|  | Bostock, David
Philosophy of Mathematics
An Introduction
 1. Auflage Februar 2009
30,90 Euro
2009. 344 Seiten, Softcover
ISBN 978-1-4051-8991-0 - John Wiley & Sons
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| Kurzbeschreibung
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 philosophy from antiquity to the present. The chapters proceed historically with an emphasis to not only describe, but to offer a critical appraisal of the views discussed. The result is an engaging, clear, and remarkably comprehensive panorama of the major issues in the field. Aimed at undergraduates in philosophy and mathematics, it will also provide an important new perspective on the subject for more experienced readers.
Aus dem Inhalt
Introduction.
Part I: Plato versus Aristotle:.
A. Plato.
1. The Socratic Background.
2. The Theory of Recollection.
3. Platonism in Mathematics.
4. Retractions: the Divided Line in Republic VI (509d-511e).
B. Aristotle.
5. The Overall Position.
6. Idealizations.
7. Complications.
8. Problems with Infinity.
C. Prospects.
Part II: From Aristotle to Kant:.
1. Medieval Times.
2. Descartes.
3. Locke, Berkeley, Hume.
4. A Remark on Conceptualism.
5. Kant: the Problem.
6. Kant: the Solution.
Part III: Reactions to Kant:.
1. Mill on Geometry.
2. Mill versus Frege on Arithmetic.
3. Analytic Truths.
4. Concluding Remarks.
Part IV: Mathematics and its Foundations:.
1. Geometry.
2. Different Kinds of Number.
3. The Calculus.
4. Return to Foundations.
5. Infinite Numbers.
6. Foundations Again.
Part V: Logicism:.
1. Frege.
2. Russell.
3. Borkowski/Bostock.
4. Set Theory.
5. Logic.
6. Definition.
Part VI: Formalism:.
1. Hilbert.
2. Gödel.
3. Pure Formalism.
4. Structuralism.
5. Some Comments.
Part VII: Intuitionism:.
1. Brouwer.
2. Intuitionist Logic.
3. The Irrelevance of Ontology.
4. The Attack on Classical Logic.
Part VIII: Predicativism:.
1. Russell and the VCP.
2. Russell's Ramified Theory and the Axiom of Reducibility.
3. Predicative Theories after Russell.
4. Concluding Remarks.
Part IX: Realism versus Nominalism:.
A. Realism.
1. Gödel.
2. Neo-Fregeans.
3. Quine and Putnam.
B. Nominalism.
4. Reductive Nominalism.
5. Fictionalism.
6. Concluding Remarks.
References.
Index
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