Rules to Infinity
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 Vi...
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| Formatua: | Online |
| Hizkuntza: | ingelesa |
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Oxford University Press
2024
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| Sarrera elektronikoa: | https://library.oapen.org/handle/20.500.12657/94768 |
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Etiketarik gabe, Izan zaitez lehena erregistro honi etiketa jartzen!
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| _version_ | 1869519828539146240 |
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| author | Povich, Mark |
| author_browse | Povich, Mark |
| author_facet | Povich, Mark |
| author_sort | Povich, Mark |
| collection | Directory of Open Access Books |
| description | 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, which I call 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. |
| format | Online |
| id | doab-20.500.12854ir-148114 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Oxford University Press |
| publisherStr | Oxford University Press |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1481142024-11-20T04:51:58Z Rules to Infinity Povich, Mark philosophy, mathematics, science, explanation, scientific explanation, semantics, models, concepts thema EDItEUR::P Mathematics and Science::PB Mathematics::PBB Philosophy of mathematics thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDA Philosophy of science thema EDItEUR::C Language and Linguistics::CF Linguistics::CFG Semantics, discourse analysis, stylistics 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, which I call 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. 2024-11-20T04:51:57Z 2024-11-20T04:51:57Z 2024-11-19T14:24:12Z 2024 book https://library.oapen.org/handle/20.500.12657/94768 9780197679012 9780197679029 https://directory.doabooks.org/handle/20.500.12854/148114 eng open access image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://library.oapen.org/bitstream/20.500.12657/94768/1/Povich_9780197679005.pdf Oxford University Press 10.1093/oso/ 9780197679005.001.0001 10.1093/oso/ 9780197679005.001.0001 db4e319f-ca9f-449a-bcf2-37d7c6f885b1 8e3a176d-a297-41fa-9695-ae07eba46479 6b8eb5b2-6a1f-44b1-bd52-e89daeaff715 9780197679012 9780197679029 336 New York University of Rochester U of R 10.13039/100008091 open access |
| spellingShingle | philosophy, mathematics, science, explanation, scientific explanation, semantics, models, concepts thema EDItEUR::P Mathematics and Science::PB Mathematics::PBB Philosophy of mathematics thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDA Philosophy of science thema EDItEUR::C Language and Linguistics::CF Linguistics::CFG Semantics, discourse analysis, stylistics Povich, Mark Rules to Infinity |
| title | Rules to Infinity |
| title_full | Rules to Infinity |
| title_fullStr | Rules to Infinity |
| title_full_unstemmed | Rules to Infinity |
| title_short | Rules to Infinity |
| title_sort | rules to infinity |
| topic | philosophy, mathematics, science, explanation, scientific explanation, semantics, models, concepts thema EDItEUR::P Mathematics and Science::PB Mathematics::PBB Philosophy of mathematics thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDA Philosophy of science thema EDItEUR::C Language and Linguistics::CF Linguistics::CFG Semantics, discourse analysis, stylistics |
| topic_facet | philosophy, mathematics, science, explanation, scientific explanation, semantics, models, concepts thema EDItEUR::P Mathematics and Science::PB Mathematics::PBB Philosophy of mathematics thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDA Philosophy of science thema EDItEUR::C Language and Linguistics::CF Linguistics::CFG Semantics, discourse analysis, stylistics |
| url | https://library.oapen.org/handle/20.500.12657/94768 |
| work_keys_str_mv | AT povichmark rulestoinfinity |