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