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Request a sales quote### Dov M. Gabbay

### Andrew Irvine

### Paul Thagard

### John Woods

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1st Edition - June 11, 2009

Editors: Dov M. Gabbay, Andrew Irvine, Paul Thagard, John Woods

Language: EnglishHardback ISBN:

9 7 8 - 0 - 4 4 4 - 5 1 5 5 5 - 1

eBook ISBN:

9 7 8 - 0 - 0 8 - 0 9 3 0 5 8 - 9

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… Read more

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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

-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

-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

-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

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)

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)

- No. of pages: 733
- Language: English
- Edition: 1
- Published: June 11, 2009
- Imprint: North Holland
- Hardback ISBN: 9780444515551
- eBook ISBN: 9780080930589

DG

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.

Affiliations and expertise

Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London.AI

Affiliations and expertise

University of British Columbia, Vancouver, CanadaPT

Affiliations and expertise

University of Waterloo, CanadaJW

Affiliations and expertise

University of British Columbia, Vancouver, CanadaRead *Philosophy of Mathematics* on ScienceDirect