Philosophy of Mathematics (eBook)
733 Seiten
Elsevier Science (Verlag)
978-0-08-093058-9 (ISBN)
It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume.
Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed.
The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics.
-Comprehensive coverage of all main theories in the philosophy of mathematics
-Clearly written expositions of fundamental ideas and concepts
-Definitive discussions by leading researchers in the field
-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics.-Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included
Front Cover 1
Philosophy of Mathematics 4
Copyright Page 5
CONTENTS 8
General Preface 6
Preface 10
List of Contributors 16
Chapter 1. Les Liaisons Dangereuses 18
Chapter 2. Realism and Anti-Realism in Mathematics 52
Chapter 3. Aristotelian Realism 120
Chapter 4. Empiricism in the Philosophy of Mathematics 174
Chapter 5. A Kantian Perspective on the Philosophy of Mathematics 248
Chapter 6. Logicism 288
Chapter 7. Formalism 308
Chapter 8. Constructivism in Mathematics 328
Chapter 9. Fictionalism 362
Chapter 10. Set Theory from Cantor to Cohen 412
Chapter 11. Alternative Set Theories 478
Chapter 12. Philosophies of Probability 510
Chapter 13. On Computability 552
Chapter 14. Inconsistent Mathematics 648
Chapter 15. Mathematics and the World 668
Index 720
| Erscheint lt. Verlag | 8.7.2009 |
|---|---|
| Mitarbeit |
Herausgeber (Serie): Dov M. Gabbay, Paul Thagard, John Woods |
| Sprache | englisch |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik | |
| Technik | |
| ISBN-10 | 0-08-093058-1 / 0080930581 |
| ISBN-13 | 978-0-08-093058-9 / 9780080930589 |
| Haben Sie eine Frage zum Produkt? |
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