Philosophy of Mathematics: An IntroductionISBN: 9781405189927
344 pages
March 2009, WileyBlackwell

Description

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 nonpartisan 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
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. NeoFregeans.
3. Quine and Putnam.
B. Nominalism.
4. Reductive Nominalism.
5. Fictionalism.
6. Concluding Remarks.
References.
Index
Author Information
The Wiley Advantage

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 nonpartisan 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
Reviews
“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 nonprofessional 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)
"The best textbook on the philosophy of mathematics bar
none" –Alexander Paseau, University of
Oxford
"Bostock's 'Philosophy of Mathematics' is remarkably comprehensive
compared to other surveys of philosophy of mathematics. The writing
is engaging and clear, and it treats a wide range of issues in
considerable depth, including issues that are often ignored or
downplayed in more general discussions." –Alan Baker,
Swarthmore College