Pantsar , M 2018 , Mathematical Explanations and Mathematical Applications . in B Sriraman (ed.) , Handbook of The Mathematics of The Arts and Sciences . Springer , pp. 1-16 . https://doi.org/10.1007/978-3-319-57072-3_30
Title: | Mathematical Explanations and Mathematical Applications |
Author: | Pantsar, Markus |
Other contributor: | Sriraman, Bharath |
Contributor organization: | Department of Philosophy, History and Art Studies Staff Services |
Publisher: | Springer |
Date: | 2018-12-23 |
Language: | eng |
Number of pages: | 16 |
Belongs to series: | Handbook of The Mathematics of The Arts and Sciences |
ISBN: | 978-3-319-57071-6 978-3-319-57072-3 |
DOI: | https://doi.org/10.1007/978-3-319-57072-3_30 |
URI: | http://hdl.handle.net/10138/325183 |
Abstract: | One of the key questions in the philosophy of mathematics is the role and status of mathematical applications in the natural sciences. The importance of mathematics for science is indisputable, but philosophers have disagreed on what the relation between mathematical theories and scientific theories are. This chapter presents these topics through a distinction between mathematical applications and mathematical explanations. Particularly important is the question whether mathematical applications are ever indispensable. If so, it has often been argued, such applications should count as proper mathematical explanations. Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics. |
Subject: | 111 Mathematics |
Peer reviewed: | Yes |
Usage restriction: | openAccess |
Self-archived version: | acceptedVersion |
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