(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.

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The problem with tolerance; or, Liberal Stockholm Syndrome

1. The word “refugee” was introduced into English around 1685 when Louis XIV revoked the Edict of Nantes – signed by Henry IV in 1598 – and thousands of Protestant Huguenots fled Catholic persecution. Under the doctrine of compelle intrare (Luke 14:23) and the authority of Romans 13:4, the Christian magistrate banished or burned the nonconformists or the heretic at the stake.

Just after the revocation of the Edict of Nantes, Locke wrote his famous Letter Concerning Toleration that, despite its title, is narrower in scope than anything that, as Goldie observes, western Europe would see for another 175 years. Nevertheless, to his credit, Locke argues that toleration ought to be extended to non-Christians, including pagans, Muslims, Jews, and Native Americans (while, however, denying tolerance for atheists and Catholics (qua antinomians), unlike Bayle, whose position was more expansive). Locke’s position was inconsistent after the Letter but the first argument he advances there would be the foundation for (classical) liberalism since: i.e., the separation of church and state.

Locke, however, remained an evangelist, merely arguing that the state was not the appropriate instrument for that mission (and, moreover, that coerced conversion was ineffective). Locke did not concede any epistemic ambivalence about a “true faith” but, rather, advanced a more or less pragmatic argument that peaceful evangelism was preferable to torture and coercion.

1a. Modern liberalism, particularly of those varieties predicated on the admission of epistemic humility, on the other hand, is not only wider than Locke’s but suffers from two unresolved inner contradictions. First, given the conflation of toleration with (the fact of) plurality, we must resolve the paradox of intolerance, i.e., to answer the accusation that intolerance of intolerance is contradictory. Yet that is not the real contradiction, since the paradox is only apparent. Locke’s solution to the paradox is the reason he did not extend his argument to Catholics (and also the reason Hobbes writes the last two books of the Leviathan): if one believes that there is a higher authority than the state – such that religious moral authority trumps that of the state, whose function is to preserve the peace – then the very grounds for community are eroded by those who refuse to accept the norms of reciprocal equality. Those who reject the détente of civil society can have no place in it. For Locke, then, the principle of liberal toleration is not that “all creeds are equally valid” but, rather, “we must co-exist”. Thus there is no paradox of intolerance (or, in other words, no contradiction in the failure to tolerate the intolerance of tolerance). To those who wish the destruction of civil society – particularly through a denial of its fundamental egalitarianism – we owe no quarter.

Modern liberalism, however, has decoupled truth from pluralism. Locke’s evangelism did not require that we disavow the truth of our position but, rather, that we seek conversion by peaceful means rather than violent. Rational discourse, for example, is not merely a game of Show and Tell but a shared endeavor toward truth. The contradiction of modern liberalism is the simultaneous commitment to the denial of truth – since “no one has it” – and an insistence on toleration for the expression of any opinion for no purpose other than its expression (thus leading to the paradox of intolerance).

“I look on bad conscience as a serious illness to which man was forced to succumb by the pressure of the most fundamental of all changes which he has experienced, – that change whereby he finally found himself imprisoned within the confines of society and peace” (Nietzsche).

2. The bad conscience of modern liberalism has produced this second inner contradiction: that it entertains and invites not only their enemies but also their sympathizers to the table from the guilt of “understanding”. But even the noble Socrates observes that, as the “midwife” that assists others to gain knowledge,

I, with God’s help, [deliver] them of this offspring [i.e., wisdom]. And a proof of this may be seen in the many cases where people who did not realize this fact took all the credit to themselves and thought that I was no good. They have then proceeded to leave me sooner than they should, either of their own accord or through the influence of others. And after they have gone away from me they have resorted to harmful company, with the result that what remained with them has miscarried; while they have neglected the children I helped them to bring forth, and lost them, because they set more value upon lies and phantoms than upon the truth; finally they have been set down for ignorant fools, both by themselves and by everybody else. … Sometimes they come back, wanting my company again, and ready to move heaven and earth to get it. When that happens, in some cases the divine sign that visits me forbids me to associate with them …” (Theaetetus 150e – 151a; emphasis added)

But it is not only the fascists and the agents of civil destruction that ought not to be legitimated by discourse and “understanding” but those who are unable to recognize them because they have been corrupted by a self-fulfilling illusion of rational conviction masquerading as an open mind that can nevertheless admit of no truth that has not already been decided. Stupidity and error are corrigible but self-hating misology is not. If virtue only exists “as a gift from the gods” (Meno 100b), we can only pray that it is not too late for more of us to learn.

