00000cmm a22000004i 4500 UP-99796217611057149 Buklod 20230504003249.0 m go j cr |nu|||auu|a 110705s2011 xx u | eng d 978-94-007-1347-5 (eBook) (iLib)UPD-00209103896 DLC DML eng DMLUC QA 9 Y44 2011eb Ye, Feng Strict finitism and the logic of mathematical applications [electronic resource] Feng Ye, author. Dordrecht Springer Netherlands 2011. 1 online resource (xii, 272 p.) Synthese library : studies in Epistemology, logic, methodology, and philosophy of science 355. 1. Introduction--2. Strict Finitism--3. Calculus--4. Metric Space--5. Complex Analysis--6. Integration--7. Hilbert Space--8. Semi-Riemann Geometry.- References--Index. IP-based subscription, access limited to within on campus computer network. Access via Electronic resources of the UPD University Library Website. 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. Electronic reproduction. New York Springerlink c2011. Available via World Wide Web through SpringerLink. Logic, Symbolic and mathematical. Mathematics Philosophy. Naturalism. Finite, The. Electronic books. SpringerLink (Online Service). Electronic Resource Available for the University of the Philippines Diliman via Springerlink. Click here to access http://link.springer.com/book/10.1007/978-94-007-1347-5 FO Monograph UPD DMLR Electronic Resource