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Strict Finitism and the Logic of Mathematical Applications [electronic resource] / by Feng Ye.

By: Ye, Feng [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science: 355Publisher: Dordrecht : Springer Netherlands : Imprint: Springer, 2011Description: XII, 272 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9789400713475.Subject(s): Philosophy (General) | Logic | Science -- Philosophy | Logic, Symbolic and mathematical | Philosophy | Philosophy of Science | Logic | Mathematical Logic and FoundationsDDC classification: 501 Online resources: Click here to access online
Contents:
1. Introduction -- 2. Strict Finitism -- 3. Calculus -- 4. Metric Space -- 5. Complex Analysis -- 6. Integration -- 7. Hilbert Space -- 8. Semi-Riemann Geometry.- References -- Index.
In: Springer eBooksSummary: 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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1. Introduction -- 2. Strict Finitism -- 3. Calculus -- 4. Metric Space -- 5. Complex Analysis -- 6. Integration -- 7. Hilbert Space -- 8. Semi-Riemann Geometry.- References -- Index.

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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