3. Resistance, however, is always too late. The need for resistance indicates that the tools which would have made it unnecessary will ipso facto be useless for it. Resistance requires not rationality but strength, as well as the courage to recognize the misplaced guilt of toleration for the guilt of responsibility. We are all guilty, Dostoevsky says, and “understand that you yourself are guilty, for you might have been a light to evil-doers … and were not a light. If you had been a light, by your light you would have illumined the path for others, too, and the person who did evil might not have done so in the presence of your light” (BK 14:291-2). Light, however, does not show the darkness but banishes it.

One and nothing: free variations

1. Along the way toward expressing the thoughts of God before the creation of the world, Hegel’s logic consumes the possibility of mathematics at the highest moment in the doctrine of being. Just before his explicit treatment of quantity, however, he includes a note on Leibniz’ monadology and observes that “plurality remains as a fixed fundamental determination, so that the connection between [monads] falls only in the monad of monads, or in the philosopher who contemplates them”. What Hegel has grasped only vaguely here is that for Leibniz mathematics and metaphysics express the same thought, i.e., that mathematics understands the world in the same way as the divine intellect (which is the real meaning of his remark at the determination of a maximum is the work of the divine mathematician who determines the greatest number of compossibles in a given world). Leibniz’ “new mathematics”, he says, “makes man commensurate with God”.

The problem of plurality to which Hegel refers is Leibniz’ notion that the infinite (number of) monads are representations of a single universe (Monadology §78) without thereby understanding this universe as substance.* Leibniz struggles to provide an adequate topological model of such a universe** and instead speaks of the “accommodation” or harmony of all things.

*One is tempted to say “Spinozist” substance were Spinoza’s definition of substance as “one” not problematic from a mathematical point of view and which would require extensive work in disambiguation. Rather, we might safely say here “Aristotelian” substance up to and including Heidegger’s interpretation of ousia.

**Elsewhere I have claimed that such a model would be something like a Klein bottle.

2. Yet we should remember that the essence of harmony is a fundamental gap or discontinuity in what the sensibility desires as unity. The law of the series that guarantees the immanence of the world in the monad (what Badiou calls the “absolute interiority” of the monad) allows us to speak of the monad as one in a strictly different sense than that of the universe.

Here we might benefit from recalling that this is the Platonic problem par excellence. Against the Aristotelian dictum that being is always a being (i.e., that unity follows immediately from being)—and Aristotle’s well-known confusion of the Indefinite Dyad as two “counted-as-one”—Plotinus’ account of substantial number accounts both for the ontogenetic differentiation of being (see, e.g., Enneads VI.6.15) and for the fact that the One is not enumerable. What is at stake, philosophically if not mathematically, in Platonist mathematics is precisely the capacity to distinguish the one in the order of intelligibility from the unity of any individual. Being, for Plotinus, exists only because it inherits unified number from the One and, conversely, multiplicity is not the division of the One but the intellect’s contemplation of the One. We might say that substantial number is the “form” of the monad—as the immediate image of the One—combined with the “matter” of the Indefinite Dyad or, in perhaps more precise language, the Indefinite Dyad is nothing other than the limitation of unity as apostasis (and reciprocally, according to the Neopythagorean conception of monadic number, the monad is the limit of quantity: the monadic number is a progression to and a regression from mulitiplicity), the intellect is nothing other than substantial number, which is why being is not itself number but number is the principle of being.

3. What does it mean, then, to be a thinker of the One? Or, perhaps more modestly, what is at stake is the character of our ethics. For a thinker of the One, ethics is beyond being, in a sort of pagan transcendence of that which cannot be counted-as-one, as opposed to an ethics of the void, which must resist, perhaps violently, the capacity for being named and that must tear itself away from the very conditions of its survival. Our choice, however, is not that between excess and subtraction since the Plotinian One is nothing other than a series of negations: not to move away and not to progress “even a little” to the two. If there is not a symmetry between these two orientations, our choice seems to be in what direction this negation operates: whether the difference that counts is a negation of the given (multiplicity) or in the (im)possibility of negating what does not exist (a double negation!).

