to its apostles from the counterculture of the 1950s to the political correctness of the 1990s): de facto, it always capitulates to the status quo. Either it is incapable of sustaining its revolutionary intuitions into practice because it cannot formulate a coherent self-rationale; or it winds up overtly drawing the only logical conclusion: that of Thrasymachus in the Republic, which of course, needs no coherence or rationale, because it is only a practice, not a discourse. This reveals why one often finds it, with a little pushing, even among people of ostensibly “conservative” positions, who one might expect to take a more rigorously realist position with regards to politics or ethics. Nine times out of ten, it suits the conservative just as well to defend the status quo in relativist terms as to insist upon argument from shared premises; it

5 Badiou, Manifesto for Philosophy pp 47-52

6 This is the case at least in Badiou’s first great book, Being and Event. In a second installment, Logics of Worlds, Badiou has also made extensive use of category theory. In some important ways, this second book, subtitled Being and Event II, nuances the approach of the earlier work, but the fundamental thesis, that of the equivalency of ontology with mathematics, is only elaborated, never gainsaid.

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takes far less time; it disarms the opponent, who usually agrees with relativism himself; and while it is less bald than saying “I am stronger than you,” the results are the same.

Plato’s countermove to Thrasymachus is mathematical, for in mathematics, there really is such a thing as truth, and to take recourse to opinion is simply to not be doing mathematics at all. The mathematical case is thus a paradigm which indicates that truth cannot be so casually dispensed with. It is thus to this expressly platonic argument that Badiou turns. His approach differs from Plato’s, however, precisely insofar as Badiou treats the legacy of Heidegger “regarded as commonplace.” It is especially the French radicalizers of Heidegger, the so-called “left Heideggerians,” such as Jacques Derrida, and above all, Gilles Deleuze, who have outlined the position that Badiou both assumes and contests. I shall leave to one side the very complex question of Badiou’s relation with his former teacher Deleuze, and treat instead his comparatively distant relationship with Derrida, for the sake of simplicity. (Badiou’s decisive and antagonistic relationship with another interpreter of Heidegger, Emmanuel Levinas, will be touched on separately later).

Derrida, a close reader of Nietzsche as well as of Heidegger and Husserl, turned Heidegger’s critique of Nietzsche against Heidegger himself. Heidegger had accused Nietzsche of being embroiled in metaphysics despite his own intentions. He latched onto Nietzsche’s self-description of his own philosophy as an “inverted Platonism” which nonetheless, Heidegger said, preserved Platonism’s structure; Nietzsche was thus “the last metaphysician.” Derrida, routing his arguments through Saussure’s structural linguistics, found in Heidegger symptoms the same lingering metaphysics which Heidegger had found in Nietzsche: a fixation on “presence” and identity at the expense of differences. At the cost of grievous oversimplification, one can characterize much work of Derrida and those influenced by him as the championing of difference against the “hegemony” of the Same, in the name of (this time for sure!) really, really having done with metaphysics. (Though to be sure, Derrida himself is clear that such “finishing” of metaphysics would never be accomplished).

This foregrounding of difference receives from Badiou a big yawn. He at once concedes the point and asks, so what? For Badiou, differences are simply what there is. He takes for granted, in other words, the demolition of “metaphysics” undertaken by Nietzsche and Heidegger and its pulverization into footnotes by Derrida. And because for Badiou, differences are what there is, there is no One in his reconstruction of Platonism. Any “unity” is attained only by what Badiou calls the “count-as-one,” an operation of thought that treats a given ensemble “as if” it were a unity. The great ordered systematicity of Being in Plato has, in Badiou, no top, no arche-term, no final Form.

Badiou aims by this revision to retain in practice a kind of Platonism without any baggage of theology. The Nietzschean proclamation of the death of God would thus be carefully dissociated from the critique of Truth. For Badiou, Nietzsche named precisely a great Truth when he signed God’s death certificate; the trick here is to keep the atheism (which is precisely not an “interpretation” of the world for Badiou) without letting Truth perish as a side-casualty of its former divine guarantor. His effort is also inspired by Marx’s critique of capitalism:

…for Marx, and for us, desacrilization is not in the least nihilistic, insofar as ‘nihilism’ must signify that which declares that the access to being and truth is impossible. On the contrary, desacrilization is a necessary condition for the disclosing of such an approach to thought. It is obviously the only thing we can

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and must welcome within Capital: it exposes the pure multiple as the foundation of presentation; it denounces every effect of One as a simple, precarious configuration; it dismisses the symbolic representations in which the bond found a semblance of being. That this destitution operates in the most complete barbarity must not conceal its properly ontological virtue.7

As this passage illustrates, Badiou aims to keep not only the truth-status of mathematics, but also of the political principles of liberty, equality, fraternity. He is equally concerned to sustain the reality-status of artistic excellence, and of subjective experience, above all of friendship and love. One will note here another Platonic theme, for these four categories (mathematics, politics, art, and love) are almost the only matter of Plato’s dialogues. These four are what Badiou calls the “generic conditions” of philosophy, and also “of truth;” they are the types of novelty that occur in the world: the sorts of events that occur. Badiou offers no rationale for his foursquare list except that “I don’t find another,” a response he offers especially to those who wish—against Badiou’s own enthusiasm for “desacralization”—to fit religion into his thought as a fifth condition. As will become clear, an attempt to marry “resacralization” (or “reenchantment,” as Badiou sometimes calls this effort) with Badiou would only be made plausible by reframing Badiou’s priorities, and contesting the Platonic lineage to which he lays claim. I will contend in this direction myself later. For his part, Badiou is clear: religion, he says, is not an event but “a fable about an event.”

Event: deciding the undecidable

But this is to get ahead of ourselves, for “event” is a technical term in Badiou’s work.8 As we have said, “Being” has no penumbra of significance for Badiou; it is a brute setting or context, not unlike Sartre’s en-soi, but without the nausea. But precisely by virtue of this “demystification,” being as such has not much interest for Badiou.

The fundamental question for Badiou is not the nature of being, but the question of novelty. What is something new? It is to this question that Badiou responds with the category event. An event, a chance happening, occurs within a situation. This is another technical term, and the explication of both may start with an example:

“John and Mary had never met; they were like two hummingbirds who had also never met.”9

7 Manifesto for Philosophy p 56-7 “Desacralization” here ought to be read vis-à-vis Max Weber’s term “disenchantment,” Entzauberung, and Karl Löwith’s use of the term “secularization,” though these differ in important ways between each other and from author to author. See especially Hans Blumenberg, The Legitimacy of the Modern Age, Marcel Gauchet, The Disenchantment of the World, and Charles Taylor, A Secular Age.

8 The question of the antecedents of this notion, and especially of its relationship with Heidegger’s Ereignis (variously translated as “Appropriation,” “Event,” “En-ownment,” and so on) is of tremendous complexity, and must be left to one side. I would hazard as a preliminary foray that Badiou’s Event is the laicizing of Ereignis as his appropriation of set theory is a laicizing of Sein.

9 This sentence is variously attributed either to a “list of worst analogies” from high school students’ writing, or to entries to the annual Bulwer-Lytton contest for “worst opening sentence” of a story or novel. The contest is named of course for Edward Bulwer-Lytton who opened his novel Paul Clifford with the clause “it was a dark and stormy night,” before plunging off into a sodden thicket of adjectival phrase.

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This haiku-like sentence gives, in fact, a good approximation to what Badiou means by “situation.” The situation of John does not include Mary; the situation of Mary does not include John. And insofar as this is the case, their situations resemble those of the two referenced hummingbirds. The sheer formalism of this resemblance may be what disqualifies it from grounding a “good” simile; but here it helps us in emphasizing just what Badiou means: the differences between John and Mary and the two hummingbirds are infinite, but they all belong to the set of those who have not met each other. At least, until they meet.

No necessity compels this meeting to occasion anything new. But the sentence is not the beginning of a story unless there is a story. So let us imagine that John and Mary meet, and fall in love. From the outside, this event will look like any other of a million such encounters. Nothing is easier to dismiss, or to condescendingly “describe.” But as we know, to John and to Mary it can be life-transforming. Whether the amorous encounter is an event in Badiou’s sense is formally undecidable; that is, nothing within the situation counts decisively for or against a judgment that the two have “fallen in love;” this is decided only by an active choice on the part of the human being(s) who, by virtue of this decision, become subject(s), the subjects of the event.

An event is a happenstance, a chance occurrence, which cannot be predicted, and which indeed remains always contestable, from within the situation. (Note that it is not the meeting of John and Mary, which might be predictable, which is an event, but their falling in love). In addition to falling in love, Badiou’s examples are political upheaval, artistic breakthrough, and scientific insight; and in each of those contexts, the “situation” has a description for what has happened that excludes its counting as genuinely new. Artistic novelty can be dismissed as simply bad art; political revolution as thuggery or bad manners or ressentiment; scientific insight as anomaly or epicycles. An artist affirms the reality of an artistic breakthrough, and so determines him or herself as a subject, by deciding the breakthrough is real and by maintaining him or herself thereafter in fidelity to it. In the same way, a political actor affirms the reality of the political truth of a historical moment (Badiou’s consistent example here is the upheavals of May 1968, but he also references the French Revolution of 1789 and the Bolshevik revolution in 1918) by both decision and fidelity; and so , too, a scientist, who must decide to abandon the prevailing paradigm in order to work out all the ramifications of this new insight. For all of these—lovers, political actors, artists, scientists—the bottom line is that things will never be the same. So long as they maintain themselves without betraying their insight, they remain subjects.

Badiou’s account of the subject shows him at his most postmodern. Despite his anti-relativism, there is for Badiou no “human nature” per se. This has epistemological as well as ethical consequences. For instance, Badiou cannot share the Husserlian or even the Sartrean account of the transcendental ego, for Badiou’s subject is always constituted with regards to a particular event. Likewise, there cannot be for him any “human rights” if this means the rights of the human per se. Indeed, Badiou says:

there is no ethics ‘in general,’ because there is no abstract [human] subject….There is only a particular kind of animal, convoked by certain circumstances to become a subject….at a certain moment, everything he is is called upon to enable the passing of a truth along its path. 10

These circumstances are “the circumstances of a truth,” Badiou continues; not of the situation in its ordinary status quo.

10 Badiou, Ethics, tr. Hallward, p 406

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[W]hat there is (multiples, infinite differences, ‘objective’ situations—for example the ordinary state of relation to the other, before a loving encounter) cannot define such a circumstance. In this kind of objectivity, every animal gets by as best it can. …whatever convokes someone to the composition of a subject must be something extra, something that happens in situations as something that they and the usual way of behaving in them cannot account for. Let us say that a subject, which goes beyond the animal (although the animal remains its sole foundation) needs something to have happened, something that cannot be reduced to its ordinary inscription in ‘what there is.’ Let us call this supplement an event, and let us distinguish multiple-being, where it is not a matter of truth (but only of opinions), from the event, which compels us to decide a new way of being.11

Notice in these excerpts the distinction Badiou makes between the animal and the subject. The animal is the biologically necessary but insufficient basis for subjecthood; the subject, however, is what the animal becomes and remains only by virtue of having recognized and maintained fidelity to the event.

To be faithful to an event is to move within the situation that this event has supplemented, by thinking the situation ‘according to’ the event. And this of course, since the event was excluded by all the regular laws of the situation, compels the subject to invent a new way of being.12

This “new way of being” sets the subject apart, in his or her fidelity to the truth, from the “animal,” in a way that Badiou describes with a remarkable trope, which one would want to call hyperbolic except that Badiou’s formulations require that it be quite precise. Because every truth is “true for everyone,” and remains true beyond the horizons of any particular situation, the subject, says Badiou, is “something other than a mortal being; an immortal.”13

Some have felt that Badiou’s account of subjecthood, the event, and the ethics he derives from it, are elitist and heroising. One would want to ask, for instance, whether there could be any sense in speaking of the eventual dimension of the small—of the ordinary occasion, which Badiou seems to rather quickly elide under the heading “getting by.” Significant moments of a life are left to one side in Badiou’s account: what, for instance, of the discernment (which does not always befall one in an instant, of course) of a personal vocation (say, as a teacher or a farmer, a doctor or a craftsman)? And why, many critics want to inquire, does Badiou not consider a religious experience to be an event? Moreover, one can ask: would one say of someone who has not fallen in love, not been possessed of a great artistic passion, not made a scientific discovery or a political commitment, that they remain “only” an animal, as opposed to the lovers, artists, scientists and militants? This is of course to put the matter tendentiously, but it is Badiou’s own formulations which provoke the inquiry. My own reservations are related to this, but I am not concerned with elitism on its own account. I concur with Simon Critchley that Badiou risks losing what Critchley calls an “everyday pathos.”14 This difficulty with the ordinary is related, I think, to Badiou’s casual reduction of ontology to mathematics.

11 Ibid., p 41

12 Ibid., p 42

13 Ibid.,p 12

14 In Polygraph 17 (2005), “The Philosophy of Alain Badiou,” ed. Wilkens, p 304.7

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Recall that Badiou has recourse to mathematics in part as a maneuver to reclaim truth in a context which has found it progressively more and more difficult to make use of truth as a category for thought. For Badiou, this amounts to a crisis of valuation—precisely what Nietzsche decried as decadence. It will be noted that in the passage quoted above, Badiou says explicitly: “there is no ethics ‘in general,’” precisely because of what Badiou denies about the subject; there is none except under “the circumstances of a truth,” and these circumstances are explicitly exceptional.

Ethics: Impossible? Premature? Rare?

It is instructive to compare this turn with the analysis of Heidegger by another thinker who also explicitly advocated a “return to Plato,” Leo Strauss. Speaking of the famous encounter in 1929 between Heidegger and Cassirer, Strauss remarked:

Cassirer had been a pupil of Hermann Cohen, the founder of the neo-Kantian school. Cohen had elaborated a system of philosophy whose center was ethics. Cassirer had transformed Cohen’s system into a new system in which ethics had completely disappeared. It had been silently dropped; he had not faced the problem. Heidegger did face the problem. He declared that ethics was impossible, and his whole being was permeated by the awareness that this fact opens up an abyss.15

Whether or not this is a fair assessment of Cassirer’s work (I think it is not) will not be discussed here, though obviously this has some ramifications for one’s evaluation of Strauss’ reception of Heidegger. Heidegger does in fact make some remarks about ethics—the most obvious are in the Letter on Humanism—which could lead one to conclude that he sees ethics’ status as, at least, very problematic. To the question raised by Jean Beaufret on “the relation of ontology to a possible ethics,” Heidegger responds, in essence, that the hope for an ethics is premature; that it remains still to think through what ethos is. He comments on the question, “when are you going to write an ethics?” addressed to him “soon after Being and Time appeared,” that it betrays a kind of impatience. Heidegger acknowledges that the question expresses

a longing…for a peremptory directive and for rules that say how man, experienced from ek-sistence towards Being, ought to live in a fitting manner[,] …a desire [which] presses ever more ardently for fulfillment as the obvious no less than the hidden perplexity of man soars to immeasurable heights.16

Nevertheless, Heidegger asks whether “this need ever release[s] thought from the task of thinking what still remains principally to be thought, and, as Being, prior to all beings, is their guarantor and their truth?”17 Such thinking, Heidegger insists, must rather come first, if ethics is to have any meaning at all. In short, ethics is, if not impossible, at least extraordinarily difficult to produce rightly, without haste and without ignoring a whole host of questions. Certainly we should attempt to think through these questions, Heidegger says, especially in such a time as ours “when technological man, delivered over to mass society, can be kept reliably on call only by gathering and ordering all his plans and activities in a way

15 Strauss, “Introduction to Heideggerian Existentialilsm,” in Strauss, Rebirth of Classical Political rationalism, p 28

16 Heidegger, “Letter on Humanism,” in Basic Writings, ed. Krell, p 255

17 Ibid.8

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that corresponds to technology.”18 Heidegger is close here in spirit to Vico. In the passage immediately following the one we have cited in our epigraph, Vico implies that it is precisely the sciences which underlie the technological that offer “certainty,” and the closer one gets to questions of ethics, the further removed one is from the possibility of that sort of knowledge:

Since human knowledge is purely abstractive, the more our sciences are immersed in bodily matter, the less certain they are. For instance, mechanics is less certain than geometry or arithmetic, because it deals with motion, but with the aid of machines; physics is less certain than mechanics, because mechanics treats the external motion of circumferences whereas physics treats the internal motion of centers; morality is less certain than physics, because the latter deals with those internal motions of bodies which are by nature certain, whereas morality examines the motions of minds which are most deeply hidden and arise mostly from desire, which is infinite.19

This contention is directed most forcefully against an effort like Spinoza’s Ethics which, on one reading, attempted via geometrical-style proof to reduce morality to a mechanics of conatus (though Vico himself significantly later claims to be following the “geometrical manner” in his New Science). Spinoza’s effort, however, had at least tried to think God, Being, and Ethics together. When Heidegger says that the thinking of Being remains to be done before one can clearly gauge what the elaboration of ethics would entail, he is outlining the dimensions of the issue, dimensions Vico sees as infinite. Badiou, of course, will argue that this infinity is of no consequence; and this indeed is, in one sense, the rub of our contention with him. But the main point here is that for Heidegger, ethics cannot be pursued as an isolated “topic;” there is thinking to be done to understand what is at stake.

