| Description |
1 online resource (200 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Handbook of the philosophy of science ; [4] |
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Handbook of the philosophy of science ; 4.
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| Summary |
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. |
| 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). |
| Bibliography |
Includes bibliographical references and index. |
| Note |
Print version record. |
| Subject |
Mathematics -- Philosophy.
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Mathématiques -- Philosophie.
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Mathematics -- Philosophy
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| Added Author |
Irvine, Andrew D. Editor.
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| Other Form: |
Print version: Philosophy of mathematics. Amsterdam ; Heidelberg : Elsevier, 2007 9780444515551 0444515550 (OCoLC)315650059 |
| ISBN |
9780444515551 |
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0444515550 |
| Standard No. |
AU@ 000047500035 |
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BWX R3797807 |
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CDX 10638638 |
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CHDSB 005989144 |
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CHNEW 001009243 |
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CHNEW 001026469 |
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DEBBG BV039834052 |
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DEBBG BV042317188 |
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DEBSZ 405325118 |
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NZ1 15192364 |
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