05067nam 22007695 450 991078613410332120200919145321.01-137-29813-810.1057/9781137298133(CKB)2670000000334885(EBL)1138363(SSID)ssj0001654709(PQKBManifestationID)16434957(PQKBTitleCode)TC0001654709(PQKBWorkID)14983900(PQKB)11056136(DE-He213)978-1-137-29813-3(MiAaPQ)EBC1138363(EXLCZ)99267000000033488520151229d2013 u| 0engur|n|---|||||txtccrPlato's Problem[electronic resource] An Introduction to Mathematical Platonism /by M. Panza, A. Sereni1st ed. 2013.London :Palgrave Macmillan UK :Imprint: Palgrave Macmillan,2013.1 online resource (323 p.)Description based upon print version of record.0-230-36549-3 0-230-36548-5 Includes bibliographical references and index.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 Theory2.4 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 Theory5 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 Commitment6.5 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; IndexWhat is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.Mathematics—PhilosophyPhilosophy, AncientMathematicsHistoryLogicPhilosophyPhilosophy of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/E34020Classical Philosophyhttps://scigraph.springernature.com/ontologies/product-market-codes/E12000History of Mathematical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M23009Logichttps://scigraph.springernature.com/ontologies/product-market-codes/E16000History of Philosophyhttps://scigraph.springernature.com/ontologies/product-market-codes/E15000Mathematics—Philosophy.Philosophy, Ancient.Mathematics.History.Logic.Philosophy.Philosophy of Mathematics.Classical Philosophy.History of Mathematical Sciences.Logic.History of Philosophy.510.1Panza Mauthttp://id.loc.gov/vocabulary/relators/aut1537455Sereni Aauthttp://id.loc.gov/vocabulary/relators/autBOOK9910786134103321Plato's Problem3786764UNINA