From love of truth to the truth of love

As her brother André was working on developing new foundations for algebraic geometry – in prison, even – Simone Weil expressed to him her philosophical excitement for Eudoxus’ solution to the problem of incommensurables because in that problem Weil found that its “essential point” for thinking was “outside geometry”. Eudoxus took the first step up Cantor’s ladder; Weil recognized the move as dialectical: by finding a way to express relations between incommensurate quantities, the real numbers include both the naturals and the incommensurates, preserving the incommensurability while also transcending the impasse of incommensurability. This discovery was “beautiful” in a precise sense for Weil:

Beauty is the manifest appearance of reality. Reality represents essentially contradiction. For reality is the obstacle, and the obstacle for a thinking being is contradiction. The beauty in mathematics lies in contradiction. Incommensurability, logoi alogoi, was the first radiance of beauty manifested in mathematics.

Although Weil seems not to have been aware of Cantor’s discoveries, like Cantor’s ladder, Weil recognized that this solution to the problem of incommensurability could not guarantee a highest unity because no matter how high we may climb, “we are denied access to the level at which [the contraries] are linked together. … Once arrived there, we can climb no further; we have only to look up, wait and love. And God descends”.

Weil’s God is necessarily a Trinitarian God, whose mystery is the ultimate incommensurability. The (Pythagorean) harmony of unity and plurality, viewed simultaneously from opposite sides,* is expressed neither in thought nor being but in love or friendship. Here theology yields to religion in the literal sense: in love we are bound to the task of producing the good and the right.

*Weil specifically uses the analogy of triangulation to describe grasping the mystery of the Trinity.

Against the more familiar ontotheologies of which philosophy is still suspicious, the Catholic mystical tradition searches not only beyond being but what lies between thought and being (always seeking the mediation, as Weil says). The metaxu is given neither in logic nor ontology, however, but in love, which is prior to the true and the good. We find God in ourselves not as an idea stamped on our minds but in our love. “The soul is united to God through love’s affection”, says Catherine of Siena, because in love the “soul becomes another [Christ]”. This love is directed neither toward ourselves nor toward God but, rather, is born from the infinite sorrow for the salvation of souls. Universality is within us through the soul’s imperfection: if our imperfection is the cause of evil, then my contrition must be for the suffering that I have caused. Conscience, not consciousness, is the indubitable fact of the mind, which is the ultimate truth of the inward journey. “In this life guilt is not atoned for by any suffering simply as suffering, but rather by suffering borne with desire, love, and contrition of the heart. … You asked for suffering, and you asked me to punish you for the sins of others. What you were not aware of was that you were, in effect, asking for love and light and knowledge of the truth.” The mind cannot resist a true idea, Spinoza says, but the truth of the mind itself is its love.

This blood [of Christ] gives you knowledge of the truth when knowledge of yourself leads you to shed the cloud of selfish love. There is no other way to know the truth. In so knowing me the soul catches fire with unspeakable love, which in turns brings continual pain. Indeed, because she has known my truth as well as her own sin and her neighbors’ ingratitude and blindness, the soul suffers intolerably.

True contrition, then, is not merely to atone for what is one’s own but the will to accept what is not. As Augustine reminds us, however, it is not by the strength of our will that we escape suffering but, as Catherine says, “by virtue of your infinite desire. For God, who is infinite, would have infinite love and infinite sorrow”.

Like the friendship between the persons of the trinity, love expresses the unity of the human and the divine in imitatio Christi. In the Itinerarium, Bonaventure describes the triplicity of being as corporeal, spiritual, and divine. The transport and unification of the mind with God is not only the understanding of the identity of being and the good in divine perfection but

this is a good of such a sort that it cannot be thought of unless it is thought of as three and one. For ‘the good is said to be self-diffusive’ [quoting Dionysius]. … In the supreme good there must be from eternity a production that is actual and consubstantial, and a hypostasis as noble as the producer, and this is the case in production by way of generation and spiration. This is understood to mean that what is of the eternal principle is of the eternal co-producer. In this way there can be both a beloved and a co-beloved, one generated and one spirated; that is, Father and Son, and Holy Spirit.

The mystery of the trinity is therefore not one of metaphysics but of love (charity) and thinking refuses ontotheology only to the extent to which it finds the identity of being and the good only in its suffering. Suffering cannot be controlled, as Heidegger warned, but perhaps it can be redeemed.

(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.

Weakness and possibility (variations on a theme)

1. In Bloch’s inversion of Hegel’s critique of Kant, he asserts that freedom is not only realized in the material community of individuals but in the positive idea of politics. The utopian “suprahistorical” idea of freedom is not real but ideal in the sense of the world-to-come in the action of political subjects. Freedom is thus not in history but, rather, the positive end of historical subjects’ conscious activity. It is against the background of such utopianism that Benjamin invokes the necessity of messianic redemption or, more precisely, the notion of history as the anticipation of the Messiah. Only the Messiah “completes” history, not through justification but by forgiveness, i.e., by disrupting history with a new order of time “beyond all remembering or forgetting”.

Here Benjamin explicitly follows Lotze’s suspicions of the grand style of world-historical thinking (or “universal history”) that leaves invisibility (including that of women) and stupidity in its wake. What good is a blessing in which we cannot participate, Lotze asks, when our toil is for the benefit of those who come after (always after)? Humanity does not, he says, “consists in a general type-character which is repeated in all individuals” and “the existence of a vast spiritual proletariat, which there seems no possibility of removing, is an objection which the idea of history as the education of mankind must find it hard [indeed impossible] to overcome” (Microcosmos 7.2,; Benjamin quotes several passages around this text repeatedly in the Passagenwerk). The logic of history, Lotze says, leaves it bereft of any moral exigency, for what can be imperative to those whose fate is outshone by the glory of the enlightened?

