Plato's Problem : An Introduction to Mathematical Platonism / Marco Panza and Andrea Sereni.

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Bibliographic Details
Uniform Title:Problema di Platone. English
Main Author: Panza, Marco
Other Authors: Sereni, Andrea, 1977-
Language:English
Language of the Original:
Italian
Published: Houndmills, Basingstoke, Hampshire ; New York : Palgrave Macmillan, 2013.
Subjects:
Mathematics > Philosophy.
Physical Description:xvi, 306 pages ; 22 cm
Format: Book
Contents:
  • 1 The Origins 16
  • 1.1 Plato as a Platonist? 17
  • 1.2 Aristotle Between Platonism and Anti-platonism 27
  • 1.3 Proclus: The Neoplatonic Interpretation of Euclid's Geometry 32
  • 1.4 Kant: The Transcendental Interpretation of Classical Arithmetic and Geometry 36
  • 2 From Frege to Gödel (Through Hilbert) 45
  • 2.1 Frege's Logicist Platonism 45
  • 2.2 Russell and the Separation of Logicism and Platonism 66
  • 2.3 Set Theory 69
  • 2.4 The Problem of Foundations 73
  • 2.5 Gödel's Platonism and the Rise of Mathematical Intuition 90
  • 3 Benacerraf's Arguments 99
  • 3.1 What Natural Numbers Could Not Be (According to Benacerraf) 101
  • 3.2 Benacerraf's Dilemma 107
  • 3.3 A Map of Responses to Benacerraf's Dilemma: Contemporary Solutions to Plato's Problem 110
  • 4 Non-conservative Responses to Benacerraf's Dilemma 112
  • 4.1 Field's Nominalism: Mathematics Without Truth and Science Without Numbers 112
  • 4.2 Mathematics as Fiction: Field and Yablo 125
  • 4.3 Eliminative Structuralism and its Modal Version 136
  • 4.4 Maddy and the Cognitive Origins of Set Theory 144
  • 5 Conservative Responses to Benacerraf's Dilemma 149
  • 5.1 Neo-logicism: A Revised Version of Frege's Programme 149
  • 5.2 Linsky, Zalta and 'Object Theory': Mathematics and Logic (or Metaphysics) of Abstract Objects 165
  • 5.3 A First Version of Non-eliminative Structuralism: Ante Rem Structuralism 177
  • 5.4 A Second Version of Non-eliminative Structuralism: Parsons and the Role of Intuition 187
  • 6 The Indispensability Argument: Structure and Basic Notions 196
  • 6.1 Four Versions of IA 197
  • 6.2 The Quine-Putnam Argument and Colyvan's Argument 201
  • 6.3 (In)dispensability 203
  • 6.4 Quine's Criterion of Ontological Commitment 210
  • 6.5 Naturalism 212
  • 6.6 Confirmational Holism 214
  • 6.7 The Dispensability of Naturalism and Confirmational Holism 215
  • 7 The Indispensability Argument: The Debate 217
  • 7.1 Against Indispensability 217
  • 7.2 Against Ontological Commitment 224
  • 7.3 Against Naturalism and Scientific Realism 235
  • 7.4 Against Confirmational Holism 241.