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The Multiplicity of Being: The Ontology of Alain Badiou
Pivoda, Tomáš ; Petříček, Miroslav (advisor) ; Kouba, Petr (referee) ; Pechar, Jiří (referee)
Tomáš Pivoda, The Multiplicity of Being: The Ontology of Alain Badiou PhD thesis Abstract The thesis introduces for the first time in the Czech philosophical context the ontology of the French philosopher Alain Badiou, as he set it out in his fundamental work Being and Event (L'être et l'événement, 1988). It first presents the starting point of Badiou's philosophy as well as the reasons of his identification of ontology with the set theory, and it points out Badiou's importance for contemporary philosophy, especially for the so called speculative realism around Quentin Meillassoux. The main axis of the exposition is then built around Badiou's four fundamental "Ideas": the multiplicity, the event, the truths and the subject, in connection with which it is shown how Badiou constructs his conceptual apparatus out of individual axioms of the set theory, whereby he follows the basic formal definition of multiplicity based on the operator . In connection with∈ the first Idea of multiplicity, the thesis exposes - with references to Martin Heidegger and Plato - Badiou's conceptual transposition of the couple one/multiple on the couple existence/being and defines the fundamental concepts of his ontology - the situation, the presentation, the representation and the void, with the help of which Badiou interprets...
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Reflection principles and large cardinals
Mrva, Mikuláš ; Honzík, Radek (advisor) ; Verner, Jonathan (referee)
This thesis aims to examine the relation between the so called Reflection Principles and Large Cardinals. Lévy has shown that the Reflection Theorem is a sound theorem of ZFC and it is equivalent to the Replacement Schema and the Axiom of Infinity. From this point of view, Reflection theorem can be seen a specific version of an Axiom of Infinity. This paper aims to examine the Reflection Principle and its generalisations with respect to the existence of Large Cardinals. This thesis will establish the Inaccessible, Mahlo and Indescribable cardinals and show how can those be defined via reflection. A natural limit of Large Cardinals obtained via reflection are cardinals inconsistent with L. This thesis will offer an intuitive explanation of why this holds. 1
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Logical background of forcing
Glivická, Jana ; Honzík, Radek (advisor) ; Chodounský, David (referee)
This thesis examines the method of forcing in set theory and focuses on aspects that are set aside in the usual presentations or applications of forcing. It is shown that forcing can be formalized in Peano arithmetic (PA) and that consis- tency results obtained by forcing are provable in PA. Two ways are presented of overcoming the assumption of the existence of a countable transitive model. The thesis also studies forcing as a method giving rise to interpretations between theories. A notion of bi-interpretability is defined and a method of forcing over a non-standard model of ZFC is developed in order to argue that ZFC and ZF are not bi-interpretable. 1
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Skolem paradox in set theory
Liepoldová, Tereza ; Honzík, Radek (advisor) ; Hykšová, Magdalena (referee)
This works aims to map the development of the Löwenheim-Skolems the- orem from Ernst Schröder to Thoralf Skolem using original mathematical notation. It describes its consequence in the form of the Skolem paradox and its influence on set theory and associated issues concerning orders of logic. 1
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The Multiplicity of Being: The Ontology of Alain Badiou
Pivoda, Tomáš ; Petříček, Miroslav (advisor) ; Kouba, Petr (referee) ; Pechar, Jiří (referee)
Tomáš Pivoda, The Multiplicity of Being: The Ontology of Alain Badiou PhD thesis Abstract The thesis introduces for the first time in the Czech philosophical context the ontology of the French philosopher Alain Badiou, as he set it out in his fundamental work Being and Event (L'être et l'événement, 1988). It first presents the starting point of Badiou's philosophy as well as the reasons of his identification of ontology with the set theory, and it points out Badiou's importance for contemporary philosophy, especially for the so called speculative realism around Quentin Meillassoux. The main axis of the exposition is then built around Badiou's four fundamental "Ideas": the multiplicity, the event, the truths and the subject, in connection with which it is shown how Badiou constructs his conceptual apparatus out of individual axioms of the set theory, whereby he follows the basic formal definition of multiplicity based on the operator . In connection with∈ the first Idea of multiplicity, the thesis exposes - with references to Martin Heidegger and Plato - Badiou's conceptual transposition of the couple one/multiple on the couple existence/being and defines the fundamental concepts of his ontology - the situation, the presentation, the representation and the void, with the help of which Badiou interprets...
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