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Idealized laws, antirealism, and applied science: A case in hydrogeology

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When is a law too idealized to be usefully applied to a specific situation? To answer this question, this essay considers a law in hydrogeology called Darcy's Law, both as it is used in what is called the symmetric-cone model, and as it is used in equations to determine a well's groundwater velocity and hydraulic conductivity. After discussing Darcy's law and its applications, the essay concludes that this idealized law, as well as associated models and equations in hydrogeology, are not realistic in the sense required by the D-N account. They exhibit what McMullin calls mathematical idealization, construct idealization, empirical-causal idealization, and subjunctive-causal idealization. Yet this lack of realism in hydrogeology is problematic for reasons unrelated to the status of the D-N account. These idealizations are also problematic in applied situations. Their problems require developing two supplemental criteria, necessary for their productive application.

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  1. Bredehoeft, J., et al.: 1976, ‘Solute Transport in Groundwater Systems’, in J. Rodda (ed.),Facets of Hydrology, John Wiley, New York.

  2. Cartwright, N.: 1983,How the Laws of Physics Lie, Clarendon Press, Oxford.

  3. Davis, Robert, Head of Documents, U.S. Geological Survey, Louisville, Kentucky office, unpublished interview, 8-2-85.

  4. Duhem, P.: 1962,The Aim and Structure of Physical Theory, Atheneum, New York.

  5. Friedman, M.: 1984, ‘The Methodology of Positive Economics’ in D. Hausman (ed.),The Philosophy of Economics, Cambridge University Press, Cambridge.

  6. Joseph, G.: 1980, ‘The Many Sciences and the One World’,Journal of Philosophy LXXVII, 773–91.

  7. Koertge, N.: 1977, ‘Galileo and the Problem of Accidents’,Journal of the History of Ideas 38, 392–409.

  8. Leplin, J. (ed.): 1984,Scientific Realism, University of California Press, Berkeley.

  9. Linsley, R., M. Kohler, and J. Paulhus: 1975,Hydrology for Engineers, McGraw-Hill, New York.

  10. McWhorter, D. and D. Sunada: 1977,Ground-Water Hydrology and Hydraulics, Water Resources Publications, Fort Collins. Colorado.

  11. McMullin, E.: 1985, ‘Galilean Idealization’,Studies in History and Philosophy of Science 16, 247–73.

  12. Meyer, G.: 1975, ‘Maxey Flats Radioactive Waste Burial Site: Status Report’, unpublished report, Advanced Science and Technology Branch, U.S. Environmental Protection Agency, February 19, 1975.

  13. Niiniluoto, I.: 1982, ‘Truthlikeness for Quantitative Statements’, in P. Asquith and T. Nickles (eds.),PSA 1982, Vol. 1, Philosophy of Science Association, East Lansing.

  14. Nowak, L.: 1979,The Structure of Idealization: Towards a Systematic Interpretation of the Marxian Idea of Science, D. Reidel, Dordrecht.

  15. Pearce, D. and V. Rantala: 1985, ‘Approximative Explanation is Deductive-Nomological’,Philosophy of Science 51, 126–40.

  16. Scheffler, I.: 1982,Science and Subjectivity, Hackett, Indianapolis.

  17. Schoeller, H.: 1974, ‘Analytical and Investigational Techniques for Fissured and Fractured Rocks’, in R. Brown and A. Konoplyantsev,et al. (eds.),Groundwater Studies, UNESCO, New York.

  18. Todd, D.: 1980,Groundwater Hydrology, John Wiley, New York.

  19. U.S. Geological Survey: 1962, Memo: July 1, —, vertical file, ‘Maxey Flats: Correspondence and Phone Conversations’, Water Resources Division, U.S. Division of the Interior, Louisville, Kentucky. (The Louisville office of the U.S.G.S. is responsible for monitoring the Maxey Flats radioactive facility.)

  20. van Fraassen, B.: 1980,The Scientific Image, Clarendon Press, Oxford.

  21. van Fraassen.: 1984, ‘To Save the Phenomena’ in Leplin.

  22. Walker, I.: 1962,Geological and Hydrological Evaluation of a Proposed Site for Burial of Solid Radioactive Wastes Northwest of Morehead, Fleming County, Kentucky, U.S. Geological Survey, Kearny, New Jersey, September 12, 1962, unpublished report. On file in the Louisville, Kentucky, office of the U.S.G.S.

  23. Walton, W.: 1970,Groundwater Resource Evaluation, McGraw-Hill, New York.

  24. Waltz, J.: 1969, ‘Ground Water’ in R. Chorley (ed.),Water, Earth. and Man, Methuen, London.

  25. Ward, R.: 1975,Principles of Hydrology, McGraw-Hill, New York.

  26. Weiss, A. and P. Columbo: 1980, ‘Evaluation of Isotope Migration — Land Burial’ NUREG/CR-1289 BNL-NUREG-51143, U.S. Nuclear Regulatory Commission, Washington, DC.

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Shrader-Frechette, K.S. Idealized laws, antirealism, and applied science: A case in hydrogeology. Synthese 81, 329–352 (1989). https://doi.org/10.1007/BF00869320

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  • Hydraulic Conductivity
  • Specific Situation
  • Applied Science
  • Productive Application
  • Groundwater Velocity