Philosophy of Mathematics

One of the most striking features of mathematics. Are numbers, sets, functions and groups? Are they objectively existing in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or to the mathematical truth of referents of any kind?

Philosophy of Mathematics and Philosophy of Mathematics. Over the centuries, a number of reasonably well-defined developments 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, probability theory, paraconsistency) is also discussed.

The result is a handbook that not only provides a comprehensive overview of the development of mathematics.

-Comprehensive coverage of all the 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

1. The Foundations of Mathematics (WD 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)