The same is true of theology. Heidegger is at pains to insist that his teaching does not lead to “indifferentism” regarding God, but rather is preliminary:

Only from the truth of Being can the Holy be thought. Only from the essence of the holy is the essence of divinity to be thought. Only in light of the essence of divinity can it be thought or said what the word “God” is to signify.20

These questions, whether preliminary to ethics or to theology, are related. Heidegger traces the term “ethics” to its Greek root ethos, and makes use of Heraclitus’ remark, 21which he interprets as meaning not “character is fate,” but “man dwells, insofar as he is man, in the nearness of a god.” Heidegger follows this revisionary translation with an anecdote from Aristotle about some strangers who went to see Heraclitus:

Having arrived they saw him warming himself at a stove. Surprised, they stood there in consternation—above all because he encouraged them, the astounded ones, and called for them to come in, with the words, “For here too the gods are present.”22

18 Ibid.

19 Vico, On the Most Ancient Wisdom of the Italians I.2 Vico’s gradations of precision here are Aristotelian.

20 “Letter on Humanism,” Basic Writings p 253

21 Heraclitus, fragment 119.

22 “Letter on Humanism” Basic Writings p 256. The source in Aristotle is in De Partibus Animalium I.59

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Heidegger’s exposition of this story is deceptively simple. Heraclitus disappoints the visitors who expect something remarkable and see instead an almost embarrassing domestic sight. But, Heidegger writes, Heraclitus reminds his visitors that “even here, in the sphere of the familiar, it is the case that the gods come to presence.”

At play here is a problematicizing of the distinction between the ordinary and the extraordinary. This distinction, and its erasure, are each very much at play in Badiou’s relegation of Heidegger to the “commonplace.” In the intertwining of Being and ethics, one can see here the outline of a clear and obvious difference between Badiou and Heidegger, as well as a likely source of the difference. For Badiou, thinking of Being has not much to do with ethics at all. Being is common. Ethics is rare, because events are rare. And indeed, despite his declaration that “there is no ethics in general,” Badiou has found no great difficulty in “writing an ethics.”23 In particular, Badiou is clear about his own political and “metapolitical” commitments, and draws explicit (though not always easy to follow) connections between his theorization of being and of the event and his ethical conclusions. But of far deeper consequence is what Badiou and Heidegger make of the quotidian, the ordinary, the “commonplace”.

There is an ordinary and perfectly describable relationship between the small wood-burning stove and the featherless biped named Heraclitus. One could easily account for it in terms of thermodynamics (Heraclitus is cold) or economics (Heraclitus is poor) or even philosophy (Heraclitus is “thinking”). Heidegger does not consider Heraclitus to gainsay the ordinariness of the situation. Rather he insists that even in its ordinariness, indeed precisely in this, “the gods are present.”

Badiou, on the other hand, does not seem to spare much time for the ordinary. Note, in the passages excerpted above, his distinguishing the “ordinary” course of things, the situation, from the eventual supplement which alone convokes the human animal to subjectivity.

So it is of considerable interest to ask, carefully, about Badiou’s recourse to Plato’s mathematics for the underpinnings of his ethical approach, since clearly one may juxtapose it with Heidegger rather starkly.

Atheism as Agnosticism

This inquiry is made with another remark by Heidegger in mind. It is the fifth and last “phenomenon of the modern age” he addresses in “The Age of the World Picture:”

Loss of the gods [Entgotterung, “degodization”]: This expression does not mean the mere doing away with the gods, gross atheism. …The loss of the gods is the situation of indecision regarding God and the gods. Christendom has the greatest share in bringing it about.  But the loss of the gods is so far from excluding religiosity that rather only through that loss is the relation to the gods changed into mere “religious experience.”  When this occurs, then the gods have fled.  The resultant void is compensated for by means of historiographical and psychological investigation of myth.24

23 His Ethics: essay on the understanding of evil is indeed in some ways the most accessible short introduction to his thought, and according to Badiou himself, “remains my most popular book.” In French it is about 90 pages long, though it makes frequent appeal to the longer and far more detailed analyses of Being and Event.

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“The loss of the gods is the situation of indecision regarding God and the gods.” Heidegger would seem here to anticipate the observation by John Millbank that

the overwhelming mood of twentieth-century philosophy was neither atheism nor religiosity but rather agnosticism. Indeed one could claim that it was just this agnosticism that distinguished it from nineteenth-century philosophy. This was exhibited in two ways: the one philosophical, the other religious in tone.25

Millbank goes on to characterize “religious” agnosticism as essentially a pluralist fideism in which everyone is respectfully granted the right to their own religion; whereas the “philosophical” agnosticism he describes as essentially the inheritance from Kant that forbids us access to things in themselves. Millbank explicitly describes this inheritance in terms of what Quentin Meillassoux (Badiou’s former student) has called “correlationism:” the style of thinking which consistently answers the claims of knowledge about the world with the insistence that such knowledge is always “about” the world “as it appears to us.” It consists

in disqualifying the claim that it is possible to consider the realms of subjectivity and objectivity independently of one another….that we never grasp an object “in itself,” in isolation from its relation to the subject, [and]…that we can never grasp a subject that would not always-already be related to an object.26

Meillassoux’s work is expressly directed against this correlationsim, which, he argues, makes it impossible to understand the results of science in the way scientists themselves understand them. Rather, correlationism takes recourse to a suspension of judgment that is, precisely, agnosticism. One can best see this in Meillassoux’s account of scientific results pertaining to the history of the universe before the emergence of life. On the correlationist account, such assertions can be strictly speaking neither true nor false, though it does not dispute the scientists’ rights to make them, or to “use” them. Such an agnosticism, Meillassoux says, cannot give a straight answer to such questions as “what is it that happened 4.56 billion years ago? Did the accretion of the earth happen, yes or no?”27 But more irksome still is the refusal such correlationism makes possible regarding rationality. As is well known, Kant determined the “limits of reason” in order to make room for faith, and Meillassoux argues that this accommodation has succeeded all too well, in effect radically undermining the ability of rationality to critique the irrational:

It becomes rationally illegitimate to disqualify irrational discourses about the absolute on the pretext of their irrationality…. In effect, religious belief has every right to maintain that the world was created out of

24 Heidegger, “The Age of the World Picture,” in The Question Concerning Technology and Other Essays, tr. Lovitt, pp 116-7.

Heidegger’s Entgotterung is also bound up with the terms “secularization” and “disenchantment” noted above.

25 Millbank, “Only Theology Saves Metaphysics: On the Modalities of Terror,” pp 453-4 in Chandler & Cunningham, eds, Belief and Metaphysics.

26 Meillassoux, After Finitude, tr. Brassier. p 5.

27 Meillassoux does not address it, but the issue becomes pressing in a deeper way when it arises in contemporary physics, where not merely practical but theoretical constraints actually forbid the formulation of “yes or no” answers to questions about the occurrence or non-occurrence of subatomic events. This theoretical impasse, often associated with the names of Heisenberg and Bohr, was famously extended to macroscopic events in Schrodinger’s thought-experiment about the cat. This line of argument, intended by Schrodinger as a reduction ad absurdum, raises questions I will not pursue here about how extendable Meillassoux’s critique of correlationism is.

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nothingness from an act of love, or that God’s omnipotence allows him to dissolve the apparent contradiction between his complete identity and His [sic] difference with his Son. These discourses continue to be meaningful—in a mythological or mystical register—even though they are scientifically and logically meaningless. …[Correlationism] pertains to the existence of a regime of meaning that remains incommensurable with rational meaning, because it does not pertain to the facts of the world but rather to the very fact that there is a world.28

Such meditation based not upon facts but upon facticity itself Meillassoux diagnoses in both Wittgenstein (e.g., “not how things are in the world, but that it is, is the mystical,” Tractatus 6:44) and Heidegger (in the shifting of emphasis from beings to Being). One may note here that both these thinkers are expressing an intuition fundamentally at odds with Badiou’s inclination to “demystify” Being, to render it banal. It is no surprise therefore to find Meillassoux speaking Badiou’s language:

Facticity forces us to grasp the “possibility” of that which is wholly other to the world, but which resides in the midst of the world as such. Yet…what is operative in facticity is not knowledge of the actual possibility of the wholly other, but rather our inability to establish its impossibility.…this “possibility” does not amount to any sort of positive knowledge…it is just the mark of our essential finitude, as well as of the world itself.29

This tolerance for a hermeneutic that has room for the (ostensibly) meaningless simply because it cannot rule it out is what Meillassoux finds so maddening. “Rule it out!” he seems to want to say; “decide!” In this respect, distant though he is from the philosophes, Meillassoux remains a true heir to the radical Enlightenment, and offers a more speculative and postmodern cousin of the critiques of theism given by Daniel Dennett. Nonetheless, Meillassoux is not as unequivocal on the matter of religion as these passages suggest. Because Meillassoux is the first student of Badiou to have a book translated from the French, the reception of Meillassoux in English-speaking philosophy has so far (as of 2009) tended to see his thought as an extension of Badiou’s. Later we shall briefly look at how Meillassoux does indeed follow Badiou in making his critique of correlationism by way of playing the philosophy of the transfinite against the finite. There is thus some legitimacy to linking Badiou and Meillassoux, as it is sanctioned by the explicit connections he draws between his own arguments and Badiou’s regarding finitude and set theory; but it will not do in the long run. Towards the end of this paper I will argue that Meillassoux has laid out an approach that varies from his teacher’s as regards the question of atheism.

What must be noted here though is the fact that while Meillassoux seems to be continuing Badiou’s campaign against the Heideggerian “mysticism” of Being, he is (by my account) apparently in line with the spirit of Heidegger in declaring against the modern “indecision regarding God and the gods,” which must be carefully distinguished from the preliminary questions Heidegger raises in the Letter on Humanism with the aim of clarifying what an avowal of God would mean. Indeed, on Heidegger’s account, it is precisely because we are too quick to speak of God without addressing the sorts of preliminary questions he lists, that we are able to slip into an indifferentism. Following the scholastics, who advise “when you encounter a contradiction, make a distinction,” we must therefore carefully distinguish between the question of hastiness and that of decision. My way of making this distinction relies on the distinction Gabriel Marcel offered between problem and mystery. This distinction must be

28 After Finitude, p 41

29 Ibid., p 4012

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problematic, at best, for Meillassoux, but I will not defend it here, only define it. A problem is a question with a conceivable answer; e.g.: how old is the earth? What causes contribute to the development of cancer? A mystery, on the other hand, is a question the asking of which involves one in the very matter about which one asks. Thus, “Is there free will?” is a question whose matter is already at work in the very asking, since I am already, as free or as determined, oriented in my freedom or unfreedom in the very act of posing the inquiry; there is no place “outside” from which I could pose the question. It does not follow that we are bound to consider such questions “meaningless;” but the meaning will elude us if we try to wrest a problem out of a mystery. This is precisely what happens in the sort of bad theology Heidegger warns against. To answer too hastily would be to preemptively congeal a mystery into a problem; to decide is to orient oneself to a mystery understood as such.

Would it then be more religious to decide against the gods, against God, than to continue in indifference and indecision—especially if such indifferentism masqueraded as a sort of piety? If so, then indeed Nietzsche’s declaration that God is dead could be precisely a religious, even a pious, even a faithful, proclamation.30 This is in fact what certain passages of Thus Spake Zarathustra suggest:

“…There is good taste in piety also. And at last that good taste said: ‘Away with such a God! Rather have no God, rather be a fate for one's self, rather be a fool, rather be God one’s self!’”“What do I hear!" said then the old pope pricking up his ears; “O Zarathustra, thou art more pious than thou believest, with such an unbelief! Some God within thee hath converted thee unto ungodliness. Is it not thy piety itself that letteth thee no longer believe in a God? And thine over-great honesty will one day lead thee even beyond good and evil!....”“Amen ! So let it be!” said Zarathustra in great astonishment.31

“Thou” or clinamen?

For Badiou’s part, the absence of God is not a matter of faith, but a principle, and one that is directly bound up with his problematic quasi-platonism. “Let us posit our axioms,” he says, towards the beginning of his Ethics:

There is no God. Which also means: the One is not. The multiple without one—every multiple being in its turn nothing other than a multiple of multiples—is the law of being. The only stopping point is the void.32

This avowal of atheism is directly occasioned by his response to another thinker, the significance of whose competing interpretation of both Plato and Heidegger can hardly be overstressed: Emmanuel Levinas. While it is beyond the scope of this chapter to offer anything like a satisfactory sketch of Levinas’ thought, the barest outline must be offered here, for it is Levinas’ critique of Heidegger that fundamentally posed the terms for what Badiou set out to contest. In a project whose revolutionary

30 The notion that honest and committed atheism is closer to salvation than an indifferent “belief” is also a strong motif in Kierkegaard and Dostoevsky, not to mention the biblical book of Revelation (“would that you were hot or cold, [rather than] lukewarm”, (3:15-16)). Note too that Dostoevsky also pursues the theme of “becoming God,” for example in Kirilov’s astonishing and terrifying equation of suicide—the ultimate expression of will and/as nihilism—with (and as means to) deification: “If you shoot yourself, you’ll become God, isn’t that right?” “Yes, I’ll become God.” (The Possessed, III 6)

31 Thus Spake Zarathustra, IV. “Off Duty”

32 Ethics p 2513

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implications have only begun to be sketched, Levinas urged the consequences of taking seriously personal ontological difference.33 The fundamental experience, he said, is the encounter with the Other, and this encounter obligates me. It is not a question, as it is for Heidegger in his tool-analysis in Being and Time, either of what I can do with any object, nor of the being of the object qua entity34; it is rather a question of what I am called upon to do for the Other. The call of ethics is always there, presented to me in the face of the other person; before I have posed the question of “is this a person?” (the skeptical question) or even “what is my duty here?” (the Kantian question), the call of ethics is already addressed to me, already, indeed, constitutes me as its hearer. This meant that for Levinas (as for Buber in a sense), ethics came before ontology. Levinas shared some of Heidegger’s critique of Plato, but like Badiou he also called for a “return to Plato.” Levinas, however, informed by the Biblical and Talmudic tradition, does not seek a grand unification of entities in the One, nor an unassailable definition of any given entity. In looking to Plato, Levinas is not seeking a ground either of epistemological certainty nor ontological subjectivity; for him, my subjectivity is constituted by my being addressed by the other. Rather, Levinas’ platonic vision is informed and motivated by Plato’s account of the Good as “beyond Being,” thus beyond the realm of the specifiable.

