Structure and applied mathematics.
‘Mapping accounts’ of applied mathematics hold that the application of mathematics in physical science is best understood in terms of ‘mappings’ between mathematical structures and physical structures. In this paper, I suggest that mapping accounts rely on the assumption that the mathematics relevan...
| Publicado en: | Synthese Vol. 200; no. 5; pp. 1 - 26 |
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| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Oct2022
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=158872154&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 158872154 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Oct2022 vid: 200 iid: 5 pid: 237 pub: Springer Nature artinfo: ui: 158872154 10.1007/s11229-022-03873-x ppf: 1 ppct: 25 formats: fmt: – @attributes: type: T – @attributes: type: P size: 877KB tig: atl: Structure and applied mathematics. aug: au: McKenna, Travis affil: University of Pittsburgh, 4200 Fifth Avenue, 15260, Pittsburgh, PA, USA sug: keyword: Inferential conception of applied mathematics Mapping accounts Philosophy of applied mathematics Philosophy of mathematics Philosophy of science ab: ‘Mapping accounts’ of applied mathematics hold that the application of mathematics in physical science is best understood in terms of ‘mappings’ between mathematical structures and physical structures. In this paper, I suggest that mapping accounts rely on the assumption that the mathematics relevant to any application of mathematics in empirical science can be captured in an appropriate mathematical structure. If we are interested in assessing the plausibility of mapping accounts, we must ask ourselves: how plausible is this assumption as a working hypothesis about applied mathematics? In order to do so, we examine the role played by mathematics in the multiscalar modelling of sea ice melting behaviour and examine whether we can indeed capture the mathematics involved in the kind of mathematical structure employed by the mapping account. Along the way, we note that the cases of applied mathematics that appear in discussions of mapping accounts almost exclusively involve the employment of a single clearly circumscribed mathematical field or domain (e.g. ‘the use of arithmetic in counting physical objects’). While the core assumption of mapping accounts may appear plausible in such situations, we ultimately suggest that the mapping account is not able to handle the important added complexities involved in our sea ice case study. In particular, the notion of mathematical structure around which such accounts are framed does not seem to be able to capture the way in which some applications of mathematics require that very different pieces of mathematics be related to one another on the basis of both mathematical and empirical information. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2022. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2022 holdings: @attributes: islocal: N |
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