0. I have begun reading Alain Badiou, Being and Event, translated by Oliver Feltham (London and New York: Continuum International Publishing Group, 2005). One reason for my doing so is that, even though I earned a doctorate from (or at least was given one by) Université Laval, il y a bien des années, I know little about contemporary French philosophy and I believe I ought to know more. A second is that an initial and very brief survey of what I might find in getting involved in the study of contemporary French philosophy suggests that a systematic and sustained reading of Badiou will present me with an intellectual challenge the responding to which will be very much worth the time and effort.

1. That reading Being and Event will offer me just such a challenge seemed to me at least partially confirmed even before I began reading the book proper, for in the “Author’s Preface” to its English translation, penned some fifteen years after its publication as L’Être et l’événement , we can read the following passage (p. xiii):

To think the infinity of pure multiples I took tools from Cantor’s set theory. To think the generic character of truths I turned to Gödel and Cohen’s profound thinking of what a “part” of a multiple is. And I supported this intervention of mathematical formalism with a radical thesis: insofar as being, qua being, is nothing other than pure multiplicity, it is legitimate to say that ontology, the science of being qua being, is nothing other than mathematics itself.

2. Let me first note a couple of things which I do not fully grasp in the passage. For one thing, at this point I do not know what the significance of the use of “to think” instead of “to think about” might be, though it must be of some significance. Perhaps, I will speculate, it reflects a view that thinking is a practical or even creative activity, rather than a theoretical.

For another, I do not know quite what to make of “the infinity of pure multiples” of which he speaks. Though I have some understanding of what infinity is in the context of Cantor’s set theory, Badiou’s “pure multiples” are new to me. I can perhaps get some sense of what they may be from his supposition that “being, qua being, is nothing other than pure multiplicity.” I can conjecture, that is, that by “being, qua being” he is first referring to the abstract being which an ontologist might hold that a concrete being has and then identifying it with an also abstract “pure multiplicity.” He would seem, then, in speaking of “the infinity of pure multiples” to be holding that there is an infinity of concrete beings. He would seem also to be holding that these concrete beings are multiples and not just multiples, but pure multiples.

Going a bit further out on my conjectural limb, the “pure” of “pure multiples” suggests to me that his concrete beings might well be beings lacking unity, i.e., they would not be units. If my conjecture is correct, then his ontology is one which stands opposed to three classical doctrines. One is the Parmenidean doctrine of monism, that all reality or all being is one. Another is that of atomism, for any “part” into which one of his multiples could be resolved would have to itself be multiple, ad infinitum, and so, one might assume contra Democritus, divisible. The third is the classical metaphysical thesis that “unity” is a “transcendental property” of “being,” i.e., that:

All beings are units.

3. a. One thing, however, which I think I do understand, at least to some degree, is the sequence of two arguments discernible in the passage from Badiou quoted above. If we can assume that the proposition

Being qua being is pure multiplicity.

is sufficiently equivalent to the proposition

Being qua being is nothing other than pure multiplicity.

then the first of two arguments can be rendered as:

Being qua being is pure multiplicity.

Ontology is the science of being qua being.

Therefore, ontology is the science of pure multiplicity.

3. b. The second argument has the conclusion of the first as one of its premises. In order, however, to arrive at Badiou’s conclusion that ontology is nothing other than mathematics, we first need to supply a second premise, one which Badiou has left unexpressed. This latter premise is the thesis that the science of pure multiplicity is mathematics, i.e., that the science of pure multiplicity is nothing other than mathematics. The argument is, then:

The science of pure multiplicity is nothing other than mathematics.

Ontology is the science of pure multiplicity.

Therefore, ontology is nothing other than mathematics.

4. The title of this post describes it as an introduction to a reading of Being and Event, but then immediately, with the “(Or Perhaps Not),” introduces a note of hesitation. That is, on the one hand, I delight in dealing with theses such as the thesis that being qua being is pure multiplicity and the thesis that the science of pure multiplicity is nothing other than mathematics; I subscribe to my own thesis of philosophical dialectics that for every great truth, there is a corresponding and equally great falsehood.

On the other hand, I also see Badiou presenting us with passages like the following (Ibid., pp. xii-xiii:

A truth is solely constituted by rupturing with the order which supports it, never as an effect of that order. I have named this type of rupture which opens up truths ‘the event’. Authentic philosophy begins not in structural facts (cultural, linguistic, constitutional, etc [sic]), but uniquely in what takes place and what remains in the form of a strictly incalculable emergence.

There may well be great truths represented here, and sound arguments, also great. Or there may be equally great falsehoods and fallacies. I trust that either the former or the latter can be extracted from Badiou’s writings; after all, he himself wrote (Ibid., p. xi)

Soon it will have been twenty years since I published this book in France. At that moment I was quite aware of having written a ‘great’ book of philosophy. I felt that I had actually achieved what I had set out to do. Not without pride, I thought that I had inscribed my name in the history of philosophy, and in particular in the history of those philosophical systems which are the subject of interpretations and commentaries throughout the centuries.

[September 3rd, 2013, Insertion: Badiou is not alone in this assessment. In speaking of such books as Badiou’s Theory of the Subject, Being and Event, and Logics of Worlds, “incredibly forbidding books steeped in mathematics and deploying Zermeol-Frankel set theory,” Stuart Jeffries tells us, in “Alain Badiou: a life in writing,” The Guardian, 18 May 2012:

These books have led him to be hailed as a great philosopher. “A figure like Plato or Hegel walks here among us,” Slavoj Žižek has written.]

But I do not know. So, for now, I will continue to read and ponder Badiou. If and as long as I find the reading and the pondering worth my time and effort, and yours, I will continue to post, thereby justifying the “An Introduction” of the title, but only if and as long as I find them worth my time and effort, and yours.