Rules to infinity : the normative role of mathematics in scientific explanation /
"One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of...
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| Format: | eBook |
| Language: | English |
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New York, NY, United States of America :
Oxford University Press,
[2024]
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | "One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should not be thought of as describing, in any substantive sense, an abstract realm of eternal mathematical objects, as traditional platonists have thought. In Rules to Infinity, this view, mathematical normativism, is updated with contemporary philosophical tools, and it is argued that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the platonistic idea that there exist abstract mathematical objects that explain such truths. Furthermore, Rules to Infinity defends a particular account of the distinction between scientific explanations that are in some sense distinctively mathematical—those that explain natural phenomena in some uniquely mathematical way—and those that are only standardly mathematical, and it lays out desiderata for any account of this distinction. Normativism is compared with other prominent views in the philosophy of mathematics such as neo-Fregeanism, fictionalism, conventionalism, and structuralism. Rules to Infinity serves as an entry point into debates at the forefront of philosophy of science and mathematics, and it defends novel positions in these debates"--Publisher's description. |
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| Physical Description: | 1 online resource |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9780197679012 0197679013 019767903X 9780197679036 9780197653463 0197653464 0197679021 9780197679029 |