Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T01:05:20.952Z Has data issue: false hasContentIssue false
  • English
  • Français

Reckoning with Continuum Idealizations: Some Lessons from Soil Hydrology

Published online by Cambridge University Press:  11 February 2022

Travis Holmes
Travis Holmes*
Affiliation:
University of Missouri-Columbia, Columbia, MO, US
*
Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Type
Article
Information
Philosophy of Science , Volume 89 , Issue 2 , April 2022 , pp. 319 - 336
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

The author would like to thank Robert Batterman, Mark Wilson, and Andre Ariew for instructive conversations pertinent to the topic of the paper.

References

Batterman, Robert W. 2002. The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction and Emergence. Oxford: Oxford University Press.Google Scholar
Batterman, Robert W. 2010. “On the Explanatory Role of Mathematics in Empirical Science.” The British Journal for the Philosophy of Science 61:1–25.CrossRefGoogle Scholar
Batterman, Robert W. 2013. “The Tyranny of the Scales.” In The Oxford Handbook of the Philosophy of Physics, edited by Robert, W. Batterman, 255–86. Oxford: Oxford University Press.CrossRefGoogle Scholar
Batterman, Robert W. 2018. “Autonomy of Theories: An Explanatory Problem.” Noûs 52:858–73.CrossRefGoogle Scholar
Batterman, Robert, W., and Green, Sara. 2021. “Steel and Bone: Mesoscale Modeling and Middle-Out Strategies in Physics and Biology.” Synthese 199:1159–84.CrossRefGoogle Scholar
Batterman, Robert W., and Rice, Collin. 2014. “Minimal Model Explanations.” Philosophy of Science 81: 349–76.CrossRefGoogle Scholar
Bear, Jacob. 1972. Dynamics of Fluids in Porous Media. Mineola: Elsevier.Google Scholar
Bohm, Helmut J. 2016. “Effects of Particle Shape on the Thermoelastoplastic Behavior of Particle Reinforced Composites.” International Journal of Solids and Structures 87:90–101.CrossRefGoogle Scholar
Bokulich, Alisa. 2018a. “Representing and Explaining: The Eikonic Conception of Scientific Explanation.” Philosophy of Science 85:793–805.CrossRefGoogle Scholar
Bokulich, Alisa. 2018b. “Searching for Non-Causal Explanations in a Sea of Causes.” In Explanation Beyond Causation, edited by Reutlinger, A. and Saatsi, J., 141–63. Oxford: Oxford University Press.Google Scholar
Bursten, Julia R. 2018. “Conceptual Strategies and Inter-Theory Relations: The Case of Nanoscale Cracks.” Studies in History and Philosophy of Modern Physics 62:158–65.CrossRefGoogle Scholar
Bursten, Julia R. 2021. “The Function of Boundary Conditions in the Physical Sciences.” Philosophy of Science 88:234–57.CrossRefGoogle Scholar
Butterfield, Jeremy. 2011. “Less is Different: Emergence and Reduction Reconciled.” Foundations of Physics 41:1065–135.CrossRefGoogle Scholar
Cain, John W., and Reynolds, Angela. 2010. Ordinary and Partial Differential Equations: An Introduction to Dynamical Systems. Virginia: Virginia Commonwealth University.Google Scholar
Cartwright, Nancy. 1983. How the Laws of Physics Lie. New York: Clarendon.CrossRefGoogle Scholar
Earman, John. 2004. “Laws, Symmetry and Symmetry Breaking: Invariance, Conservation Principles and Objectivity.” Philosophy of Science, 71:1227–41.CrossRefGoogle Scholar
Fletcher, Samuel C., Palacious, Patricia, Reutsche, Laura, and Shech, Elay. 2019. “Infinite Idealizations in Science: An Introduction.” Synthese 196:1657–69.CrossRefGoogle Scholar
Frisch, U., Hasslacher, B., and Pompeau, Y.. 1986. “Lattice-Gas Automata for the Navier-Stokes Equation.” Physical Review Letters 56:1505–8.CrossRefGoogle ScholarPubMed
Green, Sara, and Batterman, Robert W.. 2017. “Biology Meets Physics: Reductionism and Multi-Scale Modeling of Morphogenesis.” Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 61:20–34.CrossRefGoogle ScholarPubMed
