Platonism and anti-Platonism in mathematics /

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Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associat...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Balaguer, Mark
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York : Oxford University Press, 1998.
Temas:
Mathematics > Philosophy.
Platonists.
Mathématiques > Philosophie.
MATHEMATICS > History & Philosophy.
Mathematics > Philosophy
Platonists
Wiskunde.
Platonisme.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Contents
  • 1 Introduction
  • 1. The Project of This Book
  • 2. Mathematical Platonism and Anti-Platonism
  • 3. Synopsis of the Book
  • ONE: Platonism
  • 2 The Epistemological Argument Against Platonism
  • 1. Introduction
  • 2. Formulating the Epistemological Argument
  • 3. A Taxonomy of Platonist Responses
  • 4. Contact with Other Worlds: Gödel
  • 5. Contact in This World: Maddy
  • 6. Knowledge Without Contact
  • 3 A New Platonist Epistemology
  • 1. Introduction
  • 2. Skeleton of the Refutation of the Epistemological Argument
  • 3. Internalist vs. Externalist Explanations
  • 4. Defending and Motivating FBP
  • 5. Consistency
  • 4 Non-Uniqueness Embraced
  • 1. Introduction
  • 2. Trying to Salvage the Numbers
  • 3. Structuralism
  • 4. The Solution
  • 5. Two Loose Ends
  • TWO: Anti-Platonism
  • 5 The Fregean Argument Against Anti-Platonism
  • 1. Introduction
  • 2. The Argument
  • 3. In Defense of Fictionalism
  • 4. Nonfictionalistic Versions of Anti-Realistic Anti-Platonism
  • 5. The Refutation of Realistic Anti-Platonism
  • 6. Platonism and the Issue of Applicability and Indispensability
  • 6 Denying the Existence of Indispensable Applications: Toward a Nominalization of Quantum Mechanics
  • 1. Introduction
  • 2. How Field Nominalizes
  • 3. Malament's Objection
  • 4. The Strategy for Nominalizing QM
  • 5. The Nominalistic Status of Propensities
  • 7 Accounting for Indispensable Applications from a Fictionalist Point of View
  • 1. Introduction
  • 2. What, Exactly, Needs to Be Accounted For?
  • 3. A Fictionalist Account of the Applicability of Mathematics
  • 4. Problems with Platonism Revisited
  • THREE: Conclusions
  • 8 The Unsolvability of the Problem and a Kinder, Gentler Positivism
  • 1. Introduction
  • 2. The Strong Epistemic Conclusion
  • 3. The Metaphysical Conclusion
  • 4. My Official View
  • Notes
  • Bibliography
  • Index
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • J
  • K
  • L
  • M
  • N
  • O
  • P
  • Q
  • R
  • S
  • T
  • U
  • V
  • W.

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