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Plato's Problem [[electronic resource] ] : An Introduction to Mathematical Platonism / / by M. Panza, A. Sereni
| Plato's Problem [[electronic resource] ] : An Introduction to Mathematical Platonism / / by M. Panza, A. Sereni |
| Autore | Panza M |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | London : , : Palgrave Macmillan UK : , : Imprint : Palgrave Macmillan, , 2013 |
| Descrizione fisica | 1 online resource (323 p.) |
| Disciplina | 510.1 |
| Soggetto topico |
Mathematics—Philosophy
Philosophy, Ancient Mathematics History Logic Philosophy Philosophy of Mathematics Classical Philosophy History of Mathematical Sciences History of Philosophy |
| ISBN | 1-137-29813-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910786134103321 |
Panza M
|
||
| London : , : Palgrave Macmillan UK : , : Imprint : Palgrave Macmillan, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Plato's Problem [[electronic resource] ] : An Introduction to Mathematical Platonism / / by M. Panza, A. Sereni
| Plato's Problem [[electronic resource] ] : An Introduction to Mathematical Platonism / / by M. Panza, A. Sereni |
| Autore | Panza M |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | London : , : Palgrave Macmillan UK : , : Imprint : Palgrave Macmillan, , 2013 |
| Descrizione fisica | 1 online resource (323 p.) |
| Disciplina | 510.1 |
| Soggetto topico |
Mathematics—Philosophy
Philosophy, Ancient Mathematics History Logic Philosophy Philosophy of Mathematics Classical Philosophy History of Mathematical Sciences History of Philosophy |
| ISBN | 1-137-29813-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910813969303321 |
|
Panza M
|
||
| London : , : Palgrave Macmillan UK : , : Imprint : Palgrave Macmillan, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||