Synthese 191 (7):1451-1467 (2014)

Nicolas Fillion
Simon Fraser University
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.
Keywords Rational reconstruction  Mathematical modeling  Modeling error   Computational error  Backward error analysis
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DOI 10.1007/s11229-013-0339-4
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References found in this work BETA

Computing Machinery and Intelligence.Alan M. Turing - 1950 - Mind 59 (October):433-60.

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Citations of this work BETA

Explanation and Abstraction From a Backward-Error Analytic Perspective.Nicolas Fillion & Robert H. C. Moir - 2018 - European Journal for Philosophy of Science 8 (3):735-759.
On the Presumed Superiority of Analytical Solutions Over Numerical Methods.Vincent Ardourel & Julie Jebeile - 2017 - European Journal for Philosophy of Science 7 (2):201-220.
The Adventures of Climate Science in the Sweet Land of Idle Arguments.Eric Winsberg & William Mark Goodwin - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 54:9-17.
Conceptual and Computational Mathematics†.Nicolas Fillion - 2019 - Philosophia Mathematica 27 (2):199-218.

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