Holmes, Travis. 2021. “Cognitive Dynamical Models as Minimal Models.” Synthese 199:2353–73.CrossRefGoogle Scholar
Icardi, Matteo, Boccardo, Gianluca, and Dentz, Marco. 2019. “Upscaling Flow and Transport Processes.” In Flowing Matter, edited by Toschi, F. and Sega, M., 137–76. Springer Open Access.CrossRefGoogle Scholar
Koestel, John, Larsbo, Mats, and Jarvis, N.. 2020. “Scale and REV Analyses for Porosity and Connectivity Measures in Undisturbed Soil.” Geoderma 366:1–20.CrossRefGoogle Scholar
Maddy, Penelope. 2008. “How Applied Mathematics Became Pure.” The Review of Symbolic Logic 1:16–41.CrossRefGoogle Scholar
Martin, Jonathan E. 2006. Mid-latitude Atmospheric Dynamics: A First Course. Hoboken: Wiley.Google Scholar
Morrison, Margaret. 2012. “Emergence, reduction and theoretical principles: Rethinking fundamentalism.” Philosophy of Science 73:876–87.CrossRefGoogle Scholar
Morrison, Margaret. 2021. “Turbulence, Emergence and Multi-Scale Modelling.” Synthese 198:5963–85.CrossRefGoogle Scholar
Norton, John D. 2012. “Approximation and Idealization: Why the Difference Matters.” Philosophy of Science 79:207–32.CrossRefGoogle Scholar
Oden, J. Tinsley. 2006. “Simulation Based Engineering Science—an NSF Blue Ribbon Report.” https://www.nsf.gov/pubs/reports/sbes_final_report.pdf.Google Scholar
Or, Dani. 2019. “The Tyranny of Small Scales—On Representing Soil Processes in Global Land Surface Models.” Water Resources Research. DOI: 10.1029/2019WR024846.CrossRefGoogle Scholar
Parker, Wendy S. 2020. “Model Evaluation: An Adequacy-for-Purpose View.” Philosophy of Science 87: 457–77.CrossRefGoogle Scholar
Potochnik, Angela. 2010. “Levels of Explanation Reconceived.” Philosophy of Science 77:59–72.CrossRefGoogle Scholar
Rice, Collin. 2019. “Models Don’t Decompose That Way: A Holistic View of Idealized Models.” The British Journal for the Philosophy of Science 70:179–208.CrossRefGoogle Scholar
Rothman, Daniel H., and Zaleski, Stiphane. 1997. Lattice-Gas Cellular Automata. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Rueger, Alexander. 2006. “Functional reduction and emergence in the physical sciences.” Synthese 151:335–46.CrossRefGoogle Scholar
Ruetsche, Laura. 2011. Interpreting Quantum Theories. Oxford: Oxford University Press.CrossRefGoogle Scholar
Shech, Elay. 2013. “What is the Paradox of Phase Transitions?” Philosophy of Science 80:1170–81.CrossRefGoogle Scholar
Shech, Elay. 2015. “Scientific Misrepresentation and Guides to Ontology: The Need for Representational Code and Contents.” Synthese 192:3463–85.CrossRefGoogle Scholar
Shech, Elay. 2018. “Infinite Idealizations in Physics.” Philosophy Compass 13:1–15.Google Scholar
Tao, Terence. 2012. “E Pluribus Unum: From Complexity and Universality.” Daedalus 141:23–34.CrossRefGoogle Scholar
Todd, David Keith, and Mays, Larry W.. 2004. Groundwater Hydrology, 3 rd ed., Hoboken: Wiley and Sons.Google Scholar
Vogel, Hans-Jorg. 2019. “Scale Issues in Soil Hydrology.” Vadose Zone Journal 18:1–10.CrossRefGoogle Scholar
Weisberg, Michael. 2007. “Three Kinds of Idealization.” Journal of Philosophy 104:639–59.CrossRefGoogle Scholar
Whitaker, Stephen. 1999. The Method of Volume Averaging. Dordrecht: Kluwer.CrossRefGoogle Scholar
Winsberg, Eric. 2006. “Handshaking Your Way to the Top: Simulation at the Nanoscale.” Philosophy of Science 73 (5):582–94.CrossRefGoogle Scholar
Winsberg, Eric. 2010. Science in the Age of Computer Simulation. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Wilson, Mark. 2017. Physics Avoidance: Essays in Conceptual Strategy. Oxford: Oxford University Press.Google Scholar
Woodward, James. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press.Google Scholar
Zhang, Yonggen, and Schaap, Marcel. 2019. “Estimation of Saturated Hydraulic Conductivity with Pedotransfer Functions: A Review.” Journal of Hydrology 575:1011–30.CrossRefGoogle Scholar