Logics of Worlds, published in 2006 (2009), is the follow up to Alain Badiou’s defining work, Being and Event. In Being and Event, Badiou seeks nothing less than to re-found philosophy itself – for the time of our time. For Badiou, any philosophy – and there are only philosophies, plural –orients itself to three elements: being, truth, subject. In regard to being, Being and Event draws the consequences in philosophy of a hitherto philosophically unheralded discovery in mathematics: Georg Cantor’s demonstration of actual infinity and the subsequent axiomatisation of the consequences of this in Set Theory. The upshot being that being as such is pure multiplicity: every ‘one’ is multiple, and as such the One is not. Mathematics is the discourse of pure multiplicity and, as Badiou therefore argues, is ontology itself. From this new thinking of being qua being, a new thinking of what being is not, namely, the Event, is required. Most importantly for Badiou, philosophy must think, above all else, true change, which requires that new conceptions of truth and subjectivity must also be forged. As is now well attested, Being and Event, this ‘re-foundational work’, spawned a remarkable series of books, interventions and activity, both by Badiou and his new cohort of readers.
However, several of Badiou’s readers—most importantly for him Jean-Toussaint Desanti—noted a lacunae in Badiou’s fundamental ontology: while Badiou’s ‘minimal, intrinsic ontology’ can think being as such, it by no means restricts being to its minimal determination in and through mathematics. Thus a maximal approach is required that can give an extensive or ‘extrinsic’ account of being, given that every being is, ontologically not only marked as a being (a pure multiple of a multiple) but as ‘being-there’; in short, to the extent that being as such appears, it has has no say in it. Taking his direction from Desanti, Badiou spends many years investigating what mathematics is available to support such a maximal approach, and then many years interrogating Category Theory as the onto-logy of appearing (see Mathematics of the Transcendental). The result is Logics of Worlds. In this text, Badiou’s thinking moves from the intrinsic to the extrinsic, or from being qua being as the theory of the pure multiple to a complementary theory of being-there (which is coextensive with being itself) as the topological localization of a being, which is its appearing in a world.
It is accurate to say that nothing of what was proposed Being and Event is changed in this transition, except that what it is for being to appear is now thought coextensively with the intrinsic determination of what is as such. Whereas in Being and Event, mathematics as set-theory is ontology for today, in Logics of Worlds, (categorial) logic is the appearing of that ontology. The set-out and demonstration of this claim forms a central part of this second part of the trilogy commenced by Being and Event.
But as mathematics frees philosophy from a certain ontological malaise, allowing philosophy to think again the truths of its time, so category theory frees philosophy from the onto-logic of thinking appearing as such. This means that philosophy remains the thinking of truths for Badiou, as sited, evental and subjective. But in Logics of Worlds, truths and subjects and the situations or worlds by and for which they are (im)possible, are all re-thought relative to what it is to be-there or to what appearing is. Hereby their relations are established. Truths are reformulated as what within a world is ultimately in most maximal exception to that world. This requires a new reformulation or ‘meta-physics’ of the subject; a new theory of objects or a phenomenology without a subject; the introduction into Badiou’s work of a theory of relations and their modalities or intensities – maximal and minimal; a theory of the body as the material support of a truth in a world; and of worlds as such in terms of a new theory of the transcendental. These are all presented with multiple examples and with several key figures from the history of philosophy and its conditions, whose thought Badiou follows to the point of its impasse so as to continue in their direction.
Badiou’s 2009 Second Manifesto for Philosophy which supports the order Logics of Worlds traces out: Opinion, Appearance, Differentiation, Existence, Mutation, Incorporation, Subjectivation and Ideation. Badiou sums up the project in this way: ‘The task remains as in Being and Event, to think the possibility of real change but this time it extends to thinking the means by which change is brought to bear in a world. The central question of Being and Event in 1988 was that of the being of truths, thought in the concept of generic multiplicity, whereas in 2006, in Logics of Worlds, the question became that of truths' appearing, with this found in the concept of a body of truth or subjectivisable body.’
