Formalist Existentialism?

The English translation of Alain Badiou’s Being and Event III: The Immance of Truths has just been published. There is not much in this book that I would recognize as philosophy; neither other philosophers nor questions of interpretation are discussed at any length. Badiou primarily wants to assert that actual infinity is established by classical set theory as an “absolute ontological referent”.

Badiou’s deepest influences are Sartrean existentialism and what at first appears to be a kind of extreme formalist view of mathematics. For Sartre, what distinguishes the human is an ability to make utterly arbitrary choices. Such views have historically been justified by appeals to human likeness to an omnipotent God that, while commonly raised by religious sectarians, actually diverge from more broadly accepted views of orthodoxy in religion, which temper appeals to raw infinite power by emphasizing that God is good and more reasonable than we are, and therefore does not act arbitrarily. Sartre and Badiou, however, are both militant atheists who aim to ground the argument for human arbitrariness in some other, nonreligious way.

I think what we need for ethics is to recognize that we are beings who partake of an active character. We do things, and along the way we make choices between alternatives, but real-world decisions — the only kind there are — are never made in a vacuum. I think activity necessarily involves purposefulness (seeking some good, i.e., something judged by someone to be good in some way, even if we would completely reject the judgment). Any kind of purpose at all is incompatible with complete arbitrariness. (See also Beings.) But Badiou would disqualify this whole line of thought, because he doesn’t believe in ethics or in purposes that are independent of arbitrary decision.

I call Badiou’s appeals to formalism in mathematics extreme because — utterly contrary to the spirit of the early 20th century program of David Hilbert, which is usually taken as the paradigm of mathematical formalism — Badiou claims that his formalist arguments directly apply to the real world. Even so-called mathematical Platonism only asserts the independence of mathematical objects, and nothing like the immediate relevance to politics claimed by Badiou. The whole point of Hilbert’s formalism is that it doesn’t care about the real world at all. For Hilbert, mathematics consisted in purely hypothetical elaboration of the consequences of arbitrary axioms and definitions. He likened this to a kind of game.

Badiou’s use of purely formal elaboration from arbitrary starting points is decidedly not hypothetical; it is combined with an extreme realism. According to Badiou, Paul Cohen’s theorems about generic subsets, for instance, are supposed to directly lead to political consequences that are supposed to be liberating. We are supposed to get some enlightenment from considering, e.g., immigrant workers as a generic subset, and this is supposed to represent a kind of unconditional or “absolute” truth that is nonetheless immanent to our concrete experience. But the treatment of arbitrary hypotheses as unconditional truths is utterly contrary to what Hegel meant by “absolute” knowledge, which I would argue is really supposed to involve the exact opposite of arbitrariness. Hegel’s “absolute” is about as far from Badiou’s “absolute ontological referent” as could be. (See also Hegelian Finitude.)

I am only a moderately well-informed mathematical layman and claim no deep understanding of Cohen’s results, but the basic idea of a generic set or subset seems to be that it is an arbitrary selection of elements from some pre-existing set. Being arbitrary, it has no definition or characteristic function (other than by sheer enumeration of its elements). But in classical set theories, new sets and subsets can be formed from an arbitrary set. Badiou relates this to Georg Cantor’s proof that any set has more subsets than elements. In itself, I find the latter unobjectionable. But Badiou likes classical set theory because it gives a putative mathematical respectability both to arbitrary beginnings and to actual infinity. (See also Categorical “Evil”; Infinity, Finitude.)

According to Badiou, belief in actual infinity is revolutionary and good, whereas disbelief in actual infinity is conservative and bad. Infinity is supposed to be revolutionary precisely because it is unbounded. This just means that it can be used as a putative license for arbitrariness. I want to insist on the contrary that there is nothing socially progressive about arbitrariness! Badiou’s recommended political models are the chaotic Maoist cultural revolution of the 1960s and the ephemeral May 1968 Paris uprising. I don’t see that the oppressed of the world gained any benefit from either.

