On the epistemological analysis of modeling and computational error in the mathematical sciences.
Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rat...
| Publicado en: | Synthese Vol. 191; no. 7; pp. 1451 - 1468 |
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| Autores principales: | , |
| Formato: | Artículo |
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Springer Nature
May2014
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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=95298490&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 95298490 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: May2014 vid: 191 iid: 7 pid: 237 pub: Springer Nature artinfo: ui: 95298490 10.1007/s11229-013-0339-4 ppf: 1451 ppct: 17 formats: fmt: @attributes: type: P size: 527KB tig: atl: On the epistemological analysis of modeling and computational error in the mathematical sciences. aug: au: Fillion, Nicolas Corless, Robert affil: Department of Statistics and Actuarial Sciences, Joseph L. Rotman Institute of Philosophy, University of Western Ontario, London Canada Department of Applied Mathematics, Joseph L. Rotman Institute of Philosophy, University of Western Ontario, London Canada su: Theory of knowledge Mathematical models Error analysis in mathematics Numerical analysis Normativity (Ethics) Perturbation theory sug: subj: Theory of knowledge Mathematical models Error analysis in mathematics Numerical analysis Normativity (Ethics) Perturbation theory keyword: Backward error analysis Computational error Mathematical modeling Modeling error Rational reconstruction ab: Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler's recipe. We then describe a general model that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2014. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2014 holdings: @attributes: islocal: N |
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