| 书目名称 | Strict Finitism and the Logic of Mathematical Applications | | 编辑 | Feng Ye | | 视频video | | | 概述 | 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 stric | | 丛书名称 | Synthese Library | | 图书封面 |  | | 描述 | .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.. | | 出版日期 | Book 2011 | | 关键词 | Constructive Mathematics; Constructivism; Elementary Recursive Arithmetic; Finitism; Foundations of Math | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-007-1347-5 | | isbn_softcover | 978-94-007-3631-3 | | isbn_ebook | 978-94-007-1347-5Series ISSN 0166-6991 Series E-ISSN 2542-8292 | | issn_series | 0166-6991 | | copyright | Springer Netherlands 2011 |
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发表于 2025-3-21 17:04:04
