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To order this title, and for more information, click here
Dov M. Gabbay, King's College London, UK
Andrew Irvine, University of British Columbia, Vancouver, Canada
Paul Thagard, University of Waterloo, Canada
John Woods, University of British Columbia, Vancouver, Canada
Included in series
Handbook of the Philosophy of Science,
Description
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.
Audience
-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
Contents
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)
| Bibliographic details |
Hardbound, 733 pages, publication date: JUN-2009
ISBN-13: 978-0-444-51555-1
ISBN-10: 0-444-51555-0
Imprint: NORTH-HOLLAND
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| Price and Ordering |
Price:
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GBP 120.99
EUR 142.95
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Last update: 25 Nov 2009
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