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Inhaltsangabe
1. Introduction.- 2. Strict Finitism.- 3. Calculus.- 4. Metric Space.- 5. Complex Analysis.- 6. Integration.- 7. Hilbert Space.- 8. Semi-Riemann Geometry.- References.- Index.
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Über die Autorin bzw. 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.
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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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Strict Finitism and the Logic of Mathematical Applications
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Strict Finitism and the Logic of Mathematical Applications
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 284 pp. Englisch. Bestandsnummer des Verkäufers 9789400713468
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Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 expl. Bestandsnummer des Verkäufers 5825540
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Strict Finitism and the Logic of Mathematical Applications
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Springer Netherlands, Springer Netherlands Jul 2011, 2011
ISBN 10: 9400713460
ISBN 13: 9789400713468
Neu
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Buch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 284 pp. Englisch. Bestandsnummer des Verkäufers 9789400713468
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Strict Finitism and the Logic of Mathematical Applications
Verlag:
Springer Netherlands, Springer Netherlands, 2011
ISBN 10: 9400713460
ISBN 13: 9789400713468
Neu
Hardcover
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Bestandsnummer des Verkäufers 9789400713468
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Strict Finitism and the Logic of Mathematical Applications (Synthese Library)
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