(Christian) theology as mathesis universalis

The Spinozist heresy is to have violated the hierarchy of the Aristotelian categories: God is not one being among many but Being itself. But there is more than one way to blur the ontological difference, i.e., as many ways as there are to count. There is, for example, the dialectic of the one and the nothing in Neoplatonic mathematics by which infinite progression telescopes to the one. It was the Christians, however, who taught us how to count directly from one to three: “we do not say that union is begotten from oneness or from equality of oneness, since union is not from oneness either through repetition or through multiplication. And although equality of oneness is begotten from oneness and although union proceeds from both [of these], nevertheless oneness, equality of oneness, and the union proceeding from both are one and the same thing …” (Cusanus).

The trinity is not only an ontological but a mathematical mystery: the simplicity and unicity of God is also the unicity of order. God is not only the infinite geometer, according to Plutarch, but infinitely arithmetizes; creation proceeds not from the word but from the number. “Number was the principal exemplar in the mind of the creator”, Boethius says (long before Leibniz’ “divine mathematician”), which is in itself a substance to which no other substance is joined (which is thus how number is then the measure of all things but not of itself). The echoes of Neoplatonic mathematics are clear: the unity of a being is at once its limit.

Cusanus gives us a clue to the passage from the ontological to the mathematical: “God is the being of things; for He is the Form of things and, hence, is also being”. For Plotinus, being consists of emanation from the one. Cusanus, however, following Thierry of Chartes (who was himself inspired by Boethius), introduces the concept of the fold into philosophy and mathematics:

a point is the enfolding of a line as oneness is the enfolding of a number. For anywhere in a line is found nothing but a point, even as in number there is nowhere found anything but oneness … Movement is the unfolding of rest, because in movement there is found nothing but rest. Similarly, the now is unfolded by way of time, because in time there is found nothing but the now.

All of these are images of the enfoldings of the Infinite Simplicity; in other words, Cusanus explains divine simplicity as nothing other than the enfolding of all things. Since, moreover, divine simplicity is the infinite mind, such that the thought of the divine mind is the creation of all things, our thought is an image of the eternal unfolding, hence guaranteeing the unity of thought and being.

The fold places multiplicity at the heart of being such that “God is so one that He is, actually, everything which is”. Cusanus is explicit in denying that oneness is number, “for number, which can be comparatively greater, cannot at all be either an unqualifiedly minimum or an unqualifiedly maximum. Rather, oneness is the beginning of all number, because it is the minimum; and it is the end of all number, because it is the maximum”. This proposition supports the paradoxes of De Docta Ignorantia: the coincidence of the absolute maximum and minimum and the assertion that “if there were an infinite line, it would be a straight line, a triangle, a circle, and a sphere” (so too Cusanus invokes an image of the divine trinity as a triangle whose angles are all right angles). More importantly, like Conway’s notion of the “intimate presence” of God to all creatures (“without any increase” in their being), the union of oneness and multiplicity folds all things in the divine without reducing being to the being of the divine (God is not-other). Against the Aristotelian convertibility of being and unity, then, Platonism in mathematics asserts not the being of number but the subordination of being to number. “The whole of nature is akin” (Meno 81d) only if the being of beings proceeds from the equality of one to one.

One and nothing: free variations (continued)

4. The distinction between Greek mathematics and modern mathematical analysis allegedly turns on certain discoveries of properties of infinite series. What this characterization obscures, however, is that we need not think of the problem of number as one of enumeration or, more generally, that the problem of multiplicity be confused with that of a series. The work from Bolzano to Cantor recognized the latter fact with the well-known consequence that there are perfectly good ways to speak of actual infinities. But the mortgage that set theory had to pay—and here the original problem returns—is, broadly speaking, an account of the structure of multiplicity, toward which we cannot remain indifferent and which has both logical and ontological consequences (the former, for example, being an effect of the reflexive problem exposed by Löwenheim-Skolem and the latter simply a consequence of the trivial fact that there is no reflection arrow for the empty set).

