Feng Ye

Strict Finitism and the Logic of Mathematical Applications

Ebook (PDF Format)

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 classica… Mehr

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Produktdetails

ISBN: 978-94-007-1347-5
EAN: 9789400713475
Produktnummer: 18249011
Verlag: Springer-Verlag GmbH
Sprache: Englisch
Erscheinungsjahr: 2011
Seitenangabe: 272 S.
Plattform: PDF
Masse: 2'189 KB
Auflage: 2011
Abbildungen: Bibliographie
Reihenbandnummer: 355

Über den Autor

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.