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Philosophy of mathematics : an introduction

Author: David Bostock
Publisher: Chichester, U.K. ; Malden, MA : Wiley-Blackwell, 2009.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

In this new introduction to the philosophy of mathematics, David Bostock guides the reader through the basic ideas on the nature of mathematics that have played a major part in the development of  Read more...

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Additional Physical Format: Online version:
Bostock, David.
Philosophy of mathematics.
Chichester, U.K. ; Malden, MA : Wiley-Blackwell, 2009
(OCoLC)622462867
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: David Bostock
ISBN: 9781405189910 1405189916 9781405189927 1405189924
OCLC Number: 232002229
Description: x, 332 p. : ill. ; 24 cm.
Contents: 1. Plato versus Aristotle --
A. Plato --
The Socratic background --
The theory of recollection --
Platonism in mathematics --
Retractions: the divided line in Republic VI (509d-511e) --
B. Aristotle --
The overall position --
Idealisations --
Complications --
Problems with infinity --
C. Prospects --
2. From Aristotle to Kant --
Medieval times --
Descartes --
Locke, Berkeley, Hume --
A remark on conceptualism --
Kant: the problem --
Kant: the solution --
3. Reactions to Kant --
Mill on geometry --
Mill versus Frege on arithmetic --
Analytic truths --
Concluding remarks --
4. Mathematics and its Foundations --
Geometry --
Different kinds of number --
The calculus --
Return to Foundations --
Infinite numbers --
Foundations again --
5. Logicism --
Frege --
Russell --
Borkowski/Bostock --
Set theory --
Logic --
Definition --
6. Formalism --
Hilbert --
Gödel --
Pure formalism --
Structuralism --
Some comments --
7. Intuitionism --
Brouwer --
Intuitionist logic --
The irrelevance of ontology --
The attack on classical logic --
8. Predicativism --
Russell and the VCP --
Russell's ramified theory and the axiom of reducibility --
Predicative theories after Russell --
9. Realism versus Nominalism --
A. Realism --
Gödel --
Neo-Fregeans --
Quine and Putnam --
B. Nominalism --
Reductive nominalism --
Fictionalism --
Concluding remarks.
Responsibility: David Bostock.
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"Given this caveat, Bostock's new book is highly recommendable as a text for undergraduate seminars in the philosophy of mathematics and also for individual study. It covers all the essentials and Read more...

 
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