Despite the fact that the question of God is very problematic in Levinas’ thought, Badiou has rightly seen that Levinas’ account of “ethics as first philosophy” is inherently bound up with this question, and he has always tended to shy away from whatever common thematic might be discerned between their two projects. Whereas a Levinasian reading of Badiou might treat the event as the irruption of the infinite in the phenomenal, Badiou can respond that the infinite for him possesses no special allure—nothing, in any case, that justifies coming to a particular ontological conclusion about it.35 Moreover, when less devout or less theologically motivated disciples have attempted to appropriate Levinas’ thought for their own constructions of ethics, they have tended to focus upon such dimensions as “respect for the other.” Such a strategy has, according to Badiou’s critique, at least three possible liabilities. Either it must inevitably secrete a rationale for itself in a hypothesized universal human nature (which means it returns to being a discourse of the Same, not of difference at all); or it condescendingly constructs the other as a victim (potential or actual); or, worst of all, it winds up inconsistently “respecting” the other insofar as the other is like it. This can be seen clearly, suggest Badiou and some influenced by him, in the west’s contemporary encounter with Islam, the desperate seeking of the Islamic “moderate,” the genuine horror with which western liberalism contemplates a mode of life that takes seriously non-enlightenment European values. Confronted by a genuine other, liberalism’s “ethic of differences” simply melts. It is incapable either of defending, or of standing by, what it avers.

Badiou’s critique of quasi-Levinasian ethics, that is to say, the “ethics of difference” which does not want to commit itself to the theological overtones of Levinas’ thought, is both severe and effective. His argument against Levinas himself, however, is less decisive, and depends far more upon one’s accepting

33 The best brief introduction to Levinas is his short book of conversations with Philippe Nemo, Ethics and Infinity. His two most important works are Totality and Infinity and Otherwise than Being; or, Beyond Essence.

34 But on this matter see also the important work of Graham Harman, Tool-Being and Guerilla Metaphysics, which develops an ontology of objects from Heidegger’s analysis that is more amenable to Badiou’s refusal of theology, albeit declining to equate ontology with mathematics.

35 See on this the remarks of Graham Harman on allure in Guerilla Metaphysics, especially pp141-314

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Badiou’s basic orientation which equates Being with a secularized infinity. For Levinas, the infinite is the ethical made present from beyond Being but instantiated in the untheorizable face of the Other. For Badiou, as we have seen, the infinite is merely what there is, and there is nothing special about the ontological otherness of neighbor or stranger; it is neither greater nor less than the difference between me and myself. Badiou thus diagnoses Levinas’ infinite as a closet theism; and it is not too much to say that, in a certain sense, this is enough to make him reject it (though of course he spells out his critique far more deftly than an out-of-hand refusal). It would be disingenuous to suggest that the only difference Badiou has with Levinas’ ethics is theism, in part because in Levinas’ thought, “theism” is not straightforward.36 It certainly does not entail positing “the One,” in the way Badiou suggests is always entailed (“there is no god; which also means, the One is not.”) No; for Badiou, the real issue seems to be the odor of “piety” about ethics construed along Levinasian lines and the possibility that piety here will substitute itself for thinking; that it might in fact turn into a new (or old) form of ideology.

To be sure, there is a danger in Levinasian discourse of fetishizing the privileged terms “encounter,” “meeting,” “other,” or “face.” All such terms are open to a very simple and venerable critique: namely, that there is nothing magical in them, nor in what they name. This objection contains nothing new. It is the critique of concepts used for what is beyond conceptualizing. It is the same critique that Xenophanes made of the language and images for the gods in his day, when he remarked that if horses or lions could draw they would depict the gods with hooves or manes.37 In our context, “hoof” or “mane” is a particular, a difference, which cannot matter to ontology. One of Xenophanes’ fragments says, “There is one god, supreme among gods and men, resembling mortals in neither form nor mind.”38 Xenophanes like Plato was concerned with making clear the non-resemblance between God and the human realm, though Plato seems more comfortable with analogies between human and divine action (though the fragmentary record of Xenophanes’ oeuvre should make us cautious in drawing conclusions). But Badiou has eschewed the One for the boundless multiplicities of postmodernity (with which he has little enough sympathy in general), so he is left only with the absolute non-resemblance.

Badiou is in quest of precision and exactitude, and his critique is as rigorous and austere as Spinoza’s or Averroes’, the two thinkers I see him as most like. He therefore eschews the Levinasian language in favor

36 In a certain sense the question of Levinas’ theism is the inverse of that concerning Heidegger’s “atheism.” In certain contexts Heidegger does indeed maintain explicitly that atheism is inherent in philosophy; symptomatic here (albeit quite extreme) is his remark that “Philosophical research is and remains atheism, which is why philosophy can allow the ‘arrogance of thinking.’” (History of the Concept of Time: Prolegomena, p80). On the other hand one can find reason to think of this as a phenomenological epoche regarding the question of God, demanded because the task of the thinker is the articulation of the question not of God, but of Being. C.f. his famous remark from his Zurich seminar of 1951: “Being and God are not identical, and I would never attempt to think the essence of God through being. Some of you perhaps know that I came out of theology, and that I harbor an old love for it and that I have a certain understanding of it. If I were yet to write a theology—to which I am still sometimes inclined—the word 'being' would not be allowed to occur in it.” This stance has been characterized as “methodological atheism,” but such a label is of little help in understanding what is at stake. Likewise, while Levinas clearly demurs from proclaiming a God who is “a being alongside beings,” or even “the ground of Being,” this is not to preclude the notion of any God. One need only reflect on how inadequate would be a characterization of this stance of Levinas’ as “methodological theism” to see the limits of the corresponding description of Heidegger. The issue is bound up with, but goes deeper than, method.

37 Xenophanes, Fragment 15 (Diels-Kranz).

38 Fragment 23. Both of these frgments are preserved in Clement of Alexandria’s Stromata V, 10915

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of the vacuum in which weightless equations describe whatever is insofar as it is (all sensible attributes having been “subtracted”), and furnishes his multiplicities with the theoretical apparatus of transfinite mathematics. Thus his truths, decided upon and grasped precisely by human subjects who are “something other than a mortal being” (and indeed are such precisely insofar as they grasp truths) cannot then be a function of being, since being is merely the realm of pure differences; nor can they be the gift of a transcendent order, since this would only displace the question. Truths arise as the result of the event, which is purely aleatory in character: a chance occurrence, like the Lucretian or Epicurean clinamen, an uncaused swerve of atoms in the void.

(Auto)theosis ancient and modern

So Badiou’s ethics is about fidelity to an event, persisting in one’s subjecthood. This account of the subject, I submit, may be read as of a piece with the ambitions of philosophy in general; ambitions which are far more than hermeneutic. As Aquinas wrote, “Philosophy does not consist in asking what men have said, but in asking after the truth of the matter,”39 and long before Aquinas, it was understood that the aspiration to know the Truth was dangerous, for it involved a degree of hubris. My initial cue here comes from another contemporary philosopher who has, like Badiou, striven to reclaim Plato’s legacy, also in express polemics against Heidegger, Stanley Rosen.

Rosen is one of the most formidable students (and sometime critics) of Leo Strauss, who wrote that “Heidegger is the only man who has an inkling of the dimensions of the problem of a world society,” and that “only a great thinker could help us in our intellectual plight. But here is the great trouble: the only great thinker in our time is Heidegger.”40 These remarks (dating from the 1950s) and many others, serve as the germ for a critique of Heidegger that Strauss never fully or systematically carried out, though he acknowledged many difficulties with Heidegger’s formulations and career. Rosen has attempted to provide something like this critique, fully fleshed out in his book The Question of Being. In particular, Rosen has argued extremely cogently that the whole account of the Ideas or Forms as found in the Republic, the Parmenides, and elsewhere, is, on the evidence of the Phaedo, not rightly understood as an ontological assertion but as a hypothesis. This alone seriously problematizes Heidegger’s account of the history of metaphysics, according to which Plato inaugurates the “eclipse of Being” by replacing it with beings.41

In the following reflections, I concentrate (without trying to provide an exhaustive account) mainly upon Rosen’s understanding of the famous dispute between his teachers Strauss and Alexander Kojève. My reasons for this detour will, I hope, be clear when we read Rosen in dialogue with Badiou’s account of the subject.

39 Commentary on Aristotle’s On the Heavens and Earth, lect. xxii; II Sent., D. xiv, a. 2, ad 1um

40 Rebirth of Classical Political Philosophy, pp 43, 29.

41 Though Rosen does not say so, his account is close, in certain respects, to that offered already in 1921 in Plato’s Doctrine of Ideas by Paul Natorp, whose chair at Marburg Heidegger assumed after Natorp’s death. Rosen’s “reversal of Heidegger” thus in some ways resembles a redressing of the balance after Heidegger’s reaction against Natorp’s neo-Kantianism.

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Kojève, whose extremely original and influential interpretation of Hegel, Kant, and many other figures in the philosophical tradition, well-known and obscure (Kojève’s doctorate work was on the Russian theosophist Vladimir Solovyov), coincided with a long and no less influential career as a civil servant in the French government (including laying the foundations for the European Union), played a key role in introducing Hegel to the French intelligentsia of two generations (thereby making possible nearly every development of French philosophy thereafter, and indeed postmodernism generally). He also produced an original and powerful synthesis of Marx, Hegel, and Heidegger, which was not only a compelling philosophical vision but served as the rationale for his own political career. Kojève contended that History-with-a-capital-H had a discernible direction (his inheritance from Hegel), materialistically understandable in terms of what humankind makes, which is, ultimately, humankind itself (his inheritance from Marx), always within a radically finite and temporal horizon (Heidegger). Kojève’s contention was that History had reached the culmination of its interior logic with the French Revolution’s declaration of universal rights, in which the aristocracy acknowledged and accepted the working classes as fully human on account of their work, resolving the Hegelian-Marxist struggle between master and slave for recognition. After this, while the struggle will be recapitulated many times as various parts of the world catch up, there is nowhere else for History itself to “go.” For the philosopher, what remains is simply the satisfaction of understanding this trajectory in toto, and thus becoming not just a philosopher, a lover of wisdom, but a sage, a wise man.

Rosen’s account of this Hegelian-cum-Kojevian willing culminates in a startling characterization:

On the Hegelian account, one denies separation of the eternal from the temporal, or identifies the two as the structure of the Concept, that is, the philosophical speech about the totalilty of the whole…. He who is able to repeat the totality of this discourse becomes a god.42

This rather surprising conclusion is Kojève’s, though the summary here is Rosen’s. Indeed, Rosen cites numerous instances from Kojève to show that Kojève did indeed describe his enterprise as divine (how tongue-in-cheek, Rosen does not ask), and that he understood this explicitly within the context of his conclusions about history and the nature of philosophy. One citation from a late interview, given shortly before his death, will suffice for many more possible quotations:

It is true that philosophical discourse, like history, is closed. That idea irritates. That is perhaps why the sages—those who succeed the philosophers and of whom Hegel is the first—are so rare, not to say nonexistent. It is true, you may not adhere to wisdom unless you are able to believe in your divinity. Well, people with a healthy esprit are very rare. To be divine: what does that mean? It might be Stoic wisdom, or even play. Who plays? The gods: they have no need to react and so they play. They are do-nothing gods…. I am a do-nothing….yes, I am a do-nothing, and I like to play, at this moment for example.43

Rosen’s account is of course not the only evaluation one could make of this project. Compare, for instance, Rosen’s last-cited statement, “He who is able to repeat the totality of this discourse becomes a god,” with Hegel’s ambition:

42 Rosen, Hermeneutics as Politics, p 96

43 Kojève, interview in La Quinzaine Litteraire 53 (1 July 1968). Quoted in Hermeneutics as Politics, p 10617

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Every single man is but a blind link in the chain of absolute necessity by which the world builds itself forth. The single man can elevate himself to dominance over an appreciable length of this chain only if he knows the direction in which the great necessity wants to move and if he learns from this knowledge to pronounce the magic words [die Zauberworte] that will evoke its shape. 44

This passage, from the same period as the Phenomenology of Mind, was put forward as Exhibit A in Eric Voegelin’s ferocious critique, “On Hegel: A Study in Sorcery,”45 in which he portrayed Hegel as an aspiring magus attempting to attain power by a kind of black art, the building of a “second reality” which would eclipse the first, a system of representations which, taken for “the thing itself,” would allow one to feel a fictive sense of mastery within it. For Voegelin, Hegel was engaging in a kind of sleight-of-hand, trying to distract both himself and his readers from Reality with a phantasmagoric display of wishful thinking, masterfully executed but ultimately empty. Note that in a sense this is precisely the Viconian account of mathematics, taken to its conclusion: humankind cannot “define the things,” so it “defines the names” and creates from these names a world:

On this basis, though it is denied to him to have hold of those elements of things from which the things themselves exist for certain, he can feign for himself the elements of words from which ideas are stimulated, without controversy.46

This is almost already Kant’s distinction of phenomena and noumena. And indeed, Kojève remarkably concedes that Hegelianism is not, in fact, true (yet); but he mitigates the inconvenience of the admission by way of a Kantian dodge. As if happily conceding Voegelin’s accusation of magic, Kojève turns Hegelianism’s falsehood into a virtue:

What is remarkable is that it is precisely because [Hegelianism] is not yet true that this philosophy alone is capable of becoming true one day. For it is alone in saying that truth is created in time thanks to error, and that there are no transcendent criteria.47

This understanding of Hegel is possible in part because of Kojève’s reading of Kant. Taking his cue from Hans Vaihinger’s characterization of Kant’s philosophy as “the philosophy of the As-If,” Kojève writes:

Man may live humanly AS IF a statement which is false, not only in fact or for us but also for itself, were true, on condition of acting in such a way as to transform the given world in such a way that the statement that was false before this transformation becomes true after it. That is, the Kantian As-if has sense and value only as a project of negating (=creative or revolutionary) efficacious action.48

And, in the lectures on Hegel, Kojève says:

44 Hegel, MS, Fortsetzung des “Systems der Sittlichkeit,” c. 1804–06

45 In Voegelin, Published Essays 1966-1985

46 On the Most Ancient Wisdom of the Italians I.2

47 “Hegel, Marx et le Christianisme,” in Critique 3-4 (1946); quoted in Roger Devlin, Alexandre Kojève and the Outcome of

Modern Thought, p 135. See too Rosen p 104. 

48 Kojève, Kant (Gallimard, 1973), p 99. Translation by Rosen; cited in Hermeneutics as Politics, p 9918

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Now, if a being that becomes God in time can be called ‘God’ only provided it uses this term as a metaphor (a correct metaphor, by the way), the being that has always been God is God in the proper and strict sense.49

One might venture that Nietzsche’s amor fati which would affirm the Eternal Return is the ne plus ultra of this line of thought concerning the recapitulation of history. I will note in passing that the Nietzschean declaration “God is dead” was first made by Hegel50, and that Nietzsche is far from the least explicit of modern philosophers in aspiring to deification. We shall come back to this towards the end of this paper.

