Authors:
- 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
Part of the book series: Synthese Library (SYLI, volume 355)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
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.
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Authors and Affiliations
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, Department of Philosophy, Peking University, Beijing, China, People's Republic
Feng Ye
About the author
Bibliographic Information
Book Title: Strict Finitism and the Logic of Mathematical Applications
Authors: Feng Ye
Series Title: Synthese Library
DOI: https://doi.org/10.1007/978-94-007-1347-5
Publisher: Springer Dordrecht
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer Netherlands 2011
Hardcover ISBN: 978-94-007-1346-8Published: 06 July 2011
Softcover ISBN: 978-94-007-3631-3Published: 15 July 2013
eBook ISBN: 978-94-007-1347-5Published: 06 July 2011
Series ISSN: 0166-6991
Series E-ISSN: 2542-8292
Edition Number: 1
Number of Pages: XII, 272
Topics: Philosophy of Science, Logic, Mathematical Logic and Foundations