Infinite Idealizations

In my talk at the celebration of the 20th Anniversary of the Vienna Circle Institute, I sketched results of recent work on approximation and idealization (Norton, forthcoming). A goal of that work was to clarify the widespread use of infinite limits in statistical physics to introduce what are informally described as idealizations. This literature examines the behavior of systems composed of very many—but always finitely many—components. Certain properties of these systems settle down to stable values if the number of components is very large, as is the case with ordinary thermal systems. These stable values can be approximated quite closely by taking a limit of the property. Each of these properties is a function of the number of components and one merely takes the limit of these functions. The key point is that the limit of these functions can be taken without considering a system that consists of an actual infinity of components
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    Robert Batterman (2005). Critical Phenomena and Breaking Drops: Infinite Idealizations in Physics. Studies in History and Philosophy of Science Part B 36 (2):225-244.

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