Badiou explicitly endorses arguments of the notorious Nazi apologist Carl Schmitt that were used to justify a permanent “state of exception” in which absolute political power is asserted. This intellectual red-brown coalition is unfortunately being taken seriously by some academic leftists. The unifying theme is the claim that metaphysical support for arbitrariness is the key to achieving social justice. There are much better ways…

Aquinas and Scotus on Power

Gwenaëlle Aubry’s Genèse du dieu souverain (Genesis of the Sovereign God) concludes with chapters on Aquinas and Scotus. She finds that Aquinas systematically substitutes power and action for Aristotle’s less familiar and more subtle ends-oriented concepts of potentiality and act. Aquinas then distinguishes between active power and receptive or passive power, neither of which has much to do with Aristotelian potentiality.

For Aristotle, Aubry says, potentiality is an indwelling tendency of a being to be attracted toward an end. Pure act is the realization of an end (and, I would add, not itself a movement but an unmoved mover that is an attractor). For Aquinas, the receptive power of beings is the power to receive being from God. Pure act is equated with God’s creation from nothing. Aquinas strongly associates being with power; the power of God, pure Being, pure Existence, is for him an active and efficient cause, not an unmoved attractor. On my reading of Aristotle, it is only the less-than-pure acts of moved movers that are active and efficient causes; the “first” cause is an end that attracts beings.

Duns Scotus, according to Aubry, seems to have originated the modern notion of purely logical possibility. For Scotus, anything at all that is noncontradictory is possible, whereas Aristotle considered possibility more pragmatically, in relation to real-world conditions.

Scotus held that the order of the world is radically contingent, able to be reshaped by God’s will. According to Aubry, he explicitly speaks of God’s arbitrary choice, and attributes a power of arbitrary choice to the human will as well. For Aristotle, the source of contingency in the world is the potentialities of things. For Scotus, it is the absolute power of God.

Whereas Bonaventure, Aquinas, and the 14th century pope John XXII treated the “absolute” power of God as only logically distinct from the “ordained” power associated with the order of the world as we know it, and as not actually separately exercised, Scotus insisted that the absolute power of God is actually exercised. He identified the absolute power of God with a kind of pure fact, and insisted that God from eternity could choose to change the order of the world. (I’m inclined to think Abelard was right, and choice is incompatible with eternity.)

God’s choice for Scotus has no reason beyond itself. Scotus explicitly rejects the passage from Plato quoted by Abelard that everything that is has a cause or reason. Aubry says that for Scotus, the good is only good because God wills it so. This is the exact opposite of the argument of Plato, Abelard, and Leibniz that goodness comes first.

Scotus strongly emphasizes the infinity of God in contrast to the finitude of creatures; infinity for Scotus is God’s most important attribute. Moreover, God’s infinite power acts immediately in the world. This reminds me of the extreme positions on omnipotence articulated by Philo and al-Ghazali. According to Aubry, Scotus also says that a worldly prince enjoys a similar absolute power.

In passing, Aubry notes that Descartes — also a voluntarist — held that God creates eternal truths. This seems to be a somewhat Scotist position. (See also Aubry on Aristotle; Leibniz on Justice vs Power; Power of the One?; Disambiguating “Power”; Not Power and Action; Nature and Justice in Augustine; Peter Abelard; 1277; Being and Essence; Being and Representation.)

Leibniz on Justice vs Power

In Meditation on the Common Concept of Justice (ca. 1703), Leibniz made points that deserve to be quoted at length. Editor Patrick Riley notes that “Leibniz’ radical formulation of this question follows Plato’s Euthyphro (9E-10E) almost literally, though Plato was dealing with ‘holiness’ rather than justice” (Leibniz, Political Writings, p. 45).

Leibniz says, “It is agreed that whatever God wills is good and just. But there remains the question whether it is good and just because God wills it or whether God wills it because it is good and just: in other words, whether justice and goodness are arbitrary or whether they belong to the necessary and eternal truths about the nature of things, as do numbers and proportions” (ibid).

For present purposes, what is important is whether justice and goodness depend on an arbitrary will or have criteria of their own, not whether those criteria are necessary and eternal.

To say that justice and goodness depend upon an arbitrary will “would destroy the justice of God. For why praise him because he acts according to justice, if the notion of justice, in his case, adds nothing to that of action? And to say… my will takes the place of reason, is properly the motto of a tyrant” (pp. 45-46; brackets in original).

