Strict finitism and the logic of mathematical applications - Ye, Feng; SpringerLink (Online Service). (Dordrecht Springer Netherlands, 2011)
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.
1. Introduction--2. Strict Finitism--3. Calculus--4. Metric Space--5. Complex Analysis--6. Integration--7. Hilbert Space--8. Semi-Riemann Geometry.- References--Index.
Electronic reproduction.
Keywords: Logic, Symbolic and mathematical; Mathematics -- Philosophy; Naturalism; Finite, The; Electronic books