Philosophy of Mathematics

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Elsevier, 8 jul. 2009 - 733 páginas
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
 

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Índice

Chapter 1 Les Liaisons Dangereuses
1
Chapter 2 Realism and AntiRealism in Mathematics
35
Chapter 3 Aristotelian Realism
103
Chapter 4 Empiricism in the Philosophy of Mathematics
157
Chapter 5 A Kantian Perspective on the Philosophy of Mathematics
231
Chapter 6 Logicism
271
Chapter 7 Formalism
291
Chapter 8 Constructivism in Mathematics
311
Chapter 10 Set Theory from Cantor to Cohen
395
Chapter 11 Alternative Set Theories
461
Chapter 12 Philosophies of Probability
493
Chapter 13 On Computability
535
Chapter 14 Inconsistent Mathematics
631
Chapter 15 Mathematics and the World
651
Index
703
Página de créditos

Chapter 9 Fictionalism
345

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Sobre el autor (2009)

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.

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