Logics of Worlds is a big book. The structure of it maps the vicissitudes of what needs to be thought and rethought regarding the laws of appearing and change and invokes a certain scholastic thematic, divided into books, sections, scholia and appendices and including at its end a selection of 66 statements, notes and digressions, as well as an iconography, dictionary and idiosyncratic index. As always, in this course, we will seek to read the whole thing, beginning to end. Accordingly, the course, a reading seminar: will work through the book in chronological order, following closely its unfolding structure, but necessarily the procedure will be truncated and, importantly, will emphasise the philosophical and thus conceptual import of what we encounter. This is not a mathematics course, even if we cannot avoid what is being (and not-being) written there.
This course presupposes no knowledge of Badiou per se, though some familiarity is always helpful. A reading of the (first) Manifesto for Philosophy which supports Being and Event (part 1) would be useful, as would Badiou’s recent Badiou By Badiou, which provides a simple summary overview of his oeuvre. The course will be both a wild ride across many seemingly disparate worlds: existential quantifiers to the battles of Alexander, La Nouvelle Heloise to the Chauvet Caves, the Commune to what it is to Live. And it will be a useful introduction to this work, Logics of Worlds, the Being and Event trilogy itself, and to the work of a thinker whose philosophy will have become, despite concerted contemporary reaction, truly transcendental.
Course Schedule
1. Intro to course and reading the Preface
2. Book I Formal Theory of the Subject (Meta-physics)
3. Book II – Forewords to Greater Logic, Introduction and Section 1 The Concept of Transcendental, (2 Hegel).
4. Book II Cont. Part 2 Sections 3 Algebra of the Transcendental, 4 Greater Logic and Ordinary Logic, 5 Classical Worlds
5. Book III Greater Logic, 2. The Object. Introduction, Section 1 For a New Thinking of the Object, 2 Kant, 3 Atomic Logic
6. Book III (part 2) Section 4 Existence and Death & A Scholium as Impressive as it is Subtle: The Transcendental Functor.
7. Book IV Greater Logic, 3. Relation Section 1 Worlds and Relations, 2 Leibniz & 3 Diagrams
8. Book V The Four Forms of Change: 1 Simple Becoming and True Change, 2 The Event According to Deleuze, 3 Formalizing the Upsurge?
9. Book VI Theory of Points: 1 The Point as Choice and as Place, 2 Kierkegaard, 3 Topological Structure of the Points of a World
10. Book VII What is a Body? : 1 Birth, Form and Destiny of Subjectivizable Bodies, 2 Lacan, 3 Formal Theory of the Body, Or, We Know Why a Body Exists, What It Can and Cannot Do, Scholium: A Political Variant of the Physics of the Subject-of-Truth.
11. Conclusion: What is it to Live
12. Notes, Commentaries Digressions & Questions, Remarks, what next – i.e. Riots, Happiness, Immanence of Truths.
Note that completion of this ‘order’ is subject to the vicissitudes of the seminar room.
Recommended Readings
- Logics of Worlds (Alain Badiou)
- Second Manifesto for Philosophy (Alain Badiou) – Second Manifesto is the accompanying, ‘explanatory and advocacy’ text to Logic of Worlds. A precise entrée into LW.
- Mathematics of the Transcendental (Alain Badiou): Introduction (Ling/Bartlett) – This text details Badiou’s journey through category theory as it becomes the onto-logic of being-there.
- Theoretical Writings (Alain Badiou): Section III – Early essays relevant to (and in parts included in) LW
- Briefing on Existence (Alain Badiou): Ch: 7, 8, 9, 10, 13 - (As above – transitional essays – being to being there)
- Badiou: Key Concepts (Bartlett & Clemens) – Wide range of introductory essays on Badiou’s conceptual armory.
- Badiou: A Subject to Truth (Peter Hallward) – first comprehensive introduction to Badiou – some early remarks on LW.
- ‘Had we but worlds enough and time, this absolute, philosopher . . .’, The Praxis of Alain Badiou (Justin Clemens) – excellent and seminal review of LW prior to its English translation. (Clemens has since modified and refined his position.)
- Alain Badiou: Live Theory (Oliver Feltham) – excellent critical overview of Badiou’s earlier work.