Philosophy of Mathematics: An Introduction / Edition 1

Philosophy of Mathematics: An Introduction / Edition 1

by David Bostock
     
 

ISBN-10: 1405189924

ISBN-13: 9781405189927

Pub. Date: 03/17/2009

Publisher: Wiley

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.  See more details below

Overview

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.

Product Details

ISBN-13:
9781405189927
Publisher:
Wiley
Publication date:
03/17/2009
Pages:
344
Product dimensions:
5.70(w) x 9.10(h) x 1.00(d)

Table of Contents

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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