The turn toward intuitionism in mathematics, viewed in a certain light, is a return to the problem of Platonism not only in the ontological (Brouwer) but also the epistemological sense, which is the explicit difference in the treatment of number between, for example, Plotinus and Proclus (but which remains a difference in aspect only). The question of number takes place not at the level of unity and multiplicity (one and many) in the order of being(s) but, rather, in the passage from being to non-being where the latter is understood not as the negation of being already counted as one under the category of quantity but as a transcendence of being (i.e., the non-being of the One, for example, is already a double negation: a negation of the first negation of being as nothing). The typical theological mistake has been to conflate Platonic cosmogony/ology with ontology.*

*Here Heidegger’s account of onto-theology has severely limited our capacity to understand the terms of anti-Aristotelian metaphysics.

Proclus’ ideal (eidetikos) number or Plotinus’ substantial (ousiodes) number are principles of the intellect understood as the ontological expression of what is prior to being and nothing other than the activity (energeia) of being. Proclus in a sense ‘domesticates’ Plotinus’ account of substantial number in the intelligible by locating it as a sort of category in the soul; but this account nevertheless is supposed to explain how mathematical number is possible within the Platonic account of number as substance against the Aristotelians. The significance of the monad in Platonic metaphysics is that it is the principle not only of the unity but also the limit in being: the monad is not itself (counted-as-)one, which explains how the dyad participates in the monad in different ways (i.e., how the dyad is both clearly discrete and continuous). The persistent mistake of Aristotelianism has been to insist that the difference between number and monad be quantitative and to fails to understand that substantial number does not count substance.

5. The ambiguity of the substantial and the mathematical one is, however, necessary insofar as it expresses the duality of thought and being; or that thought and being are expressions of substance considered under different attributes à la Spinoza; or that thought is the reverse of being and vice versa. Modern mathematics has simply given rigorous formulation to the perennial Pythagorean proposition: not only that being is number but that being is number as structure. The absence of structure has been nominated variously as One (Plotinus), as zero (Peirce), or as void (Badiou). Everything turns, however, on how we interpret the nature of this absence and that we should not be misled neither by the nomination of the transcendental,** the confusion of number with enumeration, nor the conflation of the One with the “all” (as universe, the whole, the set of all sets, etc).

**Badiou is exemplary here: “I say ‘void’ rather than ‘nothing’, because the ‘nothing’ is the name of the void correlative to the global effect of structure. … The name I have chosen, the void, indicates precisely that nothing is presented [emphasis added], no term, and also that the designation of that nothing occurs ‘emptily’, it does not locate it structurally”.

6. The symbol of the monad is the circle since it “preserves the specific identity of any number with which it is conjoined” (Iamblichus), just as the void can be added to (and/or subtracted from) any set. For the Pythagoreans, the monad was also the intellect insofar as it was seminally (“potentially”) all beings; the circle has therefore long been the geometric expression or symbol of infinity.***

***See, for example, Augustine’s famous image of God or, more interestingly, Spinoza’s curious remark that “number is not applicable to the nature of the space between two non-concentric circles. Therefore if anyone sought to express all those inequalities by a definite number, he would also have to being it about that a circle should not be a circle”.

While the monad is often characterized as stability (monad is derived from “menein”, “to be stable”), stability is distinguished from nothingness as nascence (or, as before, harmony is only possible by forgetting a fundamental disharmony):

“[T]his incessant movement and progression which all things partake could never become sensible to us but by contrast to some principle of fixture or stability in the soul. Whilst the eternal generation of circles proceeds, the eternal generator abides. That central life is somewhat superior to creation … and contains all its circles. For ever it labors to create a life and thought as large and excellent as itself; but in vain; for that which is made instructs how to make a better.” (Emerson, emphasis added)