“This is why certain persons, too devoted to the absolute right of God, who have believed that he could justly condemn innocent people and even that this might actually happen, have done wrong to the attributes that make God lovable, and, having destroyed the love of God, they left only fear [behind]” (p. 46; brackets in original).

“Thus all [Lutheran] theologians and most of those of the Roman Church, and also most of the ancient Church Fathers and the wisest and most esteemed philosophers, have been for the second view, which holds that goodness and justice have their grounds… independent of will and of force.”

“Plato in his dialogues introduces and refutes a certain Thrasymachus, who, wishing to explain what justice is, [says] that is just… which is agreeable or pleasant to the most powerful. If that were true, there would never be a sentence of a sovereign court, nor of a supreme judge, which would be unjust, nor would an evil but powerful man ever be blameworthy. And what is more, the same action could be just or unjust, depending on the judges who decide, which is ridiculous. It is one thing to be just and another to pass for it, and to take the place of justice.”

“A celebrated English philosopher named Hobbes, who is noted for his paradoxes, had wished to uphold almost the same thing as Thrasymachus: for he wants God to have the right to do everything, because he is all-powerful. This is a failure to distinguish between right and fact. For what one can do is one thing, what one should do, another” (pp. 46-47; brackets added).

“[I]f power were the formal reason of justice, all powerful persons would be just, each in proportion to his power; which is contrary to experience.”

“It is thus a question of finding this formal reason, that is to say, the why of this attribute, or this concept which should teach us what justice is” (p. 48). By “formal” Leibniz here means something like “essential”.

Aubry on Aristotle

Gwenaëlle Aubry’s brilliant Dieu sans la puissance (2006) recovers a distinctly Aristotelian theology. Aristotelian potentiality is to be distinguished from Platonic power, even though Aristotle used the same Greek word (dunamis) for it. For Aristotle, god is moreover pure energeia or act (what I have translated as “at-workness”) with no admixture of potentiality.

Aubry says, “As such, [Aristotle’s god] is distinguished from the Platonic Idea of the Good, exceeding being in power, as much as from the Christian God in whom power and being merge to exceed the Good. Because he is act, the god of Aristotle is not the essential Good (the Idea of the Good), but the essentially good substance. And because he is without power, he does not act as an efficient cause. But he is not, however, powerless: his efficacy is non-efficient. If he acts, it is as end…. Aristotle thus thinks the causality proper to the good as being not power, but potentiality as tendency toward the end” (p. 201, my translation, emphasis added).

(Side note — this seems to assume that an efficient cause does involve the kind of power at issue here, but I question that common assumption as well. I like the argument based on Aristotle’s Physics that it is the art of building — not the carpenter or the hammer or the hammer blow — that is most properly the efficient cause of the building of a house. Only in an indirect sense that is not Aubry’s here can the art of building be called a power. But this does not detract from her argument.)

In a 2015 lecture “Genesis of the Violent God” at Cornell, anticipating her second volume Genèse du dieu souverain (2018), she develops in fine historical detail various theological positions on omnipotence that eclipsed Aristotle’s view, explicitly subordinating goodness to absolute power. She traces the way divine omnipotence has served as an explicit model for political doctrines of sovereignty, from the absolute monarchist Jean Bodin through Hobbes to the Nazi legal theorist Carl Schmitt. Noting that various writers who have grappled with the moral significance of Auschwitz ended up suggesting a “weak” God, she instead urges us to take more seriously Aristotle’s view of a god of pure act.

This work is a development out of her 1998 doctoral thesis. She has worked extensively on Plotinus. She has co-edited volumes of essays on Aristotle’s ethics and on ancient concepts of self, as well as editing a volume on Proclus’ Elements of Theology. Aubry is actually better known as a novelist, and has won several literary awards.

Perils of Utility

Hegel derives the historic Enlightenment notion of Utility from a simple alternation of perspectives (being-in-itself, being-for-another, being-for-self) that is abstracted from all particular content. It is a sort of objective correlate for the “Pure Insight” that results from free use of the Understanding in practical matters.