Politics and democracy

Recently, La Fabrique éditions asked a series of fashionable authors to comment on the sense of the word “democracy” and whether the word should today be abandoned. The collection (Démocratie, dans quel état?) is prefaced by invoking, as a provocation, the spirit of La Révolution surréaliste.*

*Posing the question in this way is only possible in Europe where the notion of “democracy” was both early and late to arrive. For this reason, none of the authors make the mistake predominant among their Anglo-American counterparts in political theory of assuming that the word “democracy” designates a particular type of constitution or state-form, which is axiomatic (in a non-technical sense) for so-called “democratic theory”. The very (odd and ultimately disastrous) distinction between political theory and political philosophy is another symptom of the confusion of the Anglophone discourse on democracy, which is yet another problem entirely than the confusion addressed by the Fabrique volume and deserves separate polemical treatment. The internal discourse of political theory itself cannot refuse to address its nebulous status as neither political science nor political philosophy (the “neither” here in the pejorative sense of being “inadequate”). The particularly banal treatment of the “return of democracy” on Obama’s election should be proof enough of this. Under the auspices of a naïve empiricism, democratic theory has ceased to understand what is at stake (dare we say, “metaphysically”?) in the very notion of “representation” which is not merely an epistemological nor even a metaphysical question that can be separated from its meaning as a political term (for Negri and Foucault, “representation” is an ontological question; for Badiou it is logical; for Deleuze it is both; etc). At best, “representation” becomes a procedural term for democratic theory and, consequently, is beholden to a problematic positivist methodology. Or, to put it another way, what calls itself “democratic theory” proceeds by assuming that there are democratic subjects—who are/not represented, who behave as political agents in ways that can be charted (“rational actors”), etc—who are constituted by “the citizen” considered as a purely legalistic entity, which leads us into an ultimately futile debate in legalism that ends in the sham proceduralism of so-called “legal process” in America or hermeneutics by another name. It is also noteworthy along these lines that Habermas—who is praised by the advocates of legalism—is not among the authors collected in the Fabrique volume.

 The provocation of La Révolution surréaliste is not its overtly communistic program but rather in its professed allegiance to the “principle” of historical materialism, i.e., in Breton’s words, the “sovereignty of thought”. The question, in its most brutal form, is simply: what is the relation of thought to politics? Obviously, “thought” is not taken here in the abstract sense of so-called “rational choice theory” or even in the metaphysical sense of a res cogitans. But if thought is to be taken in its substantive or concrete sense, then the question is not how to relate thought to politics insofar as the conditions for thought are always already political. But to say this is still too abstract, since the liberal democrat would affirm the same thing: the end of politics is to establish the form but not the material of association (i.e., the “human being”).

Rather, the question at hand is a Nietzschean question: what are the conditions under which thought is possible? This is, essentially, what Badiou posits in his reading of the Republic (in the Fabrique volume) in what he identifies as two fundamental theses:

1. The democratic world is not really a world.

2. The democratic subject is not constituted with respect to its pleasure [jouissance]. [My translations; “pleasure” is preferable to “enjoyment” here insofar as Badiou is responding to the usual treatment of hedonism in Plato.]

The first of these is readily recognizable as an extension of Logiques des Mondes. The second is (and this is now my reading of Badiou’s reading of Plato) an intervention in the question of political education—that there are not political subjects but that we must become political subjects. The democrat tries to claim the transparency of the political subject (particularly to itself!) problematically both as the condition and the result of political education. But if there is anything we can learn from the democratic impulse it is just that the very site of politics is the disjunction between thought and its transparency.

This, it seems to me, is one step in avoiding two tendencies in continental political philosophy: 1) to reduce politics to democracy tout court (e.g., democracy is always deferred, impossible, etc);** 2) to reduce politics to the operations of the state or, conversely, 3) to reduce politics to the attempt to insert some distance between the subject and the state.  Rather, I submit, politics is nothing other than the continuous construction of the state. The simultaneous separation of subject and state is what, following Abensour, might be called metapolitics.