Precisely because they have been forgotten by history, Benjamin says, the moment of their recognizability has passed. The task of the critic is to expose the discontinuities and contradictions through which we might infer the “barely missed” opportunities from what history has forgotten, whether through its blindness or its mendacity. The past becomes visible not only objectively in the traces of time but also subjectively in the awareness of what is missing, viz., in the “secret agreement between past generations and the present one” that we shall be the gate through which the Messiah passes. On the one hand, we must wait; yet the work of anticipation is not mere complacency since the “weak messianic power” of redemption is only a possibility. Jewish messianism refuses to bind the individual into the corpus mysticum of universal history but at the same time also rails against the vanity of injustice. Anticipation begins in remembrance because it is through the dialectical image that we recognize the discontinuity between past and present, i.e., that there was a certain moment in the past when the present became possible and, since there can be no resurrection or redemption of the past, we must look for the traces of the future that will remain after our time has been shattered.

2a. Modernity begins the moment creation is recognized as infinite decomposition. “We are dying from the moment we are born”, so the cliché goes and only an essential fatigue could have precipitated the fall into time. Eternal happiness, it turns out, is unbearable if only because it is interminably boring.*

*Boredom, Heidegger says, is the Grundstimmung of modernity and the necessary condition for the metaphysics of Da-sein in which being is revealed as time itself. As Goodstein argues, however, in what is perhaps still the best treatment of boredom as a modern phenomenon, what gets presented existentially in Heidegger is irreducibly cultural and historical.

But our consciousness of this fall makes it impossible to desire eternal happiness (again) without thereby perversely desiring our present wretchedness. The truly religious desire is not for paradise but patience:

“When you have seen a corruption in every conviction and in every attachment a profanation, you no longer have the right to expect, on earth or elsewhere, a fate modified by hope. You must choose some ideal, absurdly solitary promontory, or a farcical star refractory to all constellations. Irresponsible out of melancholy, your life has flouted its moments; now, life is the piety of duration, the feeling of a dancing eternity, time transcending itself, and vies with the sun. . . .” (Cioran)

Consciousness is caught between the impossibility of a justified life as much as it is by a justified death (as Cioran reminds us, while the thought of suicide is fundamental to consciousness, for example, it is contradicted by the act). Happiness denies justification to every suffering as much as the converse. To make suffering the end of consciousness, however, is not an act of strength, since, lest we fall victim to the most vicious ressentiment, we must also realize that, ultimately, suffering offers neither vengeance nor remuneration.

2b. Is this not the lesson of Christian generosity, i.e., that weakness is the precondition for actual generosity (Lk 6:30)? Abundance and surplus preclude generosity, because it is neither generous to give what one does not need nor to be freed from the appearance of necessity (on the other hand, infirmity of character also excludes generosity since it is not “generous” merely to be taken advantage of). This is Marion’s point, for example, in his recent argument against the notion of sacrifice as destruction. The gift, he argues, “is accomplished in an unconditioned immanence, which not only owes nothing to exchange, but dissolves its conditions of possibility”. His point here is similar to Caputo’s notion of the “weak force” of creation, i.e., that an actual creation ex nihilo cannot be a gift since nothing is “given up”. But while Caputo resists the image of the causal—and ultimately pantheistic—God that imbues existence with goodness, equally we must resist the God from whom “significance and promise” follow; instead, in a slight turn of phrase, the event offers only a “promise of significance”. Weak theology names the transcendental, however, only by renouncing the claims of justice.

On the other hand, for Derrida, the true transcendental is nothing other than democracy and why messianism is structural and not religious (as he explicitly claims in Specters of Marx). Democratic anarchy must necessarily resist the ideology of hope or any passage from existence to goodness. “If I happen to have written that [democracy] “remains” to come, this remaining [restance] … pending [en souffrance], withdraws from its ontological dependence. It does not constitute the modification of an “is,” of an ontological copula marking the present of essence or existence, indeed of substantial or subjective substance” (Rogues, cf. “The Supplement of the Copula”). If we must wait, we seek not the good but the possibility of what, at present, has been made desperate and even unthinkable.

3. If the fundamental insight of contemporary (critical) hermeneutics is that being is nothing other than language and, consequently, that mediation is everywhere and the structure of the real is in itself dialogical (and thus historical), it follows that language, the beautiful, and the good are co-constitutive and that there is a convertibility between truth and rhetoric. Vattimo has argued this point most directly through the collapse of ontology into hermeneutics. If, then, it is not Da-sein but simply being itself that is disclosure,*** “the ‘objects’ toward which the verwindend and andenkend attitude of post-metaphysical thought turns itself are not exclusively the messages of the past. Metaphysics is not only transmitted to us in the contents of the Geisteswissenschaften, in the humanistic heritage of our culture; it is ‘realized’ in the Gestell, the scientific-technological organization of the modern world”. The task of thought, then, is to interpret the real as this organization and structure. Just as there is no seeing without seeing-as (Wittgenstein), all being is adverbial.

***Just as information theory posits that the fundamental nature of reality is the transfer of information, the hermeneutic-semiotic equivalent here is simply to say that to be is at least to be a sign.

Nihilism then has a positive destiny for Vattimo not only in the destruction of the highest values (Nietzsche) but in the narrative construction of communal existence. But this existence has neither ground nor justification in anything other than the possibility of its coming-to-be in persuasion (which, of course, need not be exclusively discursive). The destiny of humanity consists in nothing other than the re-definition of what it means to be human as the principal task of interpretation. Instead of deploying a voracious will-to-truth as scientific victory, hermeneutic thought posits the possibility of truth neither as given nor to be found either objectively or in the confidence of an inner certitude but, rather, in a world that we, together, might one day actually affirm in good conscience.

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”.]

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”).