Strict Finitism and the Logic of Mathematical Applications

2011
ISBN: 978-94-007-1346-8
Verlag: Springer Netherlands

Buch, Englisch, 272 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 594 g

Reihe: Synthese Library

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.

Zielgruppe

Research

Autoren/Hrsg.

Ye, Feng

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

1. Introduction.- 2. Strict Finitism.- 3. Calculus.- 4. Metric Space.- 5. Complex Analysis.- 6. Integration.- 7. Hilbert Space.- 8. Semi-Riemann Geometry.- References.- Index.

Über Autor(innen)

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.