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Badiou's Being and event and the mathematics of set theory /
"Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. A...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London ; New York :
Bloomsbury Academic, an imprint of Bloomsbury Publishing Plc,
2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Title Page; Copyright Page; Contents; List of Figures and Tables; Acknowledgements; Note on Abbreviations, Citations and Translations; Introduction; The question of the event; Statement of purpose and delimitation of purview; Chapter 1 Mathematics = Ontology; Mathematics, ontology and philosophy; The other conditions of philosophy and the compossibilization of truths; The grand style versus the little style of philosophical inquiry; Badiou is not a structuralist; Being is not essentially mathematical; Metaontology versus the mathematical sciences; Metaontology versus humanistic philosophy.
- Chapter 2 Ontology of Axiomatic Set TheoryMathematical concept of the set; Intensional specification of multiples; Russell's Paradox and the Axiom of Separation; Relation of inclusion and the notions of subset and power set; Basic set operations; Supplementary properties, relations and functions; Notion of the formal axiomatic system (FAS); Introduction to model theory; Deduction, consistency, completeness and undecidability; Gödel's Completeness Theorem and the two types of consistency; The Zermelo-Fraenkel Axioms of Set Theory plus the Axiom of Choice.
- Gödel's Incompleteness Theorems and the foundation of mathematicsChapter 3 Metaontology of Situations and Presentation; Precedents to the concept of situation; Two confusions about situations; Situation as set; Situation as model; The flat plane of presentation; Universes and quasi-complete situations; The ontological decision that the one is not; Consistency and militant commitment; Following through the multiplicity of being; ZFC as the a priori conditions for ontology; Resolving the two Hurdles; ZFC as a laicized and consistent science of inconsistent multiplicity.
- Metaontology of the Axiom of the VoidAxiom of Existence; Foundational edge-of-the-void elements; Inconsistency and the void; The void as the ontological atom; Chapter 4 Metaontology of the State and Representation; Properties, subsets and representations; Names and singletons; The power set and the regime of representation; Power set of Cartesian products and the regimes of relation; Representation versus predication; The state prevents the situation from encountering its own inconsistency; The state of the empty set and of a quasi-complete situation.
- Chapter 5 Ontology and Metaontology of the Cardinal and Ordinal NumbersBasic extensions to the notion of number; Cardinal numbers, set sizes and one-to-one correspondences; Cantor's Theorem and the uncountability of the continuum; The Continuum Hypothesis; The first few ordinal numbers; Ordinal numbers and well-orderings; An ordinal is the set of the ordinals preceding it; Ordinals and homogeneous transitivity; Cardinals as specific ordinals; Summary of the mathematics; Ontology versus onticology of nature; The typology of relations between structure and metastructure.