The Western Ontario Series in Philosophy of Science

The Arché Papers on the Mathematics of Abstraction

Editors: Cook, Roy T. (Ed.)

  • Unique in presenting a thoroughgoing examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns)
  • Provides an overview of the Neo-Fregean position in philosophy of mathematics
  • Collects together hard to find material on Neo-Fregean set theory and real analysis
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eBook $209.00
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  • ISBN 978-1-4020-4265-2
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Hardcover $269.00
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  • ISBN 978-1-4020-4264-5
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Softcover $269.00
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  • ISBN 978-90-481-7090-6
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About this book

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines.

Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege’s enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in presenting a thorough going examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns). Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut - or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies. As a result, the volume provides a test of the scope and limits of the neo-logicist project, detailing what has been accomplished and outlining the desiderata still outstanding.

All papers in the anthology have their origins in presentations at Arché events, thus providing a volume that is both a survey of the cutting edge in research on the technical aspects of abstraction and a catalogue of the work in this area that has been supported in various ways by Arché.

Table of contents (20 chapters)

Buy this book

eBook $209.00
price for USA (gross)
  • ISBN 978-1-4020-4265-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $269.00
price for USA
  • ISBN 978-1-4020-4264-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $269.00
price for USA
  • ISBN 978-90-481-7090-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Arché Papers on the Mathematics of Abstraction
Editors
  • Roy T. Cook
Series Title
The Western Ontario Series in Philosophy of Science
Series Volume
71
Copyright
2007
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-4265-2
DOI
10.1007/978-1-4020-4265-2
Hardcover ISBN
978-1-4020-4264-5
Softcover ISBN
978-90-481-7090-6
Series ISSN
1566-659X
Edition Number
1
Number of Pages
XXXVIII, 454
Topics