Far from being a merely modern aberration, however, this theme of deification is explicitly traced by Rosen to the beginnings of philosophy in the west.51 “The man of religious faith,” Rosen writes, “regards it as madness to attempt to become a god. The pagan philosophers, especially those of the Socratic school, thought otherwise.” This is put into the context of the “ancient quarrel” between philosophy and poetry: “The ancient philosophers rejected the warnings of the poets, as exemplified in Pindar’s admonition: ‘do not strive to be a god.’”52 This is attributed to both Plato and Aristotle. “As Socrates puts it, the classical philosopher wills that the intellect be god,” a contention Rosen illustrates by illustration from the Philebus, where Socrates says, “The wise all agree, thereby exalting themselves, that intellect [nous] is the king for us of heaven and earth.”53 Rosen glosses “the philosophical question of the Platonic dialogues, and in particular of the Phaedrus” as “how can a human being become a god?” For his part, Aristotle has it in the Ethics that one will love the theoretical life, higher than the vita practica, “not qua human… but he will achieve it by virtue of something divine in him.”54 Rosen comments: “Aristotle is even more explicit than Plato…[his] representation of himself as divine is a radical simplification of Plato’s poetic evasiveness.” By contrast, in the modern age the drive has been inverted. The famous “quarrel between the ancients and the moderns,” Rosen says, “has its inner or esoteric meaning in the question quid sit deus?” This question, “What is god?”, remarks Strauss, is “the all-important question which is coeval with philosophy.”55 The quarrel turns out to be, at least in one respect, about which faculty is the best candidate for deification. Whereas classical philosophy “wills that the intellect be god,” Rosen says, now the situation is reversed, for “from Descartes forward, the intellect resolves that the will be god.”

Thus the debate about God is also a debate about the human subject; but note that the difference between ancients and moderns is not that the moderns agree with the religious assertion that it is “madness to strive to be a god;” on Rosen’s account, both ancients and modern philosophers have this ambition; it is

49 Kojève, Introduction to the Reading of Hegel p 120

50 Hegel, Phenomenology of Spirit, VII C 1

51 Citations from Rosen in this paragraph are from Hermeneutics as Politics, pp 54; 16; 180; 44; 65; 59;17; 180.

52 Olympian Odes V 24

53 Philebus 28c

54 Aristotle, Nichomachean Ethics, 1177b

55 Strauss, The City and Man, p 241.19

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only a question of which human faculty is primarily involved.56 From this perspective, Badiou is modern through and through, for it is not the intellect but the will which decides, commits, and persists in fidelity to the truth revealed by the event. Recall that this means, for Badiou, that the human subject is “something other than a mortal being: an immortal.” Such construing oneself as an immortal is in fact not too far from becoming a “god;” it is, in essence, the de-theologized version, and while Badiou has eschewed the term (that is, the phoneme) “god,” he does not seem to have abandoned the sense, at least as used by the “moderns.” Might it be that Badiou must axiomatically insist that “there is no God” in order to follow Nietzsche, in order, that is, to “rather be God oneself”? The trend Rosen observes, replacing the intellect with the will, we may observe, comes to its apotheosis (so to speak) in Nietzsche’s championing of the will to power, which has everything to do with the death of God:

How shall we comfort ourselves, murderers of all murderers? What was holiest and mightiest of all the world has yet owned has bled to death under our knives. Who will wipe this blood off us? …Is not this deed too great for us? Must we not become gods ourselves simply to appear worthy of it?57

And Badiou is emphatic with regards to this theme: “We're far from having exhausted the consequences of the question of the death of God,” he remarks in one interview58.

What does such becoming divine mean? Rosen says that to be a god is to be casua sui; but it is not merely a matter of causing oneself, but causing one’s world. “[A]ll great philosophers engage[…] in the divine prerogative of willing a world into being and hence creating a way of life,” he remarks apropos Nietzsche. On our reading, Badiou follows Sartre in reading every acting person, or at least every human subject, as a “philosopher” in Rosen’s sense. Recall that for Sartre, man in fact is fundamentally “the desire to be God;” that is, the desire to unify the pour-soi with the en-soi, freedom with its own limits. This formulation, in which Sartre discerns the “meaning” of all human projects as such, is nonetheless (Sartre contends) contradictory, which famously leads him to the melancholy conclusion that “we lose ourselves in vain.” One might conclude then that this project or meta-project must be, in Sartre’s terms, doomed to failure. But one should also note that one cannot, properly speaking, “fail” in any project according to

56 In this respect the difference is unlike that between Christian and pagan notions of deification. Christian deification or theosis, , is frequently spoken of by the Church fathers and by more modern monastic sources as both the process and end of Christian salvation. Ancient mentions are frequent; e.g. St. Irenaeus Against Heresies 5, preface, “the Word of God, our Lord Jesus Christ, who did, through his transcendent love, become what we are, that He might bring us to be even what He is Himself;” St. Athanasius On the Incarnation 54:3, “God became man in order than man might become God;” or St. Augustine, Exposition of the Psalms L:2 God “hath called men gods that are deified of His Grace, not born of His Substance.” More detailed, though no more explicit, is St. Maximus the Confessor: “Let us become the image of the one whole God, bearing nothing earthly in ourselves, so that we may consort with God and become gods, receiving from God our existence as gods.” “A sure warrant for looking forward with hope to the deification of human nature is provided by the incarnation of God, which makes man God to the same degree as God himself became man. For it is clear that He who became man without sin (cf. Heb. 4:15) will divinize human nature without changing it into the divine nature, and will raise it up for his own sake to the same degree as He lowered himself for man's sake.” (“Various Texts on Theology, the Divine Economy, Virtue & Vice,” Century 2, texts 28 and 65, in The Philokalia tr. Palmer, Sherrard, Ware, vol 2 pp171, 177-8). Ubiquitous throughout this motif of Christian thought is the emphasis that theosis is bestowed upon the created order by divine grace. Thus the difference between Christian and philosophical theosis is not (as between ancient and modern philosophical theosis) between what human faculty is the engine of deification, but rather what ontological source the energy of deification comes from. The historical and philosophical relationships between these competing notions of theosis is of great interest, but further exploration of this matter would be a chapter unto itself. See however below, note 63.

57 Nietzsche, The Gay Science III, sec. 125, “The Madman.” 20

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Sartre, since as pure freedom, the en-soi is absolutely responsible and chooses whatever outcome it attains. In another interview, when Badiou spells out what he thinks is the single decisive consequence of the death of God, he says: the uncoupling of meaning from truth.

[T]he consequence of the death of God is a conclusive difference between meaning and truth…. Actually, I think that the simplest definition of God and of religion lies in the idea that truth and meaning are one and the same thing. The death of God is the end of the idea that posits truth and meaning as the same thing.59

This definition of God is not far from Sartre’s impossible synthesis of en-soi-pour-soi. Badiou appears here to be more optimistic, as his subjects are not doomed to contradictory bad faith, though one might ask whether, when Badiou says that “the animal remains [the subject’s] sole foundation,” he in essence concede s same limits imposed by the Sartrean en-soi. Nonetheless, Badiou can brush off God with an (admittedly programmatic) axiom, whereas for Sartre, at least in a certain rhetorical mode, “it is very distressing that God does not exist,”

because all possibility of finding values in a heaven of ideas disappears along with Him; there can no longer be any a priori idea of Good, since there is no infinite and perfect consciousness to think it. Nowhere is it written that the Good exists, that we must be honest, that we must not lie; because the fact is that we are on a plane where there are only human beings.60

To be sure, at the conclusion of this same essay, Sartre insists that God’s existence would not matter, because human beings would still have the responsibility of positing values in any case: “Existentialism ….declares, rather, that even if God existed that would make no difference from its point of view.” 61 Badiou picks up from this later strain in Sartre, but he refuses its glib indifferentism.

Contingency and Insight

58 Lauren Sedofsky, “Being by Numbers,” interview with Badiou, ArtForum Oct. 1994. Elsewhere (Briefings on Existence, pp

21-32) Badiou makes a distinction between three gods—of “faith,” “philosophy,” and “poetry”—clearly following Heidegger (and Pascal) in this respect. His aim is to pursue to the death the third of these gods, visiting upon him the death already a foregone conclusion with respect to the other two. In contrast, I am contending that Badiou, Heidegger, and Pascal have all overstated the case. With Tillich, I contend, “against Pascal,” that “the God of Abraham, Isaac, and Jacob and the God of the philosophers is the same God. He is a person and the negation of himself as a person.” (Tillich, Biblical Religion & the Search for Ultimate Reality, p98). Indeed, the discourse of both poets and philosophers have always been understood by religious tradition to be usable, albeit often inverted, by mystical discourse. That is: the “death” of God has already been anticipated in the tradition itself. For instance, I would assert that philosophy does indeed posit a vocabulary for speaking of God, but it cannot—just as Aquinas would say—bring us to experience of revelation. In this I am wholly with Badiou (and Pascal): the experience of religious faith is indeed an aleatory one, a wager. But to argue this would be to hold that such faith can be, in Badiou’s sense, an event.

59 Mario Goldenberg “Interview with Alain Badiou,” Lacanian Ink 23

60 Sartre, “Existentialism is a Humanism,” in Existentialism and Human Emotions p 22

61 Ibid., p 5021

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Badiou carries out his critique of finitude via the explication of Cantorian transfinite set theory. The denial of any “set of all sets” is the same thing, for Badiou, as the denial of the One, or of God. For ancient and medieval philosophy, “Infinite” was a divine epithet; in the absence of God, however, it is seen to pertain merely to everything that is, to existence per se. It is not difficult to see why Badiou concludes this. Following upon Heidegger and Kierkegaard, Christian theology took human finitude to be the symptom or index of the failure of human being to be self-grounding. In one variation after another, philosophers from Dooyeweerd and Løgstrup to Weil and Marion (not to mention theologians like Barth, Rahner, Macquarrie or Millbank), read finitude as implicitly isomorphic with createdness or even sinfulness. This train of thought picks up in many respects from the Kantian cartography that mapped the limits of human capacity and “reason alone.”62 Against all of this, Badiou asserts the complete sovereignty of reason, its essential limitlessness, and its sole prerogative in naming truths as opposed to opinion. With a completely secularized, laicized notion of infinity, one simply does not need God; one has banished the difference between the created and the creating order, in just the same way that the Galilean and Newtonian revolution dispensed with the difference between sub- and superlunary realms.63

One can see how this erasure is accomplished by referring again to Meillassoux, who distinguishes chance from contingency, in order to affirm the actuality of scientific knowledge (that is, scientific regularity is real, not just patterns we imagine or have observed “so far” but which could alter tomorrow) without conceding anything to cosmological arguments for God on the one hand, or to necessitarian arguments for the inevitability of the laws of nature on the other. Both Kant (who is for Meillassoux the father of correlationism) and his precursor Hume, who set the terms of Kant’s problems, had argued, each in their own way, for the reality of laws of nature based on a probabilistic argument that one is justified in concluding that events are “loaded” (as dice may be) when the same outcome from repeatedly occurs, to the exclusion of an infinite number of other conceivable outcomes. But such rationale only works,

62 It is also a mark of the divergence between post-Kantian and Patristic theology. While the Cappadocian fathers, for instance, make no attempt to minimize either human createdness nor human sinfulness, it is characteristic of Gregory of Nyssa to emphasize the infinity of the soul’s potential and that of the whole created order. C.f. Against Eunomius 8; II, 797a: Creation “has not begun merely at one point or another to exist, but at every moment it is perceived to be in its beginning stages on account of its perpetual growth toward that which is the best.” See too 1; II, 340d: “Never will the soul reach its final perfection, for it will never encounter a limit, ... it will always be transformed into a better thing.”

63 It is here that the decisive difference between Christian and philosophical theosis may be most pronounced. This comes to the

fore not merely in that Christian deification is always considered a gift of divine grace, but because the ontology assumed in each framework is radically different. One might almost say that for the Christian conception, deification is the transumption of one ontological order into participation in another order. The early tradition especially is extremely hesitant to posit any anologia entis and every comparison between created and uncreated orders is hedged about with qualifications underscoring its radical inadequacy. Thus, e.g. St. Gregory Nazianzen, Theological Orations 24:4 “It is difficult to conceive God but to define Him in words is an impossibility, as one of the Greek teachers of Divinity taught, not unskilfully, as it appears to me; with the intention that he might be thought to have apprehended Him; in that he says it is a hard thing to do; and yet may escape being convicted of ignorance because of the impossibility of giving expression to the apprehension. But in my opinion it is impossible to express Him, and yet more impossible to conceive Him.” (Gregory’s citation is from Plato, Timaeus 28 E.: “Now that which is created must, as we affirm, of necessity be created by a cause. But the father and maker of all this universe is past finding out; and even if we found him, to tell of him to all men would be impossible.”) Likewise, St. Maximus the Confessor: “Created beings are termed intelligible, because each of them has an origin that can be known rationally. But God cannot be termed intelligible, while from our apprehension of intelligible beings we can do no more than believe that He exists. On this account, no intelligible being is in any way to be compared with him.” (“Two Hundred texts on Theology and the Incarnate Disposition of the Son of God,” Century 1, text 8, in the Philokalia, vol.II p 115.) If modern theosis is a “secularization” of the Christian version (a thesis which would need considerable documentation), Badiou’s laicization in this case erases what Christianity considers an unbridgeable gap.

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Meillassoux contends, if one illegitimately extends probabilistic thinking about events within the universe to the universe as a whole. Meillassoux observes that it depends upon the possibility of totalizing all possibilities.

When I attempt to apply probabilistic reasoning to the universe as a whole, I assume—without there being anything in experience that could validate this assumption—that it is legitimate to consider the conceivable as another instance of the totality of cases. Thus, I subject the conceivable to a mathematical hypothesis: I turn it into a set, however large. I turn it into a set of possible worlds because I consider it a priori legitimate to think the possible as a Whole.64

One can perhaps already guess what the objection will be, from this telltale word Whole. The “set of all sets” is precisely the thing that is forbidden after the paradoxes of Russell were shown by Gödel to be unavoidable despite whatever theory of types might be attempted. Badiou’s dictum “the One is not,” derived from set theory and serving as an atheological axiom, thus here works to underscore the radical contingency of the world. For Meillassoux, this serves to lead up to his conclusion that it really is legitimate to respond to the question “why is there anything rather than nothing?” not by dismissing it as a pseudo-question, (Carnap), or by accounting it as a surface of “the limits of language” (Wittgenstein), but to answer it with the reply: “for no reason.” To dismiss it would be, Meillassoux fears, to return it to the realm of opinion, a realm in which one may say whatever one likes because rationality does not have a claim. To answer, on the other hand, is to give a truth.

Wittgenstein:

I can well understand what Heidegger means by Being and Angst. Man has an impulse to run up against the limits of language. Think, for example, of the wonder that anything exists. This wonder cannot be expressed in the form of a question, nor is there any answer to it. All we can say about it can a priori be only nonsense. Nevertheless we run up against the limits of language. This running-up-against Kierkegaard also saw, and indicated in a completely similar way—as running up against the paradox. This running up against the limits of language is Ethics.65

One can think of few remarks in the history of philosophy more inimical to Badiou’s thought than this declaration of Wittgenstein’s. For while Wittgenstein acknowledges that one cannot say anything meaningful, he does not dispute the right to speak, and grants these utterances a position not below, but above ordinary discourse. This is precisely to invert the right order of things for Badiou, who insists in Ethics that “Opinion is beneath the true and the false, precisely because its sole office is to be communicable” (my emphasis).66 Here is one place where we may judge the great distance not only between Badiou and Wittgenstein, but between Badiou and Heidegger. Badiou is attempting to distinguish opinion, doxa, from truth, in the Platonic manner; and as we have seen, he believes he follows Plato’s example in taking mathematics to be the paradigmatic case of the site of truth. But one may recall the distinction Heidegger makes in What Is a Thing?:

64 After Finitude p 103

65 Recorded in Waismann, Ludwig Wittgenstein and The Vienna Circle, ed. McGuinness, p 68

66 Ethics p. 5123

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The word mathematical stems from the Greek expression ta mathemata which means what can be learned and thus at the same time what can be taught. Manthanein means to learn, mathesis the teaching, and this in a twofold sense: First, it means studying and learning; then it means the doctrine taught. … ta mathemata [are] things insofar as we learn them…things insofar as we take cognizance of them as what we already know them to be in advance, the body as the bodily, the plant-like of the plant, the animal-like of the animal, the thingness of the thing, and so on. This genuine learning is therefore an extremely peculiar thing, a taking in which he who takes only takes what he basically already has. Teaching corresponds to this learning. …true learning only occurs where the taking of what one already has is a self-giving and is experienced as such.67

Now Heidegger makes a crucial distinction between the numerical and the mathematical.

