Philosophy of Mathematics

Buch | Hardcover

733 Seiten

2009
North-Holland (Verlag)
978-0-444-51555-1 (ISBN)

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Surveys historical and modern positions of mathematics. This book analyzes and evaluates traditional theories (Platonism, Aristotelianism, and Kantianism), and modern theories (logicism, formalism, constructivism, and fictionalism). It discusses research in related fields (set theory, computability theory, probability theory, and paraconsistency).

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.

Dov M. Gabbay is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. He has authored over four hundred and fifty research papers and over thirty research monographs. He is editor of several international Journals, and many reference works and Handbooks of Logic.

1. The Foundations of Mathematics (W.D. Hart)
2. Realism (Mark Balaguer)
3. Aristotelian Realism (James Franklin)
4. Empiricism (David Bostock)
5. Kantianism (Mary Tiles)
6. Logism (Jaakko Hintikka)
7. Formalism (Peter Simons)
8. Constructivism (David McCarty)
9. Fictionalism (Daniel Bonevac)
10. Structuralism (Fraser MacBride)
11. Set Theory from Cantor to Cohen (Akihiro Kanamori)
12. Alternative Set Theories (Peter Apostoli, Roland Hinnion, Akira Kanda & Thierry Libert)
13. Philosophies of Probability (Jon Williamson)
14. Computability (Wilfried Sieg)
15. Inconsistent Mathematics (Chris Mortensen)
16. Mathematics and the World (Mark Colyvan)

Erscheint lt. Verlag	11.6.2009
Reihe/Serie	Handbook of the Philosophy of Science
Mitarbeit	Herausgeber (Serie): Dov M. Gabbay, Paul Thagard, John Woods
Sprache	englisch
Maße	165 x 240 mm
Gewicht	1480 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
ISBN-10	0-444-51555-0 / 0444515550
ISBN-13	978-0-444-51555-1 / 9780444515551
Zustand	Neuware