David Bostock

Philosophy of Mathematics

• Broschiertes Buch

Produktbeschreibung

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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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

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 344
• Erscheinungstermin: 13. Februar 2009
• Englisch
• Abmessung: 229mm x 152mm x 19mm
• Gewicht: 492g
• ISBN-13: 9781405189910
• ISBN-10: 1405189916
• Artikelnr.: 25868538

Autorenporträt

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).

Inhaltsangabe

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

Rezensionen

"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

"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)

"This book is an undergraduate introduction to the basic ideas on the nature of mathematics that have played a significant role in the development of philosophy from Antiquity to contemporary debates . . . throughout the book the emphasis is on the basic ideas as well as their current variations, leading up to recent debates between realists and nominalists." (Mathematical Reviews, 2011)