Synthese Library

Strict Finitism and the Logic of Mathematical Applications

Authors: Ye, Feng

  • Provides the first logical analysis of the applicability of infinite mathematics to finite physical things, by eliminating infinity in the applications
  • Defends radical naturalism, nominalism and strict finitism while offering a literally true explanation of applicability
  • Accessible to readers with only a knowledge of calculus and the basics of mathematical logic
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eBook $119.00
price for USA (gross)
  • ISBN 978-94-007-1347-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-94-007-1346-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-94-007-3631-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book intends to show that radical naturalism (or physicalism), nominalism and strict finitism account for the applications of classical mathematics in current scientific theories. The applied mathematical theories developed in the book include the basics of calculus, metric space theory, complex analysis, Lebesgue integration, Hilbert spaces, and semi-Riemann geometry (sufficient for the applications in classical quantum mechanics and general relativity). The fact that so much applied mathematics can be developed within such a weak, strictly finitistic system, is surprising in itself. It also shows that the applications of those classical theories to the finite physical world can be translated into the applications of strict finitism, which demonstrates the applicability of those classical theories without assuming the literal truth of those theories or the reality of infinity.

Both professional researchers and students of philosophy of mathematics will benefit greatly from reading this book.

About the authors

Feng Ye is a professor of philosophy at Peking University, China. He has a B.S. degree in mathematics from Xiamen University, China, and a Ph.D. degree in philosophy from Princeton University, U.S.A.. His research areas include constructive and finitistic mathematics, philosophy of mathematics, and philosophy of mind and language. He used to prove, for the first time, a constructive version of the spectral theorem and Stone’s theorem for unbounded linear operators on Hilbert spaces. He is currently developing a radically naturalistic, nominalistic, and strictly finitistic philosophy of mathematics, a naturalistic theory of content, and a naturalistic interpretation of modality. His research articles have been published in The Journal of Symbolic Logic, Philosophia Mathematica, and Synthese, among others. He is also the author of the book Philosophy of Mathematics in the 20th Century: a Naturalistic Commentary (in Chinese, Peking University Press, 2010). His philosophical interests revolve around naturalism.

Reviews

"Strict finitism is a very attractive view that has generally suffered just from the sense that it couldn't reproduce enough mathematics. This book takes strides toward removing that worry and making the view a viable alternative." James Tappenden, University of Michigan, Ann Arbor, U.S.A.

Table of contents (8 chapters)

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-94-007-1347-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-94-007-1346-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-94-007-3631-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Strict Finitism and the Logic of Mathematical Applications
Authors
Series Title
Synthese Library
Series Volume
355
Copyright
2011
Publisher
Springer Netherlands
Copyright Holder
Springer Netherlands
eBook ISBN
978-94-007-1347-5
DOI
10.1007/978-94-007-1347-5
Hardcover ISBN
978-94-007-1346-8
Softcover ISBN
978-94-007-3631-3
Edition Number
1
Number of Pages
XII, 272
Topics