This is the real (ethical) meaning of transcendence or the “moral fact of the Universe”: that the given is never sufficient and that “every ultimate fact is only the first of a new series”. The very condition of possibility for thought is its inadequacy to being, which thus constitutes its fundamental imperative: to recognize this deficiency not in itself but in what is given to it. “Beware when the great God lets loose a thinker on this planet. Then all things are at risk.” The weakness of thought—its inadequacy—calls not for its mystical renunciation but a persistent refusal of that temptation toward cessation, whether in its annihilation or defeat by the overwhelming burden of totality or its pacification by the illusory satisfaction of identity—“I’m just me” or “I’m only human, after all”. The Pythagorean monad is the limit of being only as a self-limitation (which is the only way to account for the priority of the monad with respect to the dyad) and in a certain sense thought is nothing other than the (reflexive) expression of this “self”. This expression, however, betrays itself only through negation: just as the Pythagoreans called the One “Apollo” (from a-pollon, “not many”) and harmony requires the impossibility of complete unity, “the one thing which we seek with insatiable desire is to forget ourselves, to be surprised out of our propriety, to lose our sempiternal memory, and to do something without knowing how or why; in short, to draw a new circle” (emphasis added). Thought fulfills its destiny not only when it ventures into the unknown but takes the leap into what, in principle, it can never know.

[Cf. the previous post from March 2010 “Dialectics at a standstill”.]

The fundamental decision of metaphysics

Ancient philosophy enforced a decision between speech and silence. When modern philosophy accused its predecessor of therefore confusing being and nothingness (since to say what “is not” cannot be said does not preclude the identity of the being of what is not), we were asked to choose between the unity or the difference of being and thought. Hence, for example, Badiou’s characterization of the constructivist position in metaphysics declares that what is unnameable simply “is not”, such that metaphysics finds itself in a position of absolute immanence that “maintains the entire dialectic of the event and intervention outside thought”. Such a position, of course, simply begs the question as this is precisely the point for someone like Deleuze (see the plane of immanence as the image of thought). Rather, between the constructivist (Deleuzian) and generic (Badiousian) orientations of thought, beyond the difference between excess and subtraction, lies perhaps this fundamental choice: whether to address the genesis of thought through an account of the names of being or whether to name the indiscernible point at the chiasmus of thought and being (what Badiou nominates as the “void”) but which therefore cannot be either. If Badiou right to insist that, for the constructivist, the event is prohibited from thought, we must decide if the vocation of philosophy is to culminate in the science of thinking (logic and metaphysics) or in the affections and passions of movement (physics).

Things (merely) are

Klemm once suggested that the defining rhetoric of contemporary theological discourse is that of God as the “breaking-in of otherness”:

“This means that theological argumentation cannot be carried out in the form of the theistic argument for the existence of a supreme being. If what we mean by God is the ground and power of being itself, no object or being, not even a “supreme being,” can be God. Arguments can be made, however, that demonstrate how it is possible for individuals to say with certainty and not as a matter of probability that “God is.” Such arguments do not make an assertion about some being. Instead, they seek to show the possibility of an event of disclosure—namely, the breaking-in of otherness.”

This is almost exactly right, even if Klemm unfortunately does not ask the important question: what does such a rhetoric betoken?

What I have called the “closure of metaphysics”—which has often been performed by God—has always served the function of grounding intelligibility. To explain the persistence of theology by appealing to a naïve desire for intelligibility is entirely to miss the point. Yet it is also true that the rhetoric of theology tends to reify the ground of intelligibility into the ideology of a desire for a truth “from elsewhere”. In other words, the very notion of an “elsewhere” is not only a religious ideology but also a theological one.

Divinity enters to save possibility. We say that all being is contingent or, more precisely, that all beings are contingent. But as soon as we grant this seemingly innocuous thesis, even the most irreligious criticism becomes theological—for the problem of affirming the universal contingency of things (i.e., undergraduate versions of Nietzsche) is simply a re-statement of the classical theological position according to which the divine is necessary not only with respect to the contingency of things (the metaphysical aspect) but also to account for contingency—i.e., for the intelligibility of contingency.

