Being and event

Author's preface

Translator's preface

Introduction.

Part one.

Being : multiple and void, Plato/Cantor: Meditation 1. The one and the multiple : a priori conditions of any possible ontology

Meditation 2. Plato

Meditation 3. Theory of the pure multiple : paradoxes and critical decision ; Technical note: Proper name of being

Meditation 4. The void : proper name of being

Meditation 5. The mark Ø: 1. The same and the other : the axiom of extensionality ; 2. The operations under condition : axioms of the powerset, of union, of separation and of replacement ; 3. The void, subtractive suture to being

Meditation 6. Aristotle.

Part two. Being : excess, state of the situation, one/multiple, whole/parts, or E/C?: Meditation 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-into-one

Meditation 8. The state, or metastructure, and the typology of being (normality, singularity, excrescence)

Meditation 9. The state of the historical-social situation

Meditation 10. Spinoza.

Part three. Being : nature and infinity, Heidegger/Galileo: Meditation 11. Nature : poem or matheme?

Meditation 12. The ontological schema of natural multiples and the non-existance 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 which it is the name ; 6. Nature does not exist

Meditation 13. Infinity : the other, the rule, and the other

Meditation 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. Inifinity finally defined ; 5. The finite, in second place

Meditation 15. Hegel: 1. The matheme of inifinity revisited ; 2. How can infinity be bad? ; 3. The return and the nomination ; 4. The arcana of quantity ; 5. Disjunction.

Part four. The event : history and ultra-one: Meditation 16. Evental sites and historical situations

Meditation 17. The matheme of the event

Meditation 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

Meditation 19. Mellarmé.

Part five. The event : intervention and fidelity, Pascal/choice, Hèolderlin/deduction: Meditation 20. The intervention : illegal choice of a name of the event, logiv of the two, temperol foundation

Meditation 21. Pascal

Meditation 22. The form-multiple of intervention : is there a being of choice?

Meditation 23. Fidelity, connection

Meditation 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

Meditation 25. Hölderlin.

Part six. Quantity and knowledge : The discernible (or constructible), Leibniz/Gèodel: Meditation 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

Meditation 27. Ontological destiny of orientation in thought

Meditation 28. Constructivist thought and the knowledge of being

Meditation 29. The folding of being and the sovereignty of language: 1. Construction of the concept of construcible 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

Meditation 30. Leibniz.

Part seven. The generic : indiscernible and truth, the event, P.J. Cohen: Meditation 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?

Meditation 32. Rousseau

Meditation 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

Meditation 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. [Female]-referent of a name and extension by the indiscerbible ; 5. The fundamental situation is part of any generic extension, and the indiscernible [female] is an element of any generic extension ; 6. Exploration of the generic extension ; 7. Intrinsic or in-situation indiscernibilty.

Part eight. Forcing : truth and the subject, beyond Lacan: Meditation 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

Meditation 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[female] : the undecidable ; 4. Errancy of excess ; 5. Absenting and maintenance of intrinsic quantity ; 6. Errancy of excess ; 7. From the indiscernible to the undecidable

Meditation 37. Descartes/Lacan.

Appendixes: Appendix 1. (Meditations 12 and 18) Principle of minimality for ordinals

Appendix 2. (Meditation 26) A relation, or a function, is soley a pure multiple

Appendix 3. (Meditation 26) Heterogeneity of the cardinals : regularity and singularity

Appendix 4. (Meditation 29) Every ordinal is constructible

Appendix 5. (Meditation 33) On absoluteness

Appendix 6. (Mediation 36) Primitive signs of logic and recurrence on the length of formulas

Appendix 7. (Mediation 36) Forcing of equality for names of the nominal rank O

Appendix 8. (Meditation 36) Every generic extension of a quasi-complete situation is itself quasi-complete

Appendix 9. (Meditation 36) Completion of the demonstration of [parts of whole numbers] within a generic extension

Appendix 10. (Mediation 36) Absenting of a cardinal [delta] of S in a generic extension

Appendix 11. (Mediation 36) Necessary condition for a cardinal to be absented in a generic extension : a non-denumerable antichain of conditions exists in S (whose cardinality in S is superior to [omega])

Appendix 12. (Mediation 36) Cardinality of the antichains of conditions.

Notes

Dictionary.