…Numbers are the most familiar form of the mathematical because, in our usual dealings with things, when we calculate or count, numbers are the closest to that which we recognize in things without deriving it from them. …but the essence of the mathematical does not lie in number as purely delimiting the pure “how much,” but vice-versa. Because number has such a nature, therefore it belongs to the learnable in the sense of mathesis.68

There are at least two things to note about this passage. First, note that mathesis is, no less than opinion for Badiou, transmittable communication: it is mathesis precisely by virtue of being communicable. This is why Plato insisted upon attention to mathematics as prerequisite for philosophy; because he was continuing (and reshaping) a tradition, the Pythagorean tradition, which was expressly bound up with close attention to the mathematical for the very same reasons of transmission and transmissibility.69 Tradition in this sense is nothing but this handing-over from teacher to student, not of a set of “doctrines” but of the experience of self-giving, of anamnesis to use the Platonic term, an experience which is not the content of the doctrines but is facilitated by them. So it is not communicability per se which distinguishes the mathematical from opinion.

Second, the transmission in question is of a peculiar sort: it is of sparking a kind of experience in the hearer, so that the hearer, the “learner,” finds “what they already had.” This experience is dramatized for us, for instance, in the Meno in the dialogue between the slave boy and Socrates.70 In this respect, opinion is indeed very much opposed to the mathematical.

Now here is Badiou again on this difference:

67 What is a Thing? Pp 69-73

68 Ibid., p 75

69 One can see the emphasis upon transmissibility in the famous passage from the “Seventh Letter” (341c) “Only after long partnership in common life devoted to [philosophy], truth is kindled as it were in one soul, by a flame leaping from another.”

70 Meno 82b-85d. It is this that made Kierkegaard (in Philosophical Fragments) juxtapose Christianity with Socratism, in that Socrates is a teacher who is less significant than his teaching and in a sense gives only what the student has already, whereas Christ is a teacher who is more significant than (or, more precisely, simply is) the teaching, and gives the believer what the believer cannot accomplish himself. The religious contrast aside, there are profound implications for pedagogy in Heidegger’s formulation, as I assume is self-evident; what is not as obvious is their intersection with democracy. I will hope to address some of these connections in a further paper.

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[W]hat needs to be emphasized is that mathematics is the only point of rupture with that is given as existing, or constituted. …Everything else that exists remains prisoner to opinion, but not mathematics. So the effective, historical, independent existence of mathematics provides a paradigm for the possibility of breaking with opinion. Of course, there is dialectical conversion, which for Plato is a superior form of breaking with But no one can say whether dialectical conversion, which is the essence of the philosophical disposition, exists. It is held up as a proposal or project, rather than as something actually existing. Dialectics is a programme, or initiation, while mathematics is an existing, available procedure.71

This is indeed the entire difference between Badiou and Plato’s conception, in a nutshell. It may seem maddening to some readers that it has taken so long to get to the point, but here it is: Badiou offers us a Platonism without dialectic, without conversion, without the periagoge; the “turning around” from the wall of the Cave, nor the emergence from it; in other words, without initiation.

For many, recognizing “what we already know” is a breakthrough, an electric moment of insight, a sudden transformation of things as they snap into a new pattern. But there is also, always, a kind of let-down, an almost post-coital tristesse; for, after all, “we already knew that.” There is a sense of “is that all?” This let-down feeds the grave ambivalence many people even today feel as regards science, which on the one hand explains so much, and yet, on the other, well, it explains: it reduces things, either to what we already know, or to some new brute datum which we must “get used to,” i.e., familiarize ourselves with. (This is the distinction between “ordinary” science and the “revolutionary” science of a Kuhnian paradigm-shift). Aristotle warned of this ambiguity when he spoke of the way in which mathematical assertions “are true and please the soul.”72 The word Aristotle uses here for “pleases” () is ambivalent in its connotations. His phrase can be rendered, “…fawns upon the soul,” and suggests the wagging of the tail by dogs. The mathematical is indeed “familiar,” and in a sense “overfamiliar.”

Now Badiou cannot be accused of wishing to reduce things to “what we already know.” His whole account of the event is precisely to underscore that the situation does not account for everything. The event is an element that belongs to the situation but cannot be proven to so belong based upon the situation; in this it resembles any indemonstrable but true axiom to which Gödel’s proof would pertain. As Meillassoux writes, Badiou

uses mathematics itself to effect a liberation from the limits of calculatory reason, a gesture altogether more powerful than any external critique of calculation in the name of some supposedly superior register of philosophical thought.73

Despite Badiou’s protestations, such an effort is completely within the tradition of Wittgenstein and Kant, both of whom delineated the boundaries of human and rational prerogative in a manner ultimately meant to be empowering. In Wittgenstein’s terms, the “running up against the limits of language” is not merely an incapacity, an experience of negation. It is an experience with content in its own right.

Less controversially for Badiou or Meillassoux, this is also the tradition of Gödel, who showed that the limits of a single method of inquiry—formalism—were not the limits of possible experience. Likewise, it

71 Badiou, Theoretical Writings, tr. Brassier & Toscano, p 29.

72 Metaphysics book N, 1090b

73 After Finitude p 10325

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is the tradition of Plato, to whom Gödel always insisted he was loyal. Plato’s effort is directed, I maintain, against the critique exemplified by Xenophanes or by the sophists; a critique which either dismantled the claims of religion to legitimate experience, or which leveled discourse into a vast, flat realm in which no knowledge was possible, but only opinion. Such a critique is as poisonous for science as it is for piety. One could say that in terms of science, Plato was trying to keep the thrill of breakthrough, to insist that this experience was a sign of something real, without gainsaying the letdown.

Music as the Mathematical, and vice-versa

We will try to understand how Plato went about this—how he tried to safeguard the experience, the “initiatory” experience if you like—by looking closely at how Plato actually deploys numbers. The divergence between those who Leo Strauss calls “great thinkers” and those he calls “scholars” is nowhere more apparent than here. Plato’s deepest modern philosophical commentators, for instance Schelling, Heidegger, Strauss, Patocka, Voegelin, or Badiou, have made far-reaching readings of considerable profundity; but one must seek extensively, and usually in vain, in their work for any sign of curiosity about details over which Plato took considerable trouble: for instance, the number of guardians in his city in the Laws or, in the Republic, the precise diameters of his nested circles in the myth of Er, or the “number governing better and worse births.” On the other hand, these matters have not entirely languished for lack of attention. There is of course no shortage of capable exegeses of Plato which pay attempt to understand what he means.74 Such philology is as indispensible as it is notable for its lack of appreciable impact upon philosophy. Doubtless, there have been Plato scholars who have produced important philosophy as well, though they may fall short of the stature of Kant, Schelling, or Heidegger. But what is lacking is a sense of connection between their philology of number and their philosophy. Neither Cornford nor Taylor, for instance, engages with number in the manner in which Plato does, but neither do they answer why, if number should have played so indispensible a role for Plato, it ought not for the philosopher today. As we have seen, Badiou has sought to provide a robust philosophy that does engage with number, but with an amendment which Plato could never have accepted, which derails the experience of meaning. On the other hand, the meaning of Plato’s numerical clues has indeed received considerable unpacking, but often in works that at best make little impact upon philosophical practice; and at worst, are consigned to the fringes of scholarship—even on “New Age” shelves.

This state of affairs reflects badly not only upon scholarship, but upon philosophy, and is, I submit, one of the signs that Badiou is more right than he knows to claim that our era is anti-platonic. Indeed, in this respect, Badiou’s own stance is entirely symptomatic. For the relegation of certain considerations to philosophical irrelevance is itself unphilosophical. We are not entitled to regard Plato’s cosmology as his “applied” ontology as though we could easily separate it from his account of knowledge, love, justice, piety, or courage in the face of death. If Plato’s use of numbers implicates him in isopsephia, geomancy,

74 Admirable works in this respect from the last century or so are, for instance, Cornford’s Plato’s Cosmology, Taylor’s Commentary on Plato’s Timaeus, Friedländer’s Plato, Brumbaugh’s Plato’s Mathematical Imagination, Vlastos’ Plato’s Universe, and Pritchard’s Plato’s Philosophy of Mathematics. Above all, there is the tremendously masterful (and controversial) volume by D.H. Fowler, The Mathematics of Plato’s Academy, and (especially) Jacob Klein’s Greek Mathematical Thought and the Origin of Algebra. This last is of preeminent importance for its understanding of the break between ancient and modern notions of number and notation, and the significance of this break for contemporary science. Klein is one of the most striking of 20th century scholar-thinkers in his effort to faithfully follow the consequences of Platonism both in logic and spirit. So too is Gödel; but Gödel’s interest in scholarship or philology, such as it was, has remained unpublished and reported only secondhand. See, e.g. Wang, Reflectionson Kurt Gödel, Dawson, Logical Dilemmas: the Life and Thought of Kurt Gödel; Hintikka, On Gödel.

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alchemy, or astrology, we ought to follow “wherever the argument leads,” rather than ignoring this out of either modern embarrassment or failure to see what such connections could possibly have to do with Plato’s “higher” concerns, or, worse, sneering at the exegete who has pointed out the trail to begin with.

While such exegetes have been out of favor for a long while, they have never been lacking.75 In the twentieth century John Michell, Giorgio de Santillana, and Ernest McClain, have all in various degrees paid Plato the compliment of taking his details seriously. I will confine myself here to offering a few necessarily brief examples from Michell and McClain76. It is a different approach to this question than most; an indirect approach, made by looking not at those passages where Plato seemingly asks explicitly after the nature of mathematics, but those where Plato uses mathematics. My two authors do not agree in every particular. Michell has concerned himself primarily with metrology and to a lesser degree with isopsephia; McClain with ancient tuning theory. Neither of them has addressed the philosophical community. Michell, indeed, has hardly addressed academia at all, publishing instead informed and engaging “popular” books addressed to the educated general reader, whereas McClain’s works are all primarily addressed to archeaomusicologists. Genre and audience aside, I will suggest that the divergences between their arguments and conclusions are a mark not of their incompatibility, but of their genuine reflection of Platonic intention, though as will be seen, this conclusion of mine necessarily involves the privileging of McClain’s solutions to some degree (albeit not necessarily in a way with which he would concur). This is because McClain underscores the fundamental importance for Plato of approximation. This importance must however be, paradoxically, precisely understood, for it only emerges in a context that gives full credit to every demand for exactitude.

It should be also understood that my fundamental contentions do not require that we accept either McClain’s or Michell’s arguments in every particular, let alone the specific synthesis I shall suggest here. My hope is rather to suggest that the kinds of questions they ask would not only enrich a properly philosophical reading of Plato (rather than merely providing more footnotes) or such an investigation into the questions of cosmology and ethics as Plato undertakes, but would in fact open up contemporary thought to directions it has thus far apparently eschewed. I will mention briefly a few such possibilities at

75 The neoplatonism of Plotinus, Proclus, and Plutarch has itself become the object of scholarship now, and while there are some voices suggesting today that it might be of philosophical interest, it is rare to seek in it for any help in accessing Plato’s thought, which it is often rather assumed to have obscured. This is all the more true of religious thinkers like Philo, Origen, Augustine, or the scholastics. Nonetheless, all these are valuable as windows on Plato because they are closer to him than to us. Such readers have, thankfully, never wholly disappeared. Ficino in the Renaissance, the Cambridge Platonists in the seventeenth century, Thomas Taylor in the eighteenth, William Stirling, James Adam, and Albert von Thimus in the nineteenth, all stand behind the efforts of the scholars I am treating here. Two modern philosophers whose work stands out in this regard are Jacob Klein and John Bremer.

76 While I will be concentrating upon a single passage from a single Platonic dialogue, it is important to realize that Michell, McClain, and de Santillana all seek to place Plato in a broader and more ancient context which includes a vast amount of mythological material, and ranges far back into Vedic, Biblical and other Indo-Europoean or Semitic contexts (and beyond). (I offer a speculation about this context in the appendix). Thus while Badiou tends to emphasize the break between Platonism on the one hand and and on the other, these three all attempt to trace continuities between Plato and what went before. This is not to deny the radicality of the rift between myth and philosophy but to recast the significance of philosophy itself: where Badiou sees Plato as merely critiquing opinion and setting up philosophy against it, I follow de Santillana in reading Plato as using philosophy to keep what is valuable in myth in the face of the undeniable validity of the critique of myth, a critique not philosophical but rather, merely, skeptical.

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the end. However, in order to appreciate that this is so, we must review some of Michell’s and McClain’s work in detail.

In a series of works, including one on Plato exclusively, McClain has unpacked from the ancients’ actual practice the cultural background of Platonic mathematical assumptions. If, taking Plato at his word, we trouble to examine the various mathematical parables of the dialogues, assuming that they are there for a reason, we find that Plato’s mathematics do not so much assert something about number, as they rather illustrate something about the human being or human society; but it can only do this, it would seem, by virtue of a close link between number and the soul, a link that is not argued for but assumed.

What is the nature of this link? If we follow the clues McClain has patiently aligned for us, clues scattered throughout Plato’s texts but not haphazardly, the answer that presents itself is: music. This conclusion may surprise us in its simplicity; but once it is seen, many curious details overtly involving the use of numbers open up. Its plausibility is not at issue; explicit occasions where Plato’s text clearly supports this conclusion are easily at hand. In short, the musical is the bridge between Plato’s mathematics and what he uses his mathematics “for.” Indeed, we may say that not only can Plato’s use of number be understood in a context that draws upon music for its “grammar,” but also that Plato’s philosophy of mathematics is determined by practical limitations, which hedge his mathematical metaphors from being mis-applied.

Tuning the World-Soul

Our example for close consideration is the Timaeus’ discussion of the World Soul (34c-36d). We will not pretend to examine everything that could be said about this passage. Its relevance to McClain’s project is overt, for references to musical intervals are there on the surface of the text. After noting that God made the world-soul from Sameness, Difference, and Essence, Plato/Timaeus speaks of how these were divided. I give Jowett’s translation with his bracketed explanations:

First of all, he took away one part of the whole [1], and then he separated a second part which was double the first [2], and then he took away a third part which was half as much again as the second and three times as much as the first [3], and then he took a fourth part which was twice as much as the second [4], and a fifth part which was three times the third [9], and a sixth part which was eight times the first [8], and a seventh part which was twenty-seven times the first [27]. After this he filled up the double intervals [i.e. between 1, 2, 4, 8] and the triple [i.e. between 1, 3, 9, 27] cutting off yet other portions from the mixture and placing them in the intervals, so that in each interval there were two kinds of means, the one (harmonic) exceeding and exceeded by equal parts of its extremes [as for example 1, 4/3, 2, in which the mean 4/3 is one-third of 1 more than 1, and one-third of 2 less than 2], the other (arithmetic) being that kind of mean which exceeds and is exceeded by an equal number. Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the connecting terms in the former intervals, he filled up all the intervals of 4/3 with the interval of 9/8, leaving a fraction over; and the interval which this fraction expressed was in the ratio of 256 to 243. 77

As has been clear from the beginning, the numbers and fractions in play here correspond to musical intervals. The intervals of 3/2, 4/3, and 9/8 are, respectively, fifths, fourths, and whole tones. The first clue is

77 Timaeus 35b-36b28

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the series 1,2,3,4,9,8,27, which as many have realized is simply arithmetical order of the values of 2n and 3n for values of n from 0 to 3. These values, as McClain clarifies, define a span of possible notes:

Powers of 2 (1:2:4:8) define three musical octaves. Powers of 3 (1:3:9:27) define three consecutive musical twelfths, which extend through the range of four octaves plus a major sixth.78

Equally important is that the ratio between 3 and 2 defines the interval of the fifth. McClain shows exhaustively how every step in Plato’s text corresponds to a possible mathematico-musical operation. The “fourths” can be “filled up” by whole tones of 9:8, which indeed does leave a remainder of 256:243, a half-tone; thus the interval from, say, middle C to the F above accommodates two whole tones (C to D, D to E) before leaving room for only a semitone more (E to F).79 While this section of McClain’s explanation is straightforward, it requires considerable patience with numbers, any of which however can be accommodated on a pocket calculator. But McClain is following very ancient practice here, going back to the earliest known commentary on the Timaeus, written by Crantor within a hundred years of Plato’s lifetime. (It has been lost, but we have fragments and reports preserved for us mainly by Plutarch80). Crantor reports that two different ways of laying out Plato’s proportions were used in the Academy: a linear exposition “exponed in one row,” and another laid out in the form of the Greek letter lambda: Λ. This second mode underlies McClain’s reconstruction of the next stage of the Timaeus’ story:

thus the whole mixture out of which he cut these portions was all exhausted by him. This entire compound he divided lengthways into two parts, which he joined to one another at the centre like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side to the right, and the motion of the diverse diagonally to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two-and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three [Sun, Mercury, Venus] he made to move with equal swiftness, and the remaining four [Moon, Saturn, Mars, Jupiter] to move with unequal swiftness to the three and to one another, but in due proportion.81

The division, “lengthwise”, here bears resemblance to the founding acts of several other creation myths, for instance the separation of the waters in Genesis or the halving of Tiamat by Marduk in the Enuma Elish. In this case, however, Plato has reworked a poetic text (which may have had its own arithmetic or musical subtext) into a mathematical parable, what we might call a story-problem. The powers of 2 and 3 are here arrayed on different legs of the figure, just as would have been done in Crantor’s lambda:

78 McClain, The Pythagorean Plato, p 59

79 Note that the wholetone ratio 9:8 is composed of the two numbers in Timaeus’ list (1,2,3,4,9,8,27) which are out of numerical order.

