Logics of Worlds: Being and Event II

Description

Logics of Worlds is the sequel to Alain Badiou's masterpiece, Being and Event. Tackling the questions that had been left open by Being and Event, and answering many of his critics in the process, Badiou supplements his pioneering treatment of multiple being with a daring and complex theory of the worlds in which truths and subjects make their mark - what he calls a materialist dialectic. Drawing on his most ambitious philosophical predecessors - Leibniz, Kant, Hegel, Kierkegaard, Lacan, Deleuze – Badiou ends this important later work with an impassioned call to 'live for an Idea'. Title Page Copyright Page Dedication Page Contents Translator’s Note Preface 1 Democratic materialism and materialist dialectic 2 For a didactics of eternal truths 3 Mathematical example: Numbers 4 Artistic example: Horses 5 Political example: The state revolutionary (equality and terror) 6 Amorous example: From Virgil to Berlioz 7 Distinctive features of truths, persuasive features of freedom 8 Body, appearing, Greater Logic Notes Technical Note Book I: Formal Theory of the Subject (Meta-physics) 1 Introduction 2 Referents and operations of the faithful subject 3 Deduction of the reactive subject: Reactionary novelties 4 The obscure subject: Full body and occultation of the present 5 The four subjective destinations 6 The final question 7 Truth-procedures and figures of the subject 8 Typology Scholium: A Musical Variant of the Metaphysics of the Subject Foreword to Books II, III and IV: The Greater Logic Foreword Book II: Greater Logic, 1. The Transcendental Introduction 1 Necessity of a transcendental organization of the situations of being 2 Exposition of the transcendental 3 The origin of negation Section 1: The Concept of Transcendental 1 Inexistence of the Whole 2 Derivation of the thinking of a multiple on the basis of that of another multiple 3 A being is thinkable only insofar as it belongs to a world 4 Appearing and the transcendental 5 It must be possible to think, in a world, what does not appear within that world 6 The conjunction of two apparents in a world 7 Regional stability of worlds: The envelope 8 The conjunction between a being-there and a region of its world 9 Dependence: The measure of the link between two beings in a world 10 The reverse of an apparent in the world 11 There exists a maximal degree of appearance in a world 12 What is the reverse of the maximal degree of appearance? Section 2: Hegel 1 Hegel and the question of the Whole 2 Being-there and logic of the world 3 Hegel cannot allow a minimal determination 4 The appearing of negation Section 3: Algebra of the Transcendental 1 Inexistence of the Whole: To affirm the existence of a set of all sets is intrinsically contradictory 2 Function of appearing and formal definition of the transcendental 3 Equivalence-structure and order-structure 4 First transcendental operation: The minimum or zero 5 Second transcendental operation: Conjunction 6 Third transcendental operation: The envelope 7 Conjunction of a being-there and an envelope: Distributivity of ∩ with regard to Σ 8 Transcendental algebra 9 Definitions and properties of the reverse of a transcendental degree 10 In every transcendental, the reverse of the minimum μ is a maximal degree of appearance (M) for the world whose logic is governed by that transcendental 11 Definition and properties of the dependence of one transcendental on another Section 4: Greater Logic and Ordinary Logic 1 Semantics: Truth-values 2 Syntax: Conjunction (‘and’), implication (‘if . . . then’), negation, alternative (‘or’) 3 The existential quantifier 4 The universal quantifier Section 5: Classical Worlds 1 What is a classical world? 2 Transcendental properties of the world of ontology 3 Formal properties of classical worlds Appendix: Demonstration of the Equivalence of the Three Characteristic Properties of a Classical World Book III: Greater Logic, 2. The Object Introduction Section 1: For a New Thinking of the Object 1 Transcendental indexing: The phenomenon 2 The phenomenon: Second approach 3 Existence 4 Analytic of phenomena: Component and atom of appearing 5 Real atoms 6 Definition of an object 7 Atomic logic, 1: The localization of the one 8 Atomic logic, 2: Compatibility and order 9 Atomic logic, 3: Real synthesis Section 2: Kant 1 Transcendental degree 2 Existence 3 Thought Section 3: Atomic Logic 1 Function of appearing 2 The phenomenon 3 Existence 4 Phenomenal component and atom of appearing 5 Real atom and postulate of materialism 6 Definition of the object 7 Atomic logic, 1: Localizations 8 Atomic logic, 2: Compatibility 9 Atomic logic, 3: Order 10 Atomic logic, 4: The relation between relations 11 Atomic logic, 5: Real synthesis Section 4: Existence and Death 1 Existence and death according to phenomenology and vitalism 2 Axiomatic of existence and logic of death Appendix: Three Demonstrations 1 On compatibility: Algebraic and topological definitions 2 Topological definition of the onto-logical order