Notice how deeply this religious presentiment has penetrated not only into philosophy and theology but into common sense. A truly irreligious criticism would not only affirm universal contingency or even acknowledge that I “should not be” (Silenus wisdom), but would instead proclaim that “I am necessary”. Of what madness or hubris would I be accuse to utter that phrase? What is the radicality necessary again to affirm Spinoza Benedictus?

Everything turns on which of the two propositions we affirm: (1) “things are”; or (2) “things merely are”. If we affirm the first (as what Desmond has recently formalized as the “idiocy of being”), we are led inevitably down the theological path and, thus, to the notion that intelligibility is the “breaking-in of otherness” that gets expressed as Ereignis, ethics, God-Beyond-Being, etc. The addition of a mere two syllables, however, in a stroke moves the entire domain of intelligibility into poetics.

This is a poetics that, instead of ethics (Lévinas), is able to bear the “evil” of the fact that “our only acquaintance with things is with their surface, not their depths. this is a being which is mere, sheer fact, the simple ‘there is’ of things” (Critchley). Yet we can go further (we do not have to be so Kantian): it is not that things “resist” us in their objectivity. We can say, more positively, that things appear and that the sense of this appearance is nothing other than the fact of their “il y a”. In other words, sense is not the result of appearance but is rather nothing other than appearance.

The task of a poetics, therefore, unlike the task of poetry, is not “to see fiction as fiction, to see the fictiveness or contingency of the world” (Crtichley again); poetics instead expresses necessity or, simply, the “that it is” without any attendant astonishment or surprise of the “fact” of existence because existence cannot be otherwise—an otherwise is always an elsewhere (possibility in the mind of God). The world really is there … but so too is otherness. This is the only way really to say that existence (more precisely, that which is) is: that the expression of the real is never itself real (Nietzsche will call this the “eternal return”).

A new orientation

7. Is there love in productivity? Is the notion of productivity—trauma, irruption, etc—necessarily masculinist and/or erotic? Is eros necessarily a discourse of lack (and thus falling within masculinity)? Eros is, after all, between poverty and resource. Can there be a discourse of creativity that is not intrinsically masculinist without also falling prey to the naïveté of “giving birth” (since this is obviously not what it means to be “feminine”)?

Instead, the answer must be in the limit (or, convertibly, in the “between”). The limit is neither masculine nor feminine (even, perhaps, the “feminine” that deconstructs discourse, logic, symbol). The limit is the point of indiscernibility—[either/or]/[both/and]. It is out of the limit that creativity is possible. The limit is virtual. The limit, therefore, allows us to refigure the transcendence/immanence problem. The novel is immanent (since there is no “no-where”), but also transcendent (it comes “from nowhere” insofar as it is indeterminate, invisible, etc, and insofar as the limit is itself not a place).

The “immanent” aspect of the limit ultimately is the question of origin—is there an “origin” to the world? The origin must be double—infinitely productive. The duality of origin is defined by the limit.

Tentative theses on origin and history

There are at least three senses in which any possible relationship to philosophy—philosophy as a history—is “archaic”. (1) As in the non-technical use of this term, philosophy is always “catching up” to us (what has Kant say about terrorism? what has Aristotle to say about evolution?) while, at the same time, we are never adequate to it (this is more than a hermeneutical problem). There is, in other words, a disjoint between us (we philosophers) and philosophy; but it is precisely this separation that makes it possible for philosophy to be historical (while, NB, constituting histories) and for philosophy to “go on”. As someone (whom I cannot remember) once said, the history of philosophy is the history of the misreading of philosophy—e.g., Aristotle misreads Plato and Derrida misreads everybody—but virtuously so. But, then, there are times when this separation of the philosopher from philosophy is one of trauma and the problem becomes one of the recuperation of philosophy, while ultimately means a recuperation of an origin (that has been lost).