80 See Plutarch, On the Generation of the Soul in the Timaeus 1022c-e; 1027d; also 1012d-1013b. See too Taylor, pp 109-136

81 Timaeus 36b-d29

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This lambda (which is also simply a variant on the Pythagorean tetraktys) is then extended into a Chi, X, by naming the reciprocal values of each of its members. This is completely legitimate in musical theory, since to double a string length is to descend an octave, whereas to halve it is to ascend. So too with the inversion of any other musical interval. We thus get a numerical array laid out as the demiurge’s X:

The middle values can then be filled in, as various means (arithmetic or harmonic) between the terms. This provides us with a table (theoretically extendable indefinitely) of tone-numbers. If we assign the root as D, for instance, the other notes of the scale fall out as follows:

Here we have the seven notes of the scale, beginning at D. Once the intervals are laid out, the demiurge then “bends” the two strands into circles. Here again, the musical meaning is easy to see: for the octave is a circle. In our modern equal temperament, twelve semitones occupy their places about this circle. In Greek music, however, the intervals were not equal, nor were they always twelve. In the present case, there are seven tones before the resolution back to the octave, that is to say, seven different tones, very much as our own major or minor scales have do-re-mi-fa-sol-la-ti.

McClain here avers that he is following ancient tradition in identifying the powers 2p with Difference, and 3p with Sameness. I tend to differ from McClain on this point, reversing the correlation. My rationale is that octave doubling or halving produces only “the same” tone, over and over, whereas powers of three are the differentiae which generate the other notes of the scale. This identification of mine is problematic, for 2 classically corresponded with the female, 3 with the male; and the male is indeed privileged as “the Same,” while female is regarded as “Difference.” This too we know from Plutarch, who makes overt reference to the tradition when he describes a Pythagorean right triangle with sides 3, 4, and 5 units long. In one respect, the question may be somewhat academic, for As McClain shrewdly observes,

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Since the material was first blended into a unity of Sameness, Difference and Existence, one can…conclude that Plato is asking us to remember that every element actually participates in both series and can be looked at from either perspective.82

However in another sense the question is important as an example of what I would call (following the ancient alchemists) the theory of correspondences, which was common in the ancient world, but came under critique with the rise of rationalism. Plato, McClain implies, is both continuing this critique and ironizing it.

Music is especially rife with such correspondences. It is common to think of notes as “low” and “high,” of intervals as “major” and “minor,” even as “happy” and “sad.” Such “artificial” associations are extremely deep-rooted in our language and in our psychology. Moreover, the association between a chord and an emotion, however peculiar, has an intra-musical precedent in the association between one note and another an octave “above” or “below.” Aural identification of the octave is a curious and remarkable thing: the apprehension of two notes as identifiably and meaningfully the same. This, to anticipate our discussion somewhat, is the primordial exemplar of what Badiou will call the “count-as-one,” the operation whereby a multiple is regarded as a unity. Here this operation is the identification of a note as “the same” note. The octave operation (halving or doubling) is by no means the only operation by which “same” notes are generated, however. The classic example is a series of twelve musical fifths (a fifth is an interval of five notes on a seven-note scale, from Do to Sol; the interval between D and A, for instance). On an equal-temperament instrument like a modern piano, moving up or down a fifth twelve times brings one “back” to one’s starting note, “the same” note but seven octaves away. This consonance is strictly an artifact of equal temperament, however, for the arithmetic of tuning theory makes it actually impossible to make notes generated by a series of octaves commensurate with notes generated by a series of fifths, for the simple reason that the ratio 1:2 taken repeatedly does not give the same string length as iterations of the ratio 2:3. There is a difference between the results of these two iterations, and no matter how the ear wishes to hear the two resultant notes as the same, the arithmetic will not oblige. The name for this incommensurability is the Pythagorean comma. The comma is “overcome” neither by strict insistence upon difference, nor by agreeing to ignore difference. It is overcome by approximation. It is only by approximation that the comma is “shared,” in modern equal temperament, among all the intervals, rather than afflicting a single one most. In Equal Temperament, the approximation of the twelfth root of 2 serves as the ratio for each semitone, rather than the rational proportion 9/8. However, other roots—notably the square, cube, and fifth—also figure in ancient tuning theory and must also be approximated, not for “purely mathematical” reasons but out of aural necessity. Such approximation is of course potentially endless; its halting occurs when the ear is satisfied, and can “count as one” “two” notes now rendered indistinguishable. I emphasize that this is a musical model (albeit a privileged one) for Badiou’s operation, not its “origin,” but then, the Timaeus itself emphasizes this very point:

If then, Socrates, amid the many opinions about the gods and the generation of the universe, we are not able to give notions which are altogether and in every respect exact and consistent with one another, do not be surprised. Enough, if we adduce probabilities as likely as any others; for we must remember that I who am the speaker, and you who are the judges, are only mortal men, and we ought to accept the tale which is probable and enquire no further.83

82 The Pythagorean Plato p 6531

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The dialogue then is a “likely story,” a series of models, and not a strict and precise depiction. Nevertheless, the model proceeds upon strict principles, which can be rightly or wrongly applied.

Modeling the model’s lapse

What is often of interest is the textual juncture where the principles of one model begin to overlap with those of another. In such instances there is a kind of metaphorical Pythagorean comma. We see this for instance in the approximation of tuning theory with astronomy. Our seven musical notes (and also the seven Greek musical “modes”) became associated, as is well known, with the orbits of the seven classical “planets,” (including the Sun and Moon), an association that is traced to the Timaeus, including the conclusion the passage under consideration. But just as with the correspondence of male and female with same and other and 2 and 3, so too here the correspondence does not work perfectly, and is known not to work perfectly. McClain notes that Plato is indeed somewhat loose in making this association, mentioning only the Moon, Sun, Venus and Mercury by name, and breaking off the “casual discussion of astronomy as being ‘a heavier task’ than is worthwhile.” This is not to say that the correspondences are not there or significant in Plato’s mind, but that Plato knows when to stop. For just as significant as the correspondences themselves are the instances where the correspondences fail. This is because every model—musical, astronomical, calendrical, sexual, mathematical, and so on—bears within it some instance where precisely this failure of models can itself be modeled. Thus, the calendar presents us with incommensurable solar and lunar years, neither of which will conform to an “ideal” 360 days; astronomy reveals the precession of equinoxes in the ostensibly “fixed” stars; geometry harbors the irrational numbers, and these in turn can reveal, as Cantor showed, the exceeding of one infinity by another; logic gives rise to paradoxes from the third man of the Parmenides to the Incompleteness Theorem of Gödel. Finally, and perhaps most elementary of all, there is an irreducible and unbridgeable chasm between any physical exemplar of a circle, a triangle, or any other geometrical shape, and its mathematical archetype. A gap between the depiction or explanation and the thing depicted or explained is a perennial characteristic of all thought that aspires to articulateness, for though it may be true that “Being and Thinking are the same,” there remains the puzzle of difference itself, which will vex, if not that unity, at least every effort at its representation.

But again, as Cantor and Gödel reveal, there are ways for that falling-short of the model to nonetheless point to what it fails to account for. In this theoretical self-similarity, music has a certain privilege, for the theoretical impossibility of perfectly commensurate musical intervals is matched by the demand for practical approximation. This is far more than a need to let go of “needlessly precise” measurements for the sake of hurrying to an actual accomplishment. The aspiration to tuning precision can show itself to be impossible to fulfill, and therefore must be re-channeled into a different task in order to render useable any tones at all. That new task is the Diophantine approximation of the various roots of 2, but I will not here examine all the ways McClain indicates that this effort is pointed to in Plato. I restrict myself to observing that the lapse of any given system allows Plato to entertain many different systems—not only different tuning systems, but also systems other than music: astronomy, metrology, and so on—and to countenance their various implications with equanimity without worrying out their every last repercussion.

83 Timaeus 29c-d. (This is immediately after the passage we found cited by Gregory of Nanzianzen above).32

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Thus when we compare Michell’s interpretation of our passage from the Timaeus,84 we will find that while it differs significantly from McClain’s, this divergence is not a reason for rejecting the one or the other. For each of them can assemble a repertoire of evidence. Michell’s case consists of isopsephiac sums, that is, the values reached by adding the numerical values of the Greek letters in certain key words used by Plato, and a reconstruction of Plato’s geometry. The two strands of the World Soul are laid criss-cross over each other in the form of a X, the letter Chi, whose value is 600; this is the value of the Greek word , world. These two strands are the Same and the Other, ; this phrase sums to 1746. Michell’s isopsephia derives this from the sum of 1080 + 666, numbers for which he claims lunar-female and solar-male connotations, respectively. I will not here inquire further into those assertions except to point out that both these numbers certainly occur elsewhere in ancient traditions which predate Plato and might easily have played roles in Pythagorean doctrine. The number 666 is, for instance, six times the magic sum (=111) of a well-attested magic square anciently associated with the sun; 1080 is a close approximation of the lunar radius in miles, a metric whose use in this context Michell is at pains to justify (but see below, n. 85). But Michell links his numbers here, via geometry, with other values we immediately recognize from elsewhere in Plato. The two arms of the Chi he bends round into intersecting circles, rather than placing one circle wholly inside the other.

He points out that as the two circles are said to be formed from the arms of the Chi, the circles would be equal in circumference, and two equal circles will not fit one inside the other. Michell’s first circle is bisected by the line bisecting the Chi (he notes that this results in a glyph not unlike the early Christian Chi-Rho); the second circle is bisected by one arm of the Chi (or rather, the line where that arm lay, as the arm itself is now bent around into the circle in question). The intersection of the two circles thus described is the famous proportion known as the vesica piscis, the fish- or almond-shaped intersection formed when two equal circles intersect, and the circumference of each crosses the other’s center. Now Michell follows this clue. Let the two arms of the X each be 1746 units long. Let each of these now be the long axis of a vesica piscis. The intersection of these two vesica now will contain a circle whose circumference may be rounded to 3168. This (reckoning with its ancient approximation 22/7) puts the radius of the circle at 504.

84 My account here is mainly derived from Michell, City of Revelation, especially chapter 8, pp 92-103.33

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Multiply these terms by a factor of 10 and one comes to 5,040 and 31,680. But as is well known, 5,040 (=7!) is Plato’s stipulation for the ideal number of families for his city of Magnesia in the Laws.85 The research of Michell, David Fideler, Kieren Barry, Connie Achilles, and others indicates that these numbers figure for Plato because they were already a part of a considerable system of number mysticism which survived and gave rise to numerous permutations of tradition86.

For instance, that 3,168 retained its mystical significance into later centuries is strongly indicated by the fact that , “Lord Jesus Christ”, also adds to precisely this sum. That such numbers derive their significance from a pattern that greatly predates Plato, and that both Michell and McClain have each seen a portion of this larger pattern, is also suggested in the research of Connie Achilles, whose work collates geomantic, metrological, musical, astronomic and isopsephiac values. Achilles’ musical demonstration relies upon the division of the octave into not 13 but 22 tones (including the root and octave), a division which finds some justification in the fact that Indian sources speak of the division of the octave into 22 intervals called shrutis. Achilles’ division follows very simply from deriving the tones’ ratios from two different series of ratios bounded, respectively, by limits of 3 and of 5, which method provides two values for every tone except for the root, fourth, fifth, and octave. This leaves nine further tones with two ratios each, a total of 18 +4 = 22). Her ratios are translated into degrees on the circle; and the total number of these degrees is in very close approximation to 3,168 (precisely 8.8 revolutions on the circle)87.

This is suggestive, albeit indirect, evidence that music, isopsephia, geometry, and other disciplines can all be at play when Plato uses numbers (and also when the numbers are not on the surface of the text). However, aside from the fact that “very close” approximations raise zetetic hackles, even such resonances as do not use approximations are of course not always in harmony with each other. This suggests a potential objection, whose strongest form is: if McClain is correct, then Michell must be mistaken, and vice-versa. Not all the correlations can work. To take an obvious example, McClain’s two circles are not the same as Michell’s; and Michell’s vesica piscis seem at first to confound McClain’s tone circles. But to assert this is to misunderstand not just Plato, but McClain; and paying closer heed to McClain will help us to see that while music in many respects has a pride of place among Plato’s schema, it is a sort of primus

85 C.f. Laws 5.737e. It is also the sum of 1080, Michell’s lunar radius in miles, and 3960—the terrestrial radius—which lends at least the force of coincidence to Michell’s case that the mile is not a purely arbitrary measure here. (See too Appendix, note 4).

86 See Fideler, Jesus Christ, Sun of God; Barry, The Greek Qabalah; Achilles’work can be found on her website, HarmonicTheory.com

87 See the technical appendix to this paper for a critical presentation and modification of some of Achilles’ results, as well as a table for the isopsephia values of the Greek alphabet.

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inter pares, and indeed, first only by virtue of being among others. Tuning theory relies upon approximation not simply as a practical expedient but as a theoretical sine qua non, and Plato makes use of it (in this respect as in many, doubtless following Pythagorean precedent) precisely in order to show that no single vision encompasses everything. But to say this is to insist that Plato’s project is about more than an intellectual system; it is not in pursuit of merely theoretical rigor, but rather of experience.88

Plato is able to countenance such varieties of resonance because the final criterion is for Plato, not mathematics itself, but, precisely what Badiou denies is real: dialectical conversion. It would be absurd to suggest that Plato has laden his dialogues with numbers and trails leading to numbers for their own sake. But because for Plato mathematics is always primarily musical, precision itself is not the end of the matter. It is indeed true that the musical scale and the orbits of the planets are in only a loose and metaphorical association with each other. But in fact, so too are the notes low and high D. Musically, hearing equates tones which in fact diverge. But knowing the divergence and the convergence simultaneously brings about an experience which drives home both the indispensability and the limits of rigor—and of laxity as well.