The correlate of the Understanding’s freedom on the objective side is its abstraction from all content, which makes it “merely formal” in the sense we have seen Hegel criticize before. An alternation without content could go on without end, which makes it an instance of what he called “bad infinity”. Utility is “the awareness of the world as useful, not the comprehension of that world as the real self” (Harris, Hegel’s Ladder II, p. 380). It is the “pure self-estrangement of the Concept” (p. 386).

As with Understanding in general, Utility by no means appears only in a bad light. It is taken to presuppose a community of equal persons, and to imply the absolutely free Rousseauian general will of a sovereign People, which Hegel presents sympathetically. Consciousness is even said to “find its concept” in Utility (p. 384). Harris notes though that in Hegelian terms, the reference to “finding” indicates a less mature attitude than making or development.

A concept that generates a “bad infinity” ultimately cannot serve as a criterion for value judgment, because it leads to an infinite regress. But Hegel is not so much concerned with the theoretical error of the British Utilitarians’ reduction of all values to utility as with the political danger of the harshly “utilitarian” attitude of those who promulgated the Terror in the late stages of the French Revolution. The idea there was effectively that whatever action was deemed “useful” by the new authorities required no further justification. It seems clear to me, as it did to Hegel, that the French Revolution was a good thing on a historical level, but to acknowledge a generality like that is by no means necessarily to endorse every detail of the way it was carried out.

I have to say I think debates about whether or not “the end justifies the means” in general are pretty meaningless and unhelpful. We can meaningfully discuss the appropriateness of particular means to particular ends. The answer will be yes in some cases and no in others. Harsh measures that are unfortunately necessary in some cases are completely unjustifiable in others. Sometimes the tradeoffs can be very difficult. “Utility” as a putative criterion is only helpful in the easy cases. In difficult cases it ends up being tautological or sophistical. What is unequivocally wrong is the notion of arbitrary license, or the claim that no more substantive development of justification for an extreme course of action is even relevant in the first place.

Hegel is indeed concerned with a slippery slope here. The slippery slope concerns not the ends-means cliché but the use of utility as a criterion, which at the shallow end seems innocuous enough. But vague generality shades into arbitrariness, and utility is a vague generality. (My own judgment is that the notions of sovereignty and the general will are also tainted with what Hegel would call “bad infinity”.)

Modernity, Voluntarism

A draft chapter on pre-Hegelian stages in the history of normativity that Brandom removed from the published Spirit of Trust is now separately available on the internet. Parts or aspects of this historical narrative are the main source of issues I’ve had with Brandom in recent times. I take his removal of the chapter as confirmation that this historical argument should be viewed as an independent, optional supplement to the main philosophical argument of this truly great work. But Brandom still implicitly relies on it in summarily characterizing what he calls the single most important transformation in history — having to do with the status of normativity in the Enlightenment — and I have issues with those statements as well.

He begins by recalling a number of core themes I would wholeheartedly endorse. Hegel “fully appreciated, as many of Kant’s readers have not” that Kant fundamentally rethought notions of self, self-consciousness, apperception, and “consciousness in the sense of apperception” in normative terms. This is a vitally important point.

“Judgment is the minimal form of apperceptive awareness because judgments are the smallest units one can commit oneself to, make oneself responsible for”. The “I” in “I think” that Kant called the “emptiest of all representations” is a kind of formal mark of taking responsibility for the judging. What is represented in the judgment is what one makes oneself responsible to, and the “I” in turn only acquires determinate reference from what we implicitly or explicitly take responsibility for. What Brandom following popular usage still calls “conscious selves”, he glosses with precision as “apperceptively unified constellations of commitments”.

Concepts are “rules that determine what commitments are reasons for and against”, and as such govern the synthesis of apperceptive unities, but they should not be thought of as pre-existing. “Judgeable contents take methodological pride of place because of their role in Kant’s normative account of judging”. Concepts used in judgments acquire their content from the activity of judging, from what one does in applying them. Brandom thinks Hegel sees Kant as a “semantic pragmatist” not just in the Fichtean sense of the primacy of practical philosophy over theoretical philosophy, but in the more radical sense that for Kant, a normative account of discursive activity has methodological explanatory authority over the determination of discursive content in both theoretical and practical philosophy.

