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Philosophy - Epistemology & Philosophy of Science | Strict Finitism and the Logic of Mathematical Applications

Strict Finitism and the Logic of Mathematical Applications

Series: Synthese Library, Vol. 355

Ye, Feng

2011, XII, 272 p.

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  • Provides the first logical analysis of the applicability of infinite mathematics to finite physical things, by eliminating infinity in the applications
  • Defends radical naturalism, nominalism and strict finitism while offering a literally true explanation of applicability
  • Accessible to readers with only a knowledge of calculus and the basics of mathematical logic

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.

Content Level » Research

Keywords » Constructive Mathematics - Constructivism - Elementary Recursive Arithmetic - Finitism - Foundations of Mathematics - Naturalism - Nominalism - Philosophy of Mathematics - Physicalism - Strict Finitism

Related subjects » Epistemology & Philosophy of Science - Logic & Philosophy of Language - Mathematics

Table of 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.

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