(2) This is what is at stake in Romanitas. One hesitates to call Romanitas a concept, for it is rather the field of production from which philosophical concepts emerged. It is, even more than this, the name for a cultural trauma from which, arguably, we have yet fully to recover. This trauma was a crisis (a “turning”) of identity or, one might say, of originality. This “originality” is not, however, the romantic notion of something “new” or “novel” that is “my own”—it is not the idea of finding a “unique” Roman identity in the world. The problem is not the allegedly derivative status of Roman philosophy as a poor imitation or amateurish extension of a greater and more elegant Greek philosophy. The problem of Roman originality is constructing the very name of Rome.

Arendt claims that authority did not exist in the world until the Romans took the Greeks as authoritative. But one wonders if it is really as simple as that. Virgil demonstrates just how traumatic and violent such an act of original authority can be. Although Aeneas is charged with the task of carrying the Trojan Penates to Italy, one wonders whether there is a paradoxical an-archy at the heart of the continuity of the established history. As the author of the poem, Virgil’s task is the thinking of this origin (of Rome), yet that thinking is shot through with the threat of an-archy within the very tradition commemorated by the act of the text. It is this threat that drives Aeneas into rage—he is unable peacefully, simply, to translate the Trojan gods to Italy. His act must be original.

(3) If the presocratics inititated Greek philosophy, then there is a straightforward sense in which philosophy has always been “archaic” through to the Hellenistics. Yet this is not a separate problem from that of the historical origin, for the Roman question has always been: how is it possible that we (here, now) are here at all? What is the world to which we have given birth and in which we are birthed? Augustine’s own understanding of his origin is in this way essentially Roman: I am not my own origin, yet I cannot, in thought, return to this origin in any straightforward way. This return to origin is the essential task of thinking, which simultaneously takes the form of metaphysics and history (or one might say politics)—hence Lucretius’ poetry presents the image of the primordial rain, Virgil’s poem establishes (in act) the origin that it simultaneously commemorates (a sort of “past that has never been present”), and Augustine (and Plotinus) finds the origin of Being beyond Being. But, if these are the paradoxes into which a thinking of the origin is thrown, then it would seem philosophy must always be inadequate to the task. Yet this is why philosophy constitutes a history, just as Augustine through his Confessions constitutes a life (in Deleuze’s sense) and why, in at least one aspect of our history, we have never escaped the Roman problem of originality (or what Arendt calls the crisis of authority). We have not “returned” to Rome in a new “Hellenistic Age”—of crises of cosmopolitanism, of the collapse of global empire, of neo-Stoicism, of law, etc—for we have never left it. Arendt is right in at least one respect: the problem of origin was never a problem for the Greeks, despite their cosmological speculations; the question of origin is, rather, quintessentially Roman (which is why, à la Nietzsche, the Romans, unlike the Greeks, cannot be tragic).

Images III

In the middle of an astonishing text (and no less remarkable because it is particularly damaging to my recent defense of Deleuze), a friend wrote the following:

“… The evental function here separates us from the sterile transcendental illusion, and from the need to desire destruction.

If meaning or the possibility of experience require contrast, then with what would we contrast the real except the impossible? God or the impossible par excellence serves the most vital function not just for elucidating existence (philosophically) but for experiencing existence. This is not something that “belongs” to philosophy as a therapeutic interval, and gets discarded in a return to life. This is philosophy’s belonging to life, as its meaning. The meaning of existence is still meaning, though the meaning of meaning is existence.”

(Full text posted on 18 October at the link to the right.)

Indulge me an oblique approach: Every image, Nancy says, is sacred. But this can equally be said of the concept insofar as religion is the attempt—in good or bad faith—to form a bond with what is separated, absolutely other, unnameable, unpronounceable. Hence, I propose two exemplary religious images: (1) the Tetragrammaton. So inviolable was this word (Word) to the ancient Hebrews that it was soon lost and now exists only in the memory of a few Qaballic mystics. And (2) the Om. Man does not speak the Word; either one articulates the sound of a Brahman mantra or utters, simply, “Mu”. The Word is not the ordering vessel of the world (logos spermatikos). The Word does not “divide being” (Cratylus). Neither does the Word divide us “from” being (or even bring us “to” being). In the Maitrayaniya Upanishad, for example, we read: “There are two [!] Absolutes, Sound and Silence … Inundated by the Absolute-that-is-Sound, one arrives in the Absolute-that-is-Silence”.

