In a recent post, I made the claim– apparently to the ire and astonishment of some –that Peter Hallward’s critique of Meillassoux’s After Finitude applies equally to Badiou’s ontology. In the course of further remarks I also suggested that, despite his self-descriptions of his own position, Badiou’s position leads to an a prioristic idealism. This wasn’t meant as an insult to Badiou, nor is it a wholesale rejection of his thought (which has influenced and inspired me deeply), but is premised on honest disagreements and perplexities I have about his ontology. The implication seems to be that one can only appreciate or endorse Badiou by dogmatically adopting his philosophy in toto, having no point of contention with it. Knowing a thing or two about Badiou the person, I suspect this is not something he would much admire or desire. Given the apparent surprise in response to this offhand observation, it is worthwhile to explain just why I think this is the case.

In his first charge against Meillassoux, Hallward contends that he equivocates between thinking and being. This charge, applies equally, I believe, and perhaps even moreso, to Badiou, and would also be one of the reasons I’ve been led to describe Badiou’s position as idealist rather than materialist. To claim that a thinker equivocates between thinking and being is to charge them with treating being as thinking and thinking as being. When Badiou equates ontology with maths, claiming that maths says all that can be said of being qua being, he essentially is committed to the thesis that thinking and being are identical. In doing so, his position necessarily collapses into an idealism regardless of whether he wishes to describe it as a materialism. [NOTE: Of course, it’s worth noting that Badiou asserts his position is a materialism premised on the claim that all we can say about matter is mathematical. Here Badiou is referring to a long history of thought pertaining to form and matter, where form exhausts matter and we are unable to say anything about matter as such because whatever we say about matter already pertains to form. For example, we try to discuss the material qualities of silver independent of what form that silver takes (a chalice, a ring, a fork, etc), only to discover that we can only articulate the formal structure of silver, e.g., it’s atomic structure.]

Now, there are good reasons pertaining to the history of philosophy that motivate him to equate being with maths. The epistemological debates of the 17th century premised on representation, culminating in Kant, had shown that there is always a dis-adequation between thought and reality (existence), such that we can never know whether or not our representations of the world match up with the world itself. Later Heidegger formalizes this conclusion, showing how as finite beings we only ever encounter being in terms of our access to being not being as it is in-itself. This opened the door to a variety of different constructivist orientations in philosophy positing a variety of different incommensurate worlds or language games, abolishing any sort of truth. In equating being with maths, Badiou’s strategy is to subtract ontology from questions of representation or knowledge (he distinguishes, as did Kant before him, between what is known and what is thinkable, such that God and the noumenal cannot be known but can be thought), instead placing being in the domain of the thinkable. Questions of representation or knowledge do not arise within mathematics because mathematical entities are not representations of things or objects. In other words, math does not refer to anything outside of itself in the way a proposition like “the cat is on the mat” refers to a state-of-affairs and a signified”. Thus we are able to know mathematical truths a priori (independent of experience through reason or thought alone), with certainty, and as a matter of deductive necessity, such that mathematical propositions are not subject to infinite dissemination, free play, or pragmatico-contextual variation as is the case with signifiers. In this respect, maths need not broach the questions of access, nor does it fall prey to the endless slippage of language that so fascinated both Anglo-American and French Continental philosophers during the twentieth century. Maths, as it were, is a language of the real in the sense of “that which always returns to its place” (Badiou, of course, would object to my reference to language here).

If maths say all that can be said of being, then we attain, at last, the identity of thought and being sought first by Parmenides. Of course, Badiou’s major innovation here is to show not that being is one and self-identical, without difference, as Parminedes had argued, but that being is pure multiplicity without one or infinite dissemination. Badiou, in short, chose the “bad option” in Plato’s dialogue Parmenides, choosing pure heterogeneity over identity. The beauty of Badiou’s move is that by equating being with maths he is able to sidestep all the debates about knowledge and representation, that lead to the reign of the sophists in the twentieth century, by showing how questions of ontology are not questions of representation at all, but investigations into pure being qua being or what is thinkable of infinite dissemination alone. Moreover, Badiou “out-differences” the philosophers and sophists of difference showing that far from spelling the ruin of thought or ontology (Derrida, Lyotard), difference, pure multiplicity qua multiplicity without one is thinkable. In a certain respect, Badiou’s thought can thus be seen as that slight “twist” he describes so well in Manifesto for Philosophy, where he shows how the Platonic gesture consisted in fully embracing the arguments of the sophist with the caveat that they produce a truth.

The problem is that Badiou’s understanding of being leaves out the signification of being involved in existence. Certainly maths cannot exhaust all that can be said of being, for there is a fundamental difference between essence and existence. When I think, for example, the properties of a triangle I can deduce many properties of that triangle. For example, I can deduce that if the other two angles of the triangle are each 45 degree, the third angle of the triangle must necessarily be 90 degrees. This belongs to the essence or form of the triangle. I know it with certainty and I can know it through thought alone. However, what I cannot know through thought alone is whether or not this triangle exists in the world. In other words, mathematical truths do not yet tell me anything about existing things in the world. With the possible exception of God, we cannot deduce existence from essence. Mathematical truths, whether set-theoretical or otherwise, are truths of essence. Whether they apply to existence is another question (which is why we can have forms of mathematics that discuss 11 dimensional topologies without yet knowing whether or not anything exists in the world corresponding to these topologies).

My point here is very simple. Clearly when we say that something exists, we are saying that something is. In other words, we are not talking about the what of being (form/essence/structure), but the that or “es gibt” of being. But if I cannot deduce existence from essence or maths, then this entails that there is something other of being than maths. This entails that maths do not say all that there is to be said of being. Just as Lacan paradoxically says “there is something of the One”, there is “something of being that is not exhausted by essence, maths, or form” that is missing in Badiou’s ontology. Let us call this element that eludes formalization or that cannot be deduced, the real. Here the real is not to be understood in the signification of that which always returns to its place, but in the signification of tuche or the “missed encounter” outlined by Lacan in The Four Fundamental Concepts of Psycho-Analysis. Put otherwise, my position is that there is something of being that eludes the thinkable (the mathematically deducible). I would argue that any and all materialist positions are committed to this thesis: Namely, to the thesis that it is the world, existence, that calls the shot, not thought. Two points then: First, I argue that Badiou is led to an a prioristic idealism because he equates being and the thinkable, where the thinkable is the mathematically deductive. In contrast to this, I argue that there is always something of being that escapes deduction, that is missing from the deductable, namely existence. This does not entail that maths is unimportant or that it is wrong to claim that science is only science insofar as it mathematical (as Kant had already claimed), but only that math does not exhaust what belongs to being. Second, I worry that should we endorse Badiou’s ontology wholesale– and make no mistake, I believe he has made a profound contribution to ontology –we will be led to ignore that which eludes essence or maths (as so often happens with rationalist orienations of thought) because we believe that we already have all that we need in maths. Contrary to Badiou’s Platonist orientation of thought, I cannot help but adopt– at least at this point –an Aristotlean orientation of thought… That is, an orientation premised on things, objects, substances, rather than maths.

More to come.