Philosophy of Mathematics An Introduction

ISBN-10: 1405189916
ISBN-13: 9781405189910
Edition: 2009
List price: $48.95 Buy it from $30.50
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Description: 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  More...

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Book details

List price: $48.95
Copyright year: 2009
Publisher: John Wiley & Sons, Incorporated
Publication date: 2/24/2009
Binding: Paperback
Pages: 344
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.100
Language: English

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

Preface
Plato versus Aristotle
Plato
The Socratic background
The theory of recollection
Platonism in mathematics
Retractions: the Divided Line in Republic VI (509d-511e)
Aristotle
The overall position
Idealizations
Complications
Problems with infinity
Prospects
From Aristotle to Kant
Mediaeval times
Descartes
Locke, Berkeley, Hume
A remark on conceptualism
Kant: the problem
Kant: the solution
Reactions to Kant
Mill on geometry
Mill versus Frege on arithmetic
Analytic truths
Concluding remarks
Mathematics and its Foundations
Geometry
Different kinds of number
The calculus
Return to foundations
Infinite numbers
Foundations again
Logicism
Frege
Russell
Borkowski/Bostock
Set theory
Logic
Definition
Formalism
Hilbert
G�del
Pure formalism
Structuralism
Some comments
Intuitionism
Brouwer
Intuitionist logic
The irrelevance of ontology
The attack on classical logic
Predicativism
Russell and the VCP
Russell's ramified theory and the axiom of reducibility
Predicative theories after Russell
Concluding remarks
Realism and Nominalism
Realism
G�del
Neo-Fregeans
Quine and Putnam
Nominalism
Reductive nominalism
Fictionalism
Concluding remarks
References
Index

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