**One possible exception to this charge is Lefort.

Poetry and poiesis

0. In a key text (Symp 205c), we learn that poiesis refers to any “creating from nothing”, although we tend to reserve the word for a certain kind of creating. It is not easy to know how to read this passage, especially given its context as an analogy with eros and the text that follows (are we really to consider romantic lovers the “proper” form of love?). But neither should we empty the word of all content into a general ontology of “poetic creation” such that poetry becomes simply identified with nature.

1. Paz: the poet of words. Another mistake is to identify the poet with the craftsman whose “material” is words, as if the poet simply found words ready-made and whose task was simply to juxtapose and combine them in experimental and unusual ways. Neither (as suggested above) should we consider the poet the demiurgic creator of forms (again, whose material is words), since this begs the question of how it is that the poet is able to communicate.

While I speak, / things imperceptibly / shake loose from themselves, / escaping toward other forms, / other names. / They leave me these words: / with them I talk to you. // Words are bridges. / And they are traps, jails, wells. / I talk to you: you do not hear me. / I don’t talk with you: I talk with a word. / That word is you …

These lines from A Tree Within—which contains, among other things, a masterful reading of the Symposium—contain what all modernists at least since Mallarmé have wanted to achieve, i.e., poetry that, while reflecting on itself, remains for all that still poetry.

The world a bundle of your images. [from Blanco]

We always already live in images; we are ourselves, of course, images. The poet does not merely need to create images but, more than simply “defamiliarizing” them, creates words themselves. This is not a claim about language “as such” (e.g., that language is “originally” poetic, metaphoric, etc); rather, we will never be able to think the relation between poetry and discourse as long as we continue to suffer the illusion that there is a Form of words. We do not make this mistake concerning the objects of our everyday experience—that the morphological identity of two bookshelves from Ikea means that there is really only one bookshelf from Ikea. That the words expressed by the poet resemble the words we use in speech and discourse should not lead us to assume that they are the same words.

The poet does not “reveal” anything—we know that a poem does not reveal the poet’s “intentions”, but neither does a poem reveal a “worldview” or an “ideology” or, worse, a “philosophy”. Neither does the poet “communicate” to us; it is we, not the poet, who fall under a task, i.e., the construction of sense from the poet’s words. The great poet is the one who offers us words that we have never before heard and, strictly speaking, will never hear again, for the task of “understanding” a poem is not discursive but, dare we say, “poetic”. We are not merely shown the world “anew” but the great poem is the one that constructs a new world—this constitutes a task precisely insofar as we are to understand this world not as the interiority of a vague feeling or even a “moment of shock” but as the very materiality of the poem (which does not, of course, refer to ink, paper, or the health and biography of the poet). In short: how does the poem (re)distribute our affects? What effects does it have? (Perhaps, however, this is too reductive…)

2. Zagajewski: the poet of melancholy. For us, at the end of a negative century, what Zagajewski calls to mind is the awareness that we live under the sign of a massive temporal suspension such that we are unable either to anticipate the future:

Music heard with you / was more than music / and the blood that flowed through our arteries was more than blood / and the joy we felt / was genuine / and if there is anyone to thank, / I thank him now, / before it grows too late / and too quiet. [“Music Heard”]

nor our origin:

And what was your childhood like? a weary / reporter asks near the end. / There was no childhood, only black crows / and tramcars starved for electricity. [from “No Childhood”]

Both past and future are in danger of slipping away. The future, we fear, will be lost to the excesses of our own ambitions—to the persistent degradation of culture, to the destruction of the biosphere, and so on. But even if, as Baudelaire had said, modernity is an endless series of losses, it is not a “break” from the past or the name of an irrecoverable trauma (the “second Fall”, etc). What has been lost is not an innocence that “should have been” but what we—here, now—have never known. We begin already in the midst of what has been lost; we are not to blame yet we are, of course, the ones responsible:

I’ll never know them, / those outmoded figures / —the same as we are, / yet completely different. / My imagination works to unlock / the mystery of their being, / it can’t wait for the release / of memory’s secret archives. // … // And I think that when I too / do my teaching / they gaze in turn at me, // revising my mutterings, / correcting my mistakes // with the calm assurance of the dead. [from “Genealogy”]

It is not only the world but we ourselves who are thus constructed by melancholy. The question that remains, then, is quite simply: who shall we have been?