Brandom identifies Hegel’s Geist or Spirit with discursive normativity, and says Hegel sees earlier moral theorists as offering important insights not just about morality, but about normativity as such. Hegel himself starts from conceptual norms expressed in language, rather than from moral norms. He says that “language is the Dasein [“being there”] of Geist”. “In another (completely unprecedented) move, Hegel historicizes his social metaphysics of normativity”. Normativity is for the first time explicitly recognized as having a history.

“The traditional metaphysics of normativity that Hegel sees all subsequent forms of understanding as developing from the rejection of is the subordination-obedience model.” On this model, obligation is instituted by the command of a superior. Brandom notes that Hegel initially discussed it under the famous figure of the relation of Master and Servant.

Protestant natural-law theorists – including Grotius, Cumberland, Hobbes, Pufendorf, Thomasius, and Locke — secularized and naturalized the voluntarism of medieval Catholic theologians like Scotus and Occam, tracing the binding force of law from “the antecedent existence of a superior-subordinate relationship”. For the theological voluntarists, Brandom says, such relations of subordination were not only matters of objective fact, but “in some sense the fundamental objective metaphysical structure of reality”, embodied in Arthur Lovejoy’s figure of a broadly neoplatonic “Great Chain of Being”. The natural-law theorists explained relations of subordination among humans in terms of different theories of God’s dominion over humans. Brandom notes that on the obedience model, the status of being a superior is itself a normatively significant status entailing a right to legislate and command, but having that status relative to other humans is reduced to a non-normative matter of presumed objective fact. (We should not rely on presumption in such important matters, and all attempts to reduce normativity to something non-normative stand in opposition to the autonomy of ethical reason championed by Kant.)

Brandom says the natural-law theorists began to question the subordination-obedience model in two ways – first by attaching some normative criteria to the status of being a superior, and second by suggesting that the right of a human to command might depend on some kind of implicit consent or attitude of the affected subordinates. I would emphasize that any such move is already a move away from voluntarism. As Brandom says, the subordination-obedience model is incapable of being extended to explain a normative status of being entitled to command. The invocation of the consent of subordinates, he says, is an “even more momentous” step forward. It is distinctive of Brandomian modernity to take normative statuses to be instituted by attitudes of acknowledgement. Ultimately, modernity for Brandom is thus related to the emergence of democratic politics.

Brandom says that for Hegel, the modern model of attitude-dependence of normative statuses expresses a genuine and important truth, but like the subordination-obedience model, it is ultimately one-sided. Hegel’s own view will make room for both an objectivity and an attititude-dependence of norms and normative statuses, by deriving objectivity itself from a vast ensemble of processes of normative mutual recognition over time. Brandom translates Hegel’s vocabulary of “independence” and “dependence” into authority and responsibility, and says that for Hegel, what self-conscious beings are “in themselves” depends on what they are “for themselves”, on what they take themselves to be, as well as on what others take them to be. What is “in itself” or “for itself” is thus a matter of normative interpretation, rather than of metaphysics in the traditional sense.

All of this seems both fine and important. Things begin to become much more problematic, however, when he briefly discusses the contrast between voluntarist and “intellectualist” views of the will in medieval Latin theology. He ends up valorizing the voluntarism of Occam at the expense of the so-called intellectualism of Aquinas, on the ground that voluntarism can be taken as grounding normativity in attitudes attributed to God. Even though he notes that Occam’s nominalism makes all universals – including normativity — the product of “brute arbitrariness”, while recognizing that for Aquinas normativity is always grounded in reasons, he is more impressed by the fact that in Aquinas, those reasons are traceable to objective statuses. Brandom’s language suggests that any reliance whatseoever on attitudes — even if they are arbitrary and do not involve any kind of recognition of an other — is ethically preferable to reliance on objective statuses.

I on the contrary much prefer Aquinas’ appeal to reasons – in spite of the fact that Aquinas ultimately relies on assumed objective statuses – to Occam’s appeal to arbitrariness, even though the latter can be argued to implicitly involve attitudes. It is a rather common motif of shallow accounts of the prehistory of modern science to valorize Occam and nominalism generally as anticipating modern developments, while overlooking both the negative ethical consequences of voluntarism and the positive value of the ethically “intellectualist” emphasis on reason.

