Philosophy of Mathematics An Introduction

Name: Philosophy of Mathematics An Introduction
Price: 33.56 USD
Availability: InStock
ISBN: 9781405189910

ISBN-10: 1405189916

ISBN-13: 9781405189910

Edition: 2009

Authors: David Bostock, Bostock

List price: $48.95

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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 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

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



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



Gï¿½del



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



Gï¿½del



Neo-Fregeans



Quine and Putnam



Nominalism



Reductive nominalism



Fictionalism



Concluding remarks


References


Index