Reckoning with Continuum Idealizations: Some Lessons from Soil Hydrology

Philosophy of Science 89 (2):319-336 (2022)
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Abstract

In scientific modeling, continuum idealizations bridge scales but at the cost of fundamentally misrepresenting the microstructure of the system. This engenders a mystery. If continuum idealizations are dispensable in principle, this de-problematizes their representational inaccuracy, since continuum properties reduce to lower-scale properties, but the mystery of how this reduction could be carried out endures. Alternatively, if continuum idealizations are indispensable in principle, this is consistent with their explanatory and predictive success but renders their representational inaccuracy mysterious. I argue for a deflationary solution, enlisting the applied scientific method of upscaling as demonstrated in a case from soil hydrology.

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Travis Holmes
University of Missouri, Columbia

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References found in this work

Three Kinds of Idealization.Michael Weisberg - 2007 - Journal of Philosophy 104 (12):639-659.
Minimal Model Explanations.Robert W. Batterman & Collin C. Rice - 2014 - Philosophy of Science 81 (3):349-376.
Model Evaluation: An Adequacy-for-Purpose View.Wendy S. Parker - 2020 - Philosophy of Science 87 (3):457-477.
On the explanatory role of mathematics in empirical science.Robert W. Batterman - 2010 - British Journal for the Philosophy of Science 61 (1):1-25.

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