Strict Finitism and the Logic of Mathematical Applications (Synthese Library, 355)
ISBN-13:
9789400736313
ISBN-10:
9400736312
Edition:
2011
Author:
Feng Ye
Publication date:
2013
Publisher:
Springer
Format:
Paperback
284 pages
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Book details
ISBN-13:
9789400736313
ISBN-10:
9400736312
Edition:
2011
Author:
Feng Ye
Publication date:
2013
Publisher:
Springer
Format:
Paperback
284 pages
Summary
Strict Finitism and the Logic of Mathematical Applications (Synthese Library, 355) (ISBN-13: 9789400736313 and ISBN-10: 9400736312), written by authors
Feng Ye, was published by Springer in 2013.
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Description
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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