Being and Event

Author’s Preface
Translator’s Preface by Oliver Feltham
Introduction
PART I BEING: MULTIPLE AND VOID. PLATO/CANTOR
1 The One and the Multiple: a priori conditions of any possible ontology
2 Plato
3 Theory of the Pure Multiple: paradoxes and critical decision Technical Note: the conventions of writing
4 The Void: Proper name of being
5 The Mark ∅
1 The same and the other: the axiom of extensionality
2 The operations under condition: axioms of the power set, of union, of separation and of replacement
3 The void, subtractive suture to being
6 Aristotle
PART II BEING: EXCESS, STATE OF THE SITUATION, ONE/MULTIPLE, WHOLE/PARTS, OR ∈/⊂?
7 The Point of Excess
1 Belonging and inclusion
2 The theorem of the point of excess
3 The void and the excess
4 One, count-as-one, unicity, and forming-intoone
8 The State, or Metastructure, and the Typology of Being (normality, singularity, excrescence)
9 The State of the Historico-social Situation
10 Spinoza
PART III BEING: NATURE AND INFINITY. HEIDEGGER/GALILEO
11 Nature: Poem or matheme?
12 The Ontological Schema of Natural Multiples and the Non-existence of Nature
1 The concept of normality: transitive sets
2 Natural multiples: ordinals
3 The play of presentation in natural multiples or ordinals
4 Ultimate natural element (unique atom)
5 An ordinal is the number of that of which it is the name
6 Nature does not exist
13 Infinity: the other, the rule and the Other
14 The Ontological Decision: ‘There is some infinity in natural multiples’
1 Point of being and operator of passage
2 Succession and limit
3 The second existential seal
4 Infinity finally defined
5 The finite, in second place
15 Hegel
1 The Matheme of infinity revisited
2 How can an infinity be bad?
3 The return and the nomination
4 The arcana of quantity
5 Disjunction
PART IV THE EVENT: HISTORY AND ULTRA-ONE
16 Evental Sites and Historical Situations
17 The Matheme of the Event
18 Being’s Prohibition of the Event
1 The ontological schema of historicity and instability
2 The axiom of foundation
3 The axiom of foundation is a metaontological thesis of ontology
4 Nature and history
5 The event belongs to that-which-is-not-being-qua-being
19 Mallarmé
PART V THE EVENT: INTERVENTION AND FIDELITY. PASCAL/CHOICE; HÖLDERLIN/DEDUCTION
20 The Intervention: Illegal choice of a name for the event, logic of the two, temporal foundation
21 Pascal
22 The Form-multiple of Intervention: is there a being of choice?
23 Fidelity, Connection
24 Deduction as Operator of Ontological Fidelity
1 The formal concept of deduction
2 Reasoning via hypothesis
3 Reasoning via the absurd
4 Triple determination of deductive fidelity
25 Hölderlin
PART VI QUANTITY AND KNOWLEDGE. THE DISCERNIBLE (OR CONSTRUCTIBLE): LEIBNIZ/GÖDEL
26 The Concept of Quantity and the Impasse of Ontology
1 The quantitative comparison of infinite sets
2 Natural quantitative correlate of a multiple: cardinality and cardinals
3 The problem of infinite cardinals
4 The state of a situation is quantitatively larger than the situation itself
5 First examination of Cantor’s theorem: the measuring scale of infinite multiples, or the sequence of alephs
6 Second examination of Cantor’s theorem: what measure for excess?
7 Complete errancy of the state of a situation: Easton’s theorem
27 Ontological Destiny of Orientation in Thought
28 Constructivist Thought and the Knowledge of Being
29 The Folding of Being and the Sovereignty of Language
1 Construction of the concept of constructible set
2 The hypothesis of constructibility
3 Absoluteness
4 The absolute non-being of the event
5 The legalization of intervention
6 The normalization of excess
7 Scholarly ascesis and its limitation
30 Leibniz
PART VII THE GENERIC: INDISCERNIBLE AND TRUTH. THE EVENT—P. J. COHEN
31 The Thought of the Generic and Being in Truth
1 Knowledge revisited
2 Enquiries
3 Truth and veridicity
4 The generic procedure
5 The generic is the being-multiple of a truth
6 Do truths exist?
32 Rousseau
33 The Matheme of the Indiscernible: P. J. Cohen’s strategy
1 Fundamental quasi-complete situation
2 The conditions: material and sense
3 Correct subset (or part) of the set of conditions
4 Indiscernible or generic subset
34 The Existence of the Indiscernible: the power of names
1 In danger of inexistence
2 Ontological coup de théâtre: the indiscernible exists
3 The nomination of the indiscernible
4 ♀-referent of a name and extension by the indiscernible
5 The fundamental situation is a part of any generic extension, and the indiscernible ) is an element of any generic extension
6 Exploration of the generic extension
7 Intrinsic or in-situation indiscernibility
PART VIII FORCING: TRUTH AND THE SUBJECT. BEYOND LACAN
35 Theory of the Subject
1 Subjectivization: intervention and operator of faithful connection
2 Chance, from which any truth is woven, is the matter of the subject
3 Subject and truth: indiscernibility and nomination
4 Veracity and truth from the standpoint of the faithful procedure: forcing
5 Subjective production: decision of an undecidable, disqualification, principle of inexistents
36 Forcing: from the indiscernible to the undecidable
1 The technique of forcing
2 A generic extension of a quasi-complete situation is also itself quasi-complete
3 Status of veridical statements within a generic extension S()): the undecidable
4 Errancy of excess (1)
5 Absenting and maintenance of intrinsic quantity
6 Errancy of excess (2)
7 From the indiscernible to the undecidable
37 Descartes/Lacan
Appendixes
1 Principle of minimality for ordinals
2 A relation, or a function, is solely a pure multiple
3 Heterogeneity of the cardinals: regularity and singularity
4 Every ordinal is constructible
5 On absoluteness
6 Primitive signs of logic and recurrence on the length of formulas
7 Forcing of equality for names of the nominal rank 0
8 Every generic extension of a quasi-complete situation is itself quasi-complete
9 Completion of the demonstration of |p(w0)| ≥ δ within a generic extension
10 Absenting of a cardinal d of S in a generic extension
11 Necessary condition for a cardinal to be absented in a generic extension
12 Cardinality of the antichains of conditions
Dictionary