I want to put greater stress on the contrast between arbitrariness and reasons than on that between relying on assumed objective statuses and relying on attitudes. Of course I agree that objective normative statuses should not be simply assumed. But I see nothing at all progressive in arbitrariness glossed as the product of an arbitrary attitude. The result is still arbitrariness. So, I cannot at all agree that theological voluntarism is “the thin leading edge of the wedge of modernity”, if modernity is supposed to be anything good. I think a transition to relying on attitudes for the constitution of normativity only becomes progressive when those attitudes are non-arbitrary.

The other odd thing in Brandom’s account is the complete absence of any mention of Plato and Aristotle. Unlike most authors of the Enlightenment, Plato and Aristotle put no limits on the free use of reason. They explicitly treated reason as bound up with normativity. And even though they did not question existing distinctions of social status as much as we might, nothing in their ethics actually presupposes the subordination-obedience model. Thus I locate the single greatest historical break with Plato and Aristotle’s invention of rational ethics, rather than with the Enlightenment’s appeal to attitudes.

However one takes the ethical “intellectualism” of Aquinas, it combines Plato and Aristotle’s merger of normativity and reason with doctrinal concerns. The assumptions about objective statuses that Brandom objects to belong to the doctrinal component of his synthesis rather than its Platonic-Aristotelian component. If we are looking for historical antecedents of the ethically good aspects of modernity, we should look to Plato and Aristotle.

Voluntarism’s endorsement of arbitrariness over reasons is quite simply the short path to evil. It is the bad attitude of the Master discussed by Hegel, raised to a sort of anti-philosophical principle. Brandom is a great champion of the importance of reasons, and presents an exemplary reading of Mastery as an evolutionary dead end with no progressive role to play, so I think it would be more consistent for him to avoid any historical valorization of voluntarist positions.

Openness of Reason

In life, we most often do not really know what we are doing, but still, most of the time we find our way. This involves many small “leaps”, or actions on based on assumptions that we don’t actually know are true. These are unavoidable, they are “reasonable”, and most of the time they are harmless.

In forming views of the world, we need the maturity to distrust systematic unity or strong coherence as a supposed accomplishment, while still pursuing it as a goal. (See also One, Many; Unity of Apperception; Error; Foundations?; Interpretation.)

If we have a concept of Reason as something well distinguished but still fundamentally open in the last instance — which I find especially clear and well developed in Aristotle, Brandom, and Ricoeur — then we have no need ever for Kierkegaardian irrational “great leaps” or arbitrary founding decisions in the style of Badiou.

“Transgression” as Ordinary?

Ricoeur’s unexpected old talk about a “transgression” (which the translator says in a note should be taken in an etymological sense, without the moral connotation it has in English) — or an overflowing, as I would put it — inherent in ordinary language use and ordinary determination of concepts makes another interesting rebuttal to the Badiouian claim endorsed by some of the Žižekians that only a few extraordinary “Events” and utterly arbitrary acts avoid chaining us to the status quo.

Arbitrariness, Inflation

Arbitrariness in practice or in theory effectively devalues distinctions, reasons, and values all to zero. Insistence on arbitrary power, arbitrary rights, or arbitrary freedom utterly abnegates normativity and reason. (See also Desire of the Master; Tyranny.) Denial of the principle of noncontradiction opens the door for unprincipled sophistry that has the same nihilistic effect. The idea that something genuinely new can only come about through arbitrariness reflects a profoundly impoverished vision.

Theoretical assertions of arbitrary power or authority originated in bad theology (see Strong Omnipotence; Occasionalism), then found their way into modern political theory via one-sided notions like sovereignty. Modern individualism and subjectivism tend to make similarly one-sided, effectively nihilistic claims on behalf of individuals. Sartrean existentialism and Badiouian decisionism are particularly extreme examples. (See also “Hard” Kantianism?)

Rather than valorizing or justifying arbitrariness in actions, we ought to always aim at contextually appropriate applications of reasonableness and respect for others. (See also Practical Judgment; Freedom from False Freedom; Categorical “Evil”.)