Badiou can maintain that ontology is mathematics, thinking thereby to once and for all abolish the penumbra of mystery that surrounds the question of being, “flattening” our universe into one of mere infinity, domesticating or laicizing it as it were, only by gainsaying the Platonic tradition he thinks to honor. His gesture is one of radicalizing mathematics, taking it to its final extreme conclusion. To reiterate, in a gesture very like that he attributes to Galileo “domesticating the heavens,” so to speak, in abolishing the difference between celestial and sublunary realms, Badiou seeks to domesticate the infinite by effectively abolishing the difference between it and the finite. But Plato himself never does this, and knows himself to refrain from doing so. McClain’s description is very apt, and underscores both Plato’s considerable modernity at the same time as it emphasizes his different emphasis:

It is interesting that Plato’s constructions exhibit so many similarities with our modern notion of a formal mathematical group. His awareness of the “associative” and “commutative” properties is indicated by the uncertainty of paternity in his cities. He is obviously interested in “identity” elements and adamant that reciprocals (“inverses” for each element) be studied. His awareness of the closure principle is indicated by his passion for interfering with its operation, rigidly limiting populations whose marriage laws would otherwise generate infinite groups. The formal group properties are implicit in his formulas, yet by limiting “form numbers” (meaning “group generators”) to the first ten integers, Plato invites the implications that his own examples should not be generalized to allow “form numbers” to exceed ten, and that his “rotations of the plane” (i.e., his tone-circles) should not include other rotations than those he himself used. For Plato to have approved so generous an attitude would have divorced his number theory from its limited ground of musical applicability, and would have dissolved the principle of “limitation,” and particularly “self-limitation,” which lies at the heart of his musical and political theories.89

88 C.f. Epinomis 991e: “To the man who pursues his studies in the proper way, all geometric constructions, all systems of numbers, all duly constituted melodic progressions, the single ordered scheme of all celestial revolutions, should disclose themselves, and disclose themselves they will, if, as I say, a man pursues his studies aright with his mind fixed on their single end. As such a man reflects he will receive the revelation of a single bond of natural interconnection between these problems.” See the passage from the “Seventh Letter,” cited above. I take it for granted that whether these passages are by Plato, or Philip of Opus, or someone else, they reflect accurately the spirit of the dialogues.

89 The Pythagorean Plato p 12935

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Platonism is not a theory of the “abstract existence” in a rational empyrean of “ideal” furniture, animals, shapes, and numbers. It is the cultivation of dispositions making for understanding, and the application of understanding to disposition. This disposition is one of openness to the experience of all things as connected. That mathematics plays an indispensible role in the grammar of such interconnection is plain: against Badiou’s account of mathematics as the itinerary of differences, I maintain another: mathematics is the (unfinished and unfinishable) articulation of relationship per se. In this, music has (in Plato’s mind and in the ancient world generally) a privileged position as the example par excellence. In tuning theory “the One” is simply our root tone. It is whatever tone we start from, whatever tone we decide to call Do in our scale, whether we ascend (Do, Re, Mi, Fa…) or descend (Do, Ti, La, Sol…). McClain is repeatedly explicit that “one” can mean anything whatsoever, but also that consequences follow from whatever definition we use. “Do” is simply the unit term. In itself it does nothing. Here, incidentally, is a plausible origin of the trope Kojève is using when he says of gods that they “do nothing.” Moreover, the Pythagorean comma is only the most obvious instance of incommensurable lengths as they arise in music, occasioning the need to approximate square, cube, cube and twelfth roots, depending upon how one attempts to accommodate it. Here again, such incommensurabilities are not of merely theoretical interest; we are compelled to interact with them on purely practical and aural grounds. As such they are the concrete instances of the presence of infinity, since they offer opportunity for ever-closer approximation; but they also show clearly that convenience allows approximation to “come to a stop.”

I am far from wishing merely to contest the adequacy of Badiou’s formulations. Badiou has made explicit the consequences of a radically secular mode of thinking. His is a logical re-articulation of a classic gesture, necessary for philosophy in every age: the critique of the correspondences. In elaborating this perennial move in the register of our own time, Badiou has repeated again the move of Xenophanes. The great irony is that in so doing he also attempts to reiterate the Platonic response; but without a sure sense of the manner in which Plato deploys his mathematical instincts, Badiou’s Platonic efforts go awry.

Plato as Perspectivist

Badiou is already the author of a tremendously formidable oeuvre, and I am painfully aware of not doing justice to him—let alone to others (Levinas, Derrida, Kojève, Rosen, and so on) whose work I have only touched upon here. I take it for granted that curious readers will either be familiar enough to recognize (or contest) the validity of my sketches, or will stipulate them provisionally in anticipation of verificatory readings on their own. In particular, it would be necessary to go over in considerable detail the (greatly controversial) relationship of Badiou’s relationship with Deleuze and the latter’s thought on multiplicity, heterogeneity, and univocality.90 I would also like to have made a close comparison between Badiou’s four conditions or sites (love, politics, art, and mathematics) and some other fourfold schemata from the history of thinking,91 for it strikes me that it is not by accident that this pattern has recurred many times

90 A full treatment would also have to allow considerable space for Badiou’s important and problematic relationship with Lacan.

91 Such foursquare schemes, astonishingly frequent (my unscientific impression is that they outnumber triads and other numerical arrangements), include Plato’s divided line; Aristotle’s senses of Being and causes; hermeneutic keys from medieval Kabbalists and Christian exegetes; Vico’s four tropes; Schopenhauer’s fourfold root; Santayana’s realms of being; Jung’s psychological typology; Heidegger’s fourfold (earth, sky, gods, and mortals); and presentations by Nicolai Hartmann, Michael Oakeshott, Paul Weiss, Northrup Frye, Mortimer Adler, Marshall & Eric McLuhan, Stephen Pepper, E. Jonathan Lowe, Ken Wilber, William

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since the ancients described the four primal elements. But I must be content here to hope to have made a case that in order to engage fruitfully with any modern permutation of Platonism, it is essential to understand the presuppositions of correspondence which Plato simultaneously assumes and critiques. For these correspondences number is a grammar, and music the privileged instance. The relationship between them is not unlike that which Wittgenstein thought, at all stages of his career, between an “ideal” and an “ordinary” language. “Ordinary” language is language as it is used in everyday occasions, full of ambiguity and slang and nudges and winks; “Ideal” language is something like Leibnitz’ Characteristica Universalis, or the logical calculus of Whitehead and Russell’s Principia Mathematica, or Schuyler and Laura Riding Jackson’s Rational Meaning; it would be a system in which each term has a single definition, its use governed by explicit rules (also expressed in the language). In Wittgenstein’s Tractatus, such pure coherence of the systematic is the surface, as it were, of the limit, of the bare mystery of haecceity, the irreducible thusness of the world; in Badiou’s terms, the pure inconsistent multiplicity92 of the void, or what the Buddhist dharma would refer to as sunyata. But note that here there is no question of a radical division between “ordinary” and exceptional. Wittgenstein comes to speak of “family resemblances” rather than definitions and logical form. It is only slightly hyperbolic to say that the ordinary is wholly comprised of exceptions.

This circumstance is simply the status quo in music, rife as it is with “accidentals.” Music is the primary context for so many of Plato’s metaphors because it is the empirical realm in which it becomes obvious that the claims of theory alone are not sufficient to establish practice. This obviousness arises in theory, but its ramifications are practical. In short, for the Socratic view, practice and theory are grounded and united in practice; or, put otherwise, theory is a form of practice. And with this in mind, “what kind of philosopher,” McClain asks, “is our Pythagorean Plato?” Perhaps surprisingly, he concludes, on the basis that the dialogues show a “readiness to ‘sacrifice’ a perspective [previously] laboriously gained,” that

Plato is in no sense what we have come to understand as a ‘Platonist.’ Neither is he a Pythagorean. His Pythagoreanism is but a prelude to philosophy, to “the song itself…which dialectic performs,” [which] establishes the multiple perspectives from which Plato understood himself …Such a vision is grounded in the arts and sciences of one’s own culture when they are treasured in rich enough measure that one possesses alternative perspectives on any phenomenon….The art of mathematics holds a very special place in Plato’s esteem: it is essentially an art of changing viewpoints, of alternative perspectives, and it gives to those who pursue it seriously a release from the imprisonment of a single viewpoint.93

Desmond, Graham Harman, and Antonio de Nicolas. De Nicolas is perhaps most immediately pertinent in our context because McClain has explicitly attributed to de Nicolas’ study of the Rg Veda, Four-Dimensional Man, the inspiration for his own efforts in The Myth of Invariance and The Pythagorean Plato. It is obvious that these (and others) are not trivially equivalent to each other.

92 The term is from a letter of Cantor’s: “Every multiplicity is either an inconsistent multiplicity or it is a set [ensemble].” (Cantor to Dedekind, 28 July 1899). Badiou is often explicit that inconsistency is what is apprehended (or manifest) in an event; e.g. “The being of a situation is in its inconsistency…. A truth…says nothing in particular about a situation except precisely its multiple-being as such, its fundamental inconsistency.” (Manifesto for Philosophy p 107). His exposition of the concept should be compared with the approach of Cornelius Castoriadis. See e.g. Castoriadis, “The Logic of Magmas and the Question of Autonomy,” The Castoriadis Reader pp290-318.

93 The Pythagorean Plato, p 13337

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Here again, McClain’s reading of Plato diverges from Michell’s. Michell has painstakingly reconstructed a tremendous system in which astronomical, numerological, musical, geometric, and other elements are all at play. Michell is careful to specify that this system is not of Plato’s own making, but is (he claims) inherited and found variously in the Vedas, the Biblical record, Egyptian religion, and the archeological leavings of megalithic culture, as well as elsewhere. His results have not been widely accepted in contemporary scholarship, albeit not always for scholarly reasons. Academia is (often rightly) suspicious or scornful of claimants to the “meaning” of Stonehenge or the Great Pyramid, and at best tends to say that speculations such as Michell’s pertain to things beyond the bounds of university departments.

But this, insofar as it holds, only shows the poverty of university departments. While Michell’s reconstructions may carry more than a whiff of the New Age bookstore, and some strains of philosophy may cringe at any suggestion that they have anything in common with ancient mysticism, a few thinkers have pointed us in a new and more fruitful direction, pointing out that ancient philosophy is therapeutic and inextricably bound up with what are clearly recognizable as spiritual practices.94 In short, I contend that we must take Rosen’s account of the divine aspirations of ancient philosophers more literally than perhaps he intends; the aim is, indeed, to “become God” to the degree that this is attainable by human agents, an aim that continues to be operative (albeit divergently understood) in traditions as different as Mormonism, eastern Orthodox monasticism, and Aleister Crowley’s magick. Nonetheless, it must be conceded that Plato does not merely take over this system of practices whole and complete. For while he presupposes it, he also proposes an extensive critique of this same system, aware that salient objections to it have been raised that cannot be dismissed or wished away by nostalgia. What Plato seeks is a way to preserve what is valid in this system without denying the legitimate claims of the rational forces that subject it to a critique like Xenophanes’. It is precisely the same effort that has motivated philosophers in every age—one only need think of Kant, for instance, seeking to reconcile faith with reason—and it explains, incidentally, what Kant called the scandal of philosophy, namely, that it makes no progress. Philosophy cannot make progress, because it is always involved in salvage operations. It is thus always in tension between the experience of insight and the explicit discourses which are in contradiction of each other, but whose contradiction generates the insight beyond discourse.

McClain clearly intuits this tension. Whereas Michell tries to put back together a single great cosmology, McClain sees Plato as offering different accounts and vantages, one after another. In some respects, McClain’s Plato is remarkably Nietzschean, and one may profitably compare McClain’s summary above with a remark of Nietzsche’s from The Will to Power. In expounding his perspectivism, championing the ability to shift from one view to another and to eschew the hankering after a single, ostensibly “true” vantage, Nietzsche summed up with a characteristic hyperbole:

The most extreme form of nihililsm would be the view that every belief, every considering-something-true, is necessarily false because there simply is no true world. Thus; a perspectival appearance whose origin lies in us (insofar as we constantly need a narrower, abbreviated, simplified world).—That it is the measure of strength, to what extent we can admit to ourselves, without perishing, the merely apparent character, the necessity of lies.

94 I am thinking in particular of Peter Kingsley, Ancient Philosophy, Mystery, and Magic; Martha Nussbaum, The Therapy of Desire; and Pierre Hadot, What is Ancient Philosophy? and Philosophy as a Way of Life. I must add that none of these thinkers necessarily would concur with each other on all points, nor, of course, with the conclusions to which I apply their accounts.

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To this extent, nihilism, as the denial of a truthful world, might be a divine way of thinking.95

Where Nietzsche yields here to the play of appearances, Plato looks, not “beyond” appearances, but at what this ability to shift from perspective to perspective means. Notice, however, that Nietzsche has described this “denial of the truthful world” as “a divine way of thinking.” While for Plato it is not nihilism, it is no less divine. As Rosen underscores, the Platonic aspiration is indeed to a sort of theosis, deification; and as we have seen, Nietzsche is far from the last to overtly aspire to this status. Kojève (following Hegel) wanted to attain it by mentally recapitulating history, and even urges that one may adopt a belief, knowing it is false, in order to make it into a truth. To act this way is the prerogative of gods. As we have seen, Badiou has his own inflections upon this trope of being “more than a mortal being” by way of exceeding the historical situation. Nietzsche trumps all with amor fati and the Eternal Recurrence. It is quite instructive that he uses precisely the same phrase, “the most extreme form of nihilism,” to describe both his radical perspectivism which denies truth, and to describe the Eternal Return:

Let us think this thought in its most terrible form: existence as it is, without meaning or aim, yet recurring inevitably without any finale of “nothingness:” the eternal recurrence. This is the most extreme form of nihilism: the nothing (the “meaningless”) eternally!96

I hasten to say that I cannot here address all the questions that arise from these philological points. That Nietzsche should have described both his absolute perspectivism and the Eternal Recurrence as “the most extreme form of nihilism” seems to me not coincidental, but I will not here argue for all the conclusions that may follow. What does seem clear to me is that in light of Nietzsche’s call to a “inverted Platonism,” the perspectivism he calls for, and the Eternal Return he both proclaimed and recoiled from, are not properly thinkable without reference to the beginnings of his thinking in “the birth of tragedy out of the spirit of music,” music which must necessarily be thought through in its Platonic contours. Moreover, insofar as any contemporary thinking through of philosophical questions would be informed by the platonic genealogy, either from scholarly or from philosophical motives, it must include an explicit and scrupulous engagement with what Plato was engaging. It is not a mere matter of exegesis, though exegesis has its part.

The Scope of Thinking and the Persistence of Faith

Badiou’s philosophy is admirable for many reasons: his militant commitment, his indefatigable consistency, his prodigious learning. Most remarkable, perhaps, is his breadth, his sense that it is perfectly within the rights of philosophy to speak of the situation of persecuted minorities or the temblors shaking financial institutions, of a painting by Rothko or a poem by Neruda, of the meaning of love according to Lacan or Sappho, of the makeup of physical reality. All of these are available for legitimate reflection by Badiou in a way they were also for Bateson, Hegel, or Leibniz; or for (to name some of Badiou’s few 20th-century rivals in terms of scope) Bernard Lonergan, Nicholas Rescher, and perhaps Karl Popper or Mario Bunge. It is refreshing to encounter a thinker for whom such latitude comes naturally and without

95 The Will to Power, §15

96 Ibid. §5539

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apology. One feels at once the excitement of reading philosophy in all its tremendous range. In this above all, Badiou shows himself a true heir to the Platonic mantle to which he lays claim.

