Philosophy of Mathematics: An Introduction / Edition 1

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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.
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Editorial Reviews

From the Publisher
“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 more. It should appeal not only to students who have already developed a preference for the general approach and style of contemporary analytic philosophy, but also to a broader audience of students and to people with a non-professional interest in philosophy and mathematics.”  (Erkenn, 2011)

"This is a concise as well as comprehensive presentation of core topics in the philosophy of mathematics, written in a clear and engaged manner, hence well readable." (Zentralblatt MATH, 2011)

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Product Details

  • ISBN-13: 9781405189927
  • Publisher: Wiley
  • Publication date: 3/17/2009
  • Edition number: 1
  • Pages: 344
  • Product dimensions: 5.70 (w) x 9.10 (h) x 1.00 (d)

Meet the Author

David Bostock has been a Fellow and Tutor in Philosophy at Merton College, and Lecturer in Philosophy at the University of Oxford. His recent publications include Intermediate Logic (1997), Aristotle’s Ethics (2000), and Space, Time, Matter, and Form: Essays on Aristotle's Physics (2006).

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Table of Contents


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.



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