The danger of these images, as we know, is that on their basis religion becomes the surest path to the death drive, one species of which is the frenetic and ascetic quest for mystic intuition of “ineffable experiences” into immortality. Neither, however, can we oppose (rational) philosophy to religion if for no other reason that, as the same friend who said the above has observed, it is a mistake to confuse the death of God with the end of history. Philosophy, rather, since the time of the presocratics has always been (i.e., is originally) religious.

This origin of philosophy is not, as those such as Freud and Jaspers have suggested, a primitive feeling of the divine within us nor its mistaken call. The origin, deconstruction tells us, is always double. The identity, the in-itself, of the origin immanently implies a reference to itself (qua origin and not to another division of itself) from which productivity and expression emerge as world, as logic, and as subject. Religion is thus immanent to philosophy itself insofar as this origin is unnameable (or “dark”, as Desmond would say) from the point of view of its world. Religious thought occurs neither in the space of mediations nor immersed in the darkness of the origin but, rather, in the space between these.

The conceptions of thought as edifying or therapeutic are extraordinarily varied and might even include some whom we might initially not want to cast in these terms (in addition to the assorted conservatisms around like Nussbaum, Hadot, Strauss, et al). One is Marx insofar as the function of philosophy is demystification of ideology (seeing through ‘distorted communication’, etc) for the sake of the material construction of free humanity. Another is Kierkegaard insofar as the function of thought is to negate totalization and edify the soul against skepticism by the construction of ideal structures for linguistic and cognitive reduction for the sake of an abstract existence (that thus requires the supplement of Christian faith to prevent a lapse into full-fledged nihilism).

In both cases—and their possible source of redemption—one sees a curious intermingling of the aesthetic and the religious that fails to live up to its promise. The one implants us by the feet and the hands into the earth and tells us that no height, no ecstasy is forbidden. The aesthetic here is what Nietzsche and Deleuze would call the affirmation and the immanence of life: not an affirmation of being because being is purely this power, this conatus essendi. Nietzsche’s/Zarathustra’s naïveté, however, consists in the doubling of this affirmation: the child’s affirmation of the affirmation. And yet this is not quite an excess. The master of excess reminds us that one only finds a real excess—that is, the explosion of an essence that pierces the sky, the limit of existence—in naked eroticism, in death.

Death is sunken into the earth, into the rhythms of nature and, thus, into life itself, just as the light of the sun pierces the earth’s skin. One often forgets the subterranean forces of decomposition and generation. But this immanentism of death forbids any commerce with any beyond of being, since all being refers either only to itself or to its conatus essendi, its will to power.

But power cannot be its own justification: the affirmation must be affirmed. This used to be the work of God (Aquinas, Leibniz, etc), particularly insofar as Being and the Good were identified (and evil consisted of a simple privation of being—Derrida, among others, has demonstrated the political consequences of such an error); and then by the autarkic moral consciousness (Kant et al). This remains the problem of religion today between fact and meaning. We cannot be done with religion (partial response to Gauchet) because the sacred, the unnameable, the impossible is the real, as Lacan as said. The real is that which is in-existent, that which is excluded from thought by thought itself, the invisible of the visible. God is unnameable precisely because he is everywhere and nowhere. (This is, of course, more than the impossibility of contradiction (NB: contradiction is one species of impossibility) and less than either a Hegelian dialectic or a leap to an other logic [logos].) The real is on neither side of the double origin; the duality of the origin (of the Absolute) is impossible—the two sides must be rigorously separated, which means that the double function of the origin cannot be limited.

What experience (taken in all of its philosophical senses) requires, thus, is not religious faith but religious thought in its perennial task: the thinking of the infinite.