He also shares its ambition, if we concur with Rosen that the Platonic aspiration is to partake of the divine life. This holds despite the fact that Badiou has resolutely ignored or contested every attempt to construe his thinking along theistic lines. It is here that Meillassoux, in drawing out some of the speculative conclusions derivable from Badiou's teaching, most obviously diverges from him, for Meillassoux has presented what looks for all the world like an argument for a possible God, an argument from Badiouan premises but structured in Kojèvean “as if” fashion. Meillassoux attempts to navigate the dilemma—which he terms a “spectral” dilemma—between religious belief and unbelief, by way of a stratagem wholly consistent with the unstinting reliance on contingency we considered above, yet with a dialectical subtlety worthy of Hegel. In this very short gloss, I shall leave to one side many nuances, details, and distinctions which Meillassoux makes, but my aim is not to present the argument or its consequences in their entirety—these are, after all, the substance of an entire book by Meillassoux97—but to give an indication of what is possible if one thinks the death of God otherwise. 

The “dilemma,” Meillassoux asserts, is precisely undecidable; undecidable, one concludes, on the basis of what Badiou would call the situation. This situation is precisely the one named by Sartre: “a situation in which there are only human beings.”  Both theism and antitheism are defenses, on Meillassoux’s terms, against a despair in the face of death. Here is an admirable application of Badiou’s premises to the existential fact that human beings do die—die no matter whether we construe them as “more than a mortal being” or as an animal. Death for Meillassoux occasions mourning, and mourning leaves something unfinished, for death, and especially the violent or premature death, always feels as though it has left a part of the life in question “unlived.” Thus the survivors are faced with a “spectre,” an unfulfilled mourning, which they deal with in contradictory ways. Believers refer their mourning to a God, a divine life in which the dead could be incorporated. But for unbelievers, this solution is unbearable, and worse than the problem it would answer. Such a God would, per hypothesis, also be responsible for the deaths in the first place. Better to disappear entirely, they say, then to be referred to an evil god who passively permits suffering and, by having the dead referred to Him, sacralises death itself. This argument between theist and antitheist is perpetual and irresolvable, says Meillassoux, as long as we conceive God under the rubric of necessity, as the one who “must be,” as, for example, any God whose existence is derived at the bottom line of a theological proof. Meillassoux’s solution is dazzlingly and deceptively simple: think God not by way of necessity, but by way of possibility98. A God who could come to be, a God who would thus could give the recovery of meaning and life the theist desires, but still have been innocent of the violence and evil the antitheist finds unbearable99.

97 See Meillassoux, “Spectral Dilemma”, in Collapse IV (May 2008). The article is a précis of a portion of Meillassoux’s unpublished (as of early 2009) L’inexistence Divine. Needless to say, I do not claim that Meillassoux would concur with any of my conclusions here.

98 The so-called “religious turn” of phenomenology, which while expressly opposed by Meillassoux (and largely drawing upon Levinas for much of its esprit) nonetheless bears comparison to Meillassoux’s speculation in its attempt to think God “without Being” as Marion puts it; that is, beyond necessity. The difference is that Meillassoux thinks necessity opposed to contingency; whereas for Marion, Levinas, and others, necessity is opposed to freedom. On the “religious turn,” see Dominique Janicaud, “The Theological Turn in French Phenomenology,” and rejoinders by Marion, among others, in Janicaud, ed., Phenomenology and the “Theological Turn”; see too the remarks of Graham Harman in the first chapter of Harman, Guerilla Metaphysics.

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This is more than a clever reversal or a word-game, for as we have noted earlier, Meillassoux stakes a great deal on his ability to demonstrate the priority of contingency over necessity. In the present context, however, we may note how it seems to recapitulate upon a cosmological100 or ontological level the audacious project which Rosen describes as the true philosopher’s from Socrates to Strauss. How far the project to become a god differs from the project to bring God into being is here an open question, all the more so when thought in conjunction with Nietzsche’s invitation to “a divine way of thinking.” I am not trying to resolve it here, but only to suggest that thinking such matters through requires a willingness to think from many angles at once; to “follow the argument wherever it leads;” and in particular, to plead the case that such classically philosophical questions as quid sit deus? will look different to us if we consider them via the formulations of the ancients, who did not despise considering the extraordinary question of the holy in light of the ordinary data of starlight or a plucked string101.

It should be clear that in some sense the breadth and the audacity I am describing are part and parcel of one another. If, when attempting to think the question of God, or infinity, or the meaning of mathematics, or any other properly philosophical question, we take our bearings (without necessarily concurring) from Nietzsche, Heidegger, Gödel, Badiou, or any other significant thinker, we must recognize that the tangle of questions—number, divinity, ethics, truth, being—must be thought together. This “together” is what was already declared in multiple inflections by Plato, and music is the organizing principle, prima inter pares, by which he thought it. Music comprises a model in which infinities (instanced by incommensurable lengths) are continually at play, either in tones that are at odds with one another (discordant because generated by different ratios), or in attempts to reconcile them by approximation. Moreover, music is a made thing, a product of human poesis, which thus serves as a continual reminder that the mathematics upon which it relies is, in a sense (the sense Vico relies upon), also an artifact. This means that mathematics’ pride of place in the sciences, even as ontology “itself,” is itself a theological conclusion: following Vico, we can say that we know with greatest certainty in mathematics because

99 The comparison between this recent effort of Meillassoux’s and several other speculations, from James, Whitehead, Hartshorne, Teilhard, Kearney, and Tippler, is striking. Of special interest perhaps is a resonance with the recent work of Ernst Tugendhat. One of the last students of Heidegger, Tugendhat attempted to combine Heidegger’s thinking on human questions with the rigor found (only to be found, Tugendhat concluded) in the Analytical tradition. He thus represents an effort comparable in important ways with Badiou’s, as well as with Rosen’s The Limits of Analysis. Tugendhat’s most recent work presents an anthropology of religious experience and mysticism which admits the possibility of mysticism outside of theism per se.

100 It would also seem to be the reverse of an actual historical process traceable in the Hebrew and Christian scriptures and noted by scholars and theologians: a gradual withdrawing of the experience of the divine, a shift from a God who walks in Eden and wrestles with Jacob to one who cannot be seen and eventually seems to withdraw entirely. (Compare Julian Jaynes’ Origin of Consciousness in the Breakdown of the Bicameral Mind.) I would suggest that the historical advent of such modes of consciousness indicated, for instance, by Xenophanes’ critique of religion, owes much to such a process. It continues to be thematic in the mythology of the deus otiosus (regarding which see e.g. Mircea Eliade, The Quest pp 81-7) and the theology of deus absconditas and in the “Eclipse of God,” as Martin Buber called it. This would have to be read in conjunction with the Entgotterung of which Heidegger speaks. Such a thematic is closely bound up with the “desacralization” or “disenchantment” which we saw Badiou lauding. If our account is correct, it has been part of Platonism from the beginning to understand such “secularization” against itself—which is not the same as merely “countering” it.

101 Thus against the thematic of the absent god, we would have to consider Heraclitus, whose insistence that “even here the gods are present” can also be read in this remark of Metropolitan Anthony Bloom: “You will find stability at the moment that you discover...God is here, and if you do not find Him here it is useless to go and search for Him elsewhere, because it is not Him that is absent from us, it is we who are absent from Him.  If you cannot find Him here you will not find Him anywhere else.” (Quoted by Esther de Waal, Seeking God p 65).

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mathematics is most wholly our own invention; it is the realm in which our knowledge most approximates God’s.102 Music is the best exemplar of mathematics because it inescapably foregrounds this relationship between mathematics and human ingenium. But to admit this is to concede with Kant and Wittgenstein that there are limits to what the human mind can legitimately aspire; in Vicos’s terms, that what we do not make exceeds our knowing. (This is to restate the problem of idolatry). Or, again, that there is an inevitable “comma” between humanity’s reach and its grasp.

Of course it can be objected: Plato’s principle it may be, but music need not be our principle. But if there is truth to the analogy posited before—to wit, music : mathematics :: ordinary language : ideal language—then we ought to wonder whether Badiou’s resistance to and stumbling over the ordinary is occasioned by his blindness to the mode in which Plato thinks through the relation, the togetherness, of the ideal and the ordinary103, the same and the different, the gods and the “even here.” And, if so, what results might follow if we think through his arguments having taken Plato’s mathematics, seriously—precisely because Plato’s mathematics is not merely mathematics. McClain again:

From Philolaus in the fifth century B.C. through Plato and Aristoxenus in the fourth, and down to Ptolemy in the second century A.D. and Aristides in the third or fourth, Greek acoustical theorists moved confidently between two modes of expression: the absolutely precise, and the conveniently approximate. …there is an urgent need to review all of these ancient materials, not simply for their intrinsic interest to musicians and to historians of science, but for their wider relevance to the philosophical foundations of Western culture.104

To think between the poles of precision and approximation could yield a dialectic capable of maintaining the respect for experience, whether ethical or phenomenological, which motivated Levinas, Heidegger, and Kant, those bêtes noir of Badiou and Meillassoux, without however denying the latter their right to insist upon the rigor of reason nor the audacity of aspiration. But this requires positing that dialectical periagoge is a real possibility. And as Badiou rightly senses, this positing at least borders upon faith.

In the late eighteenth century, in an epistolary exchange with Moses Mendelssohn, Friedrich Jacobi asserted that Spinozism was the logical conclusion of rationalist philosophy, and was the equivalent of atheism. Jacobi launched no arguments against Spinoza’s thought—to the contrary, he averred that the presuppositions of Leibniz, Wolff, or even Kant led directly to Spinozism if followed through consistently. Rather, what Jacobi objected to was the jettisoning of faith105. It was Jacobi who coined the

102 Thus when Badiou stipulates his axiom that “there is no God,” he is simply denying the ground for the analogy Vico assumes. Hence too Meillassoux’s need to demonstrate the radical contingency of the world, i.e., to undo this analogy by removing once and for all the notion of the divine creator. It should be emphasized that this Viconian claim that mathematics is a human contrivance in no way entails either a psychologism about mathematics (such as Husserl decried) nor a mere formalism.

103 Rosen has devoted his book The Elusiveness of the Ordinary (which contains his strongest criticisms of Strauss) to various modern philosophical engagements with “the ordinary” and argued that only in the face of a threat of loss of the ordinary does the ordinary become foregrounded as such. Contending that once we have lost touch with the ordinary we are left to attempt to “laboriously reconstitute it by abstract methodologies that are intrinsically unsuited for the task,” Rosen sounds very much like Heidegger lamenting the “forgetting of Being,” though he subjects Heidegger to considerable critique.

104 The Pythagorean Plato p 162

105 Anyone familiar with the so-called “Pantheism controversy” will recognize that I have grievously simplified and abbreviated the issues here. The pertinent texts can be consulted in English in Jacobi, Main Philosophical Works and the Novel “Allwill”, tr.

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phrase “leap of faith” (a salto mortale he urged upon Lessing), later made so much of by Kierkegaard; and is not by chance that Kierkegaard wrote his first book (and conducted his entire career as an author) “with constant reference to Socrates.” My suggestion is that Badiou’s admirably consistent and zealously anti-hermeneutic thinking is today’s version of Spinozism. What Strauss said of Heidegger—that he was the only thinker who had an inkling of the dilemmas that face the contemporary mind; that he was in fact the only great thinker of our age—cannot be said of Badiou (nor was it really true of Heidegger); but it is the case that Badiou’s thinking is the most elaborately conceived and powerfully systematic presentation of the consequences of rationalism available at present. Badiou’s account of the world is at a deep level very like Spinoza’s. Yet, though he insists that his master is Plato, he has nonetheless given over far more than he knows to the thinker who, by his own acknowledgment, is the guiding director of anti-platonism: Nietzsche. Badiou’s Spinozism is Platonism without God, and without the One. Notwithstanding his difference from Nietzsche, Badiou’s thought is thus, paradoxically and precisely, what Nietzsche said describing his own: inverted Platonism106. Plato himself would have contemplated this inversion with equanimity; for music is already a paradox, an inversion in itself: silence made eloquent.

If the analysis presented here is correct, in spirit if not in every detail, then while Badiou’s general encompassing thrust is truly platonic, his understanding of mathematics as ontology is not; for Plato would have considered Badiou’s surrender of dialectical periagoge too high a price to pay for “precision.” As Plato’s best student reminded us, “it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits.”107 While we are prepared therefore to follow Badiou in his reclamation of the reach and audacity of philosophy, it remains to undertake again many of his tasks with this different understanding, the understanding that precision must be balanced by an acceptable approximation. This is not to surrender the rights of truth to opinion, but to enter into the practical engagement with truth in the ordinary. Such a rethinking will have profound consequences especially for ethics and politics. It will decline to share Badiou’s militant disdain (a disdain, it must be said, that is quite Nietzschean in tone) for the imprecision of parliamentary democracy, while acknowledging the force of Badiou’s motives108. It will attempt, in the name of reinventing again the discipline and spiritual exercises of philosophy, a different engagement than Badiou’s with his undecidable problematic of the relationship between ethics and asceticism.109 And it will reassert the dialectical chiasmus between truth and meaning, not as a result of merely denying the “death of God,” but

& ed. Di Giovanni; and The Spinoza Conversations between Lessing and Jacobi: Text with Excerpts from the Ensuing Controversy, trs Vallée, Lawson, Chapple.

106 This is of course what Heidegger emphasized regarding Nietzsche (who he links with Marx—implicitly, Marx’s inversion of Hegel—in this respect); it is sometimes overlooked that he also said of Bergson that Bergson had merely “reversed Platonism.” (It is also how Rudolf Steiner described Bacon’s philosophy). Here as often, Badiou is following in the footsteps of Deleuze.

107 Nichomachean Ethics 1094b. I might remark here that the long, tired habit of merely opposing Plato to Aristotle rests, in this as in all matters, on at best a half-truth.

108 While most of Badiou’s disparaging remarks against democracy are aimed at what he sees as the term’s cooption by capitalism and statist ideologies, it is difficult to avoid the impression that Badiou suspects democracy per se to be inherently prone to being co-opted, by virtue of its necessarily appealing to “public opinion.” See, e.g., Badiou Metapolitics tr. Barker; ch 5 “A Speculative Disquisition on the Concept of Democracy.”

109 Cf. Ethics, pp 53-643

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of thinking through precisely what this strange declaration of Nietzsche’s could mean—and what it means that it was asserted first of all by the very tradition that Nietzsche called “platonism for the masses.”110

The key to this revision is our rejoinder to Badiou’s reduction of ontology to mathematics. Being is neither the mathematical nor the musical, but music is the best representation for Being, because music requires inexactitude and therefore cannot mistake itself for an accurate representation. At the same time, music’s own inexactitude can model the falling-short of any representation of being. The musical subtext of Plato’s myths is the precise articulation of the necessity to supplement precision by approximation, articulation by apprehension, and word by flesh.111

110 Nietzsche, Beyond Good and Evil, preface: “The fight against Plato, or, to speak more clearly and for ‘the people,’ the fight against the Christian-ecclesiastical pressure of millennia—for Christianity is Platonism for ‘the people’—has created in Europe a magnificent tension of the spirit the like of which had never yet existed on earth: with so tense a bow we can now shoot for distant goals.” And what if the tension of that bow was the project from the beginning? The danger of merely inverting Platonism is not, as Heidegger thought, that it “remains metaphysical,” but that it unstrings the bow. I add that nothing necessitates that such an unstringing be a peaceful release of tension, instead of an explosion. Such an explosion, I would suggest, was felt in the 20th century; and its aftershocks have not ceased yet.

111 “Platonism for the masses” means Platonism rendered into the language of opinion and myth. If Badiou were right, this would

make Christianity itself the first “inverted Platonism.” But if McClain and Michell are correct (and in this respect they are of one accord), then those Church fathers who asserted the continuity (which is not to say identity) between Plato and the Gospel were right, against those like Tertullian who insisted that Athens and Jerusalem had nothing to do with each other. Thus to turn Badiou’s inverted Platonism right-side-up and set it on its feet again, might look very much like resolving Plato’s chi into—a cross, on which hung a dying god.

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