Feng Ye

Strict Finitism and the Logic of Mathematical Applications

• Gebundenes Buch

Produktbeschreibung

Exploring the logic behind applied mathematics to the physical world, this volume illustrates how radical naturalism, nominalism and strict finitism can account for the applications of classical mathematics in current theories about natural phenomena.

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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.

Produktdetails

• Synthese Library 355
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 80036772, 978-94-007-1346-8
• 2011
• Seitenzahl: 284
• Erscheinungstermin: 6. Juli 2011
• Englisch
• Abmessung: 241mm x 160mm x 20mm
• Gewicht: 574g
• ISBN-13: 9789400713468
• ISBN-10: 9400713460
• Artikelnr.: 32984123

Autorenporträt

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.

Inhaltsangabe

1. Introduction.- 2. Strict Finitism.- 3. Calculus.- 4. Metric Space.- 5. Complex Analysis.- 6. Integration.- 7. Hilbert Space.- References.- Index.

Rezensionen

"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.