Cargando…
Plato's Problem : an Introduction to Mathematical Platonism.
What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary tre...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Palgrave Macmillan,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Contents; Preface; Acknowledgements; Terminological Conventions; Introduction; Platonism in the Philosophy of Mathematics; Nominalism in the Philosophy of Mathematics; The Indispensability Argument; 1 The Origins; 1.1 Plato as a Platonist?; 1.2 Aristotle Between Platonism and Anti-platonism; 1.3 Proclus: The Neoplatonic Interpretation of Euclid's Geometry; 1.4 Kant: The Transcendental Interpretation of Classical Arithmetic and Geometry; 2 From Frege to Gödel (Through Hilbert); 2.1 Frege's Logicist Platonism; 2.2 Russell and the Separation of Logicism and Platonism; 2.3 Set Theory.
- 2.4 The Problem of Foundations2.5 Gödel's Platonism and the Rise of Mathematical Intuition; 3 Benacerraf's Arguments; 3.1 What Natural Numbers Could Not Be (According to Benacerraf); 3.2 Benacerraf's Dilemma; 3.3 A Map of Responses to Benacerraf's Dilemma: Contemporary Solutions to Plato's Problem; 4 Non-conservative Responses to Benacerraf's Dilemma; 4.1 Field's Nominalism: Mathematics Without Truth and Science Without Numbers; 4.2 Mathematics as Fiction: Field and Yablo; 4.3 Eliminative Structuralism and its Modal Version; 4.4 Maddy and the Cognitive Origins of Set Theory.
- 5 Conservative Responses to Benacerraf's Dilemma5.1 Neo-logicism: A Revised Version of Frege's Programme; 5.2 Linsky, Zalta and 'Object Theory': Mathematics and Logic (or Metaphysics) of Abstract Objects; 5.3 A First Version of Non-eliminative Structuralism: Ante Rem Structuralism; 5.4 A Second Version of Non-eliminative Structuralism: Parsons and the Role of Intuition; 6 The Indispensability Argument: Structure and Basic Notions; 6.1 Four Versions of IA; 6.2 The Quine-Putnam Argument and Colyvan's Argument; 6.3 (In)dispensability; 6.4 Quine's Criterion of Ontological Commitment.
- 6.5 Naturalism6.6 Confirmational Holism; 6.7 The Dispensability of Naturalism and Confirmational Holism; 7 The Indispensability Argument: The Debate; 7.1 Against Indispensability; 7.2 Against Ontological Commitment; 7.3 Against Naturalism and Scientific Realism; 7.4 Against Confirmational Holism; Concluding Remarks; Notes; References; Index.