Philosophy of Mathematics: An Introduction / Edition 1

Philosophy of Mathematics: An Introduction / Edition 1

by David Bostock
     
 

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ISBN-10: 1405189916

ISBN-13: 9781405189910

Pub. Date: 03/04/2009

Publisher: Wiley

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.

  • Offers beginning readers a critical appraisal of philosophical viewpoints throughout history
  • Gives a separate chapter to

Overview

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.

  • Offers beginning readers a critical appraisal of philosophical viewpoints throughout history
  • Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism
  • Provides readers with a non-partisan discussion until the final chapter, which gives the author’s personal opinion on where the truth lies
  • Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals

Product Details

ISBN-13:
9781405189910
Publisher:
Wiley
Publication date:
03/04/2009
Edition description:
New Edition
Pages:
344
Product dimensions:
6.00(w) x 8.90(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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