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Alain Badiou's Big Books Part 3: Logics of Worlds

Lecturer: A.J. Bartlett

Originally Taught: Evening Sem 2 2015

This course is the third of three (so far) devoted to Alain Badiou’s major works of philosophy: Theory of the Subject, Being and Event, Logics of Worlds.

Logics of Worlds, published in 2006 (2009), is the follow up to Badiou’s foundational work of ontology, Being and Event. In Being and Event, Badiou seeks to re-found philosophy itself, relevant to 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. From this new thinking of being as such, a new thinking of truth and subjectivity is also forged.

However, several of Badiou’s readers, most importantly, Jean-Toussaint Desanti, note a lacunae in Badiou’s fundamental ontology: that while Badiou’s ‘minimal, intrinsic ontology’ can think being as such it by no means means being is itself restricted to this minimal determination. Thus a maximal approach is required, which can give an extensive or ‘extrinsic’ account of being; of what it is for being to appear. Taking his direction from Desanti, Badiou spends many years investigating what mathematics is available to support such a necessity and then many years interrogating Category Theory as the onto-logy of appearing as such. Thus Badiou 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, or of its appearing in a world.

It is accurate to say nothing of Being and Event is changed in this except that what it is of or 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 appearing. The set-out and demonstration of this forms a central part of this Big Book.  

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 this work, 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. Truths are reformulated as what, within a world, is in exception to it.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 its 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. Throughout, he treats as always with several key figures from the history of philosophy and its conditions, following their thought to the point of its own impasse so as to continue in their direction.

To follow the order set out in the Second Manifesto for Philosophy, which supports this Big Book, Logics of Worlds traces out: Opinion, Appearance, Differentiation, Existence, Mutation, Incorporation, Subjectivation and Ideation. Badiou sums it 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 subjectivizable body.’

Logics of Worlds is a big book. The structure of it maps the vicissitudes of what needs to be thought and rethought qua appearing and invokes a certain scholastic thematic, divided into Books, sections, scholia and appendices and including at the end a selection of 66 statements, notes and digressions, an iconography, dictionary and an idiosyncratic index. As always we will seek to read whole thing, beginning to end. Accordingly, the course will work through the book in chronological order, following closely the order of its unfolding, 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 crucial there.

This course presupposes no knowledge of Badiou nor are the first two Big Books courses on Theory of the Subject & Being and Event in any way a prerequisite – though some familiarity is always helpful. It will be both a wild ride and a useful introduction to this work and the work of a thinker whose philosophy will have become, despite concerted contemporary reaction, truly phenomenal.


  • Logics of Worlds (Alain Badiou)
  • Second Manifesto for Philosophy (Alain Badiou)
  • Mathematics of the Transcendental (Alain Badiou)
  • Badiou: Key Concepts (Bartlett & Clemens)
  • Badiou: A Subject to Truth (Peter Hallward)
  • ‘Had we but worlds enough and time, this absolute, philosopher . . .’, The Praxis of Alain Badiou (Justin Clemens).
  • Alain Badiou: Live Theory (Oliver Feltham)

Course Schedule: Badiou’s Big Books Part 3, Logics of Worlds.

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 Sections 1 The Concept of Transcendental, 2 Hegel.

4. Book II 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.


Evening Sem 2 2015