How to avoid inconsistent idealizations
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Idealized scientific representations result from employing claims that we take to be false. It is not surprising, then, that idealizations are a prime example of allegedly inconsistent scientific representations. I argue that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the idealization can be interpreted consistently. The main example discussed is the claim that models of ocean waves typically involve the false assumption that the ocean is infinitely deep. While it is true that the variable associated with depth is often taken to infinity in the representation of ocean waves, I explain how this mathematical transformation of the original equations does not require the belief that the ocean being modeled is infinitely deep. More generally, as a mathematical representation is manipulated, some of its components are decoupled from their original physical interpretation.
KeywordsIdealization Wave dispersion Perturbation theory Asymptotic analysis
Earlier versions of this paper were presented to the Society for Realist/Antirealist Discussion (Group Session), Central Division American Philosophical Association Meeting, Chicago, IL, USA, February 2009 and the Department of History and Philosophy of Science, University of Athens, Athens, Greece, March 2009. I am grateful to both audiences for their useful suggestions. In addition, I would like to thank the issue editors and the anonymous referees for their help in improving this paper.
- Batterman, R. (2002). The devil in the details: Asymptotic reasoning in explanation, reduction, and emergence. New York: Oxford University Press.Google Scholar
- Colyvan, M. (2009). Applying inconsistent mathematics. In O. Bueno & O. Linnebo (Eds.), New waves in the philosophy of mathematics (pp. 160–172). Basingstoke: Palgrave Macmillan.Google Scholar
- Kundu, P. K., & Cohen, I. M. (2008). Fluid mechanics (4th ed.). San Diego, CA: Academic Press.Google Scholar
- Maddy, P. (1998). Naturalism in mathematics. Oxford: Clarendon Press.Google Scholar
- Pincock, C. (2009). Towards a philosophy of applied mathematics. In O. Bueno & O. Linnebo (Eds.), New waves in the philosophy of mathematics (pp. 173–194). Basingstoke: Palgrave Macmillan.Google Scholar