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Extra resources for Reduction in Science: Structure, Examples, Philosophical Problems
With M = Nm and V(r) = N2y(r) we consider the limit N ~ 00, m ~ 0, v(r) ~ 0, keeping M,V and V(r) fixed. In this limit we obtain a kinetic equation of the Vlasov type (see for instance, Balescu (1963)). But is this equation a good approximation to a real situation with given N,V, and v(r)? It is a good approximation only if the range rQ of the interaction v(r) is larg~ compared to the typ~cal dIstance (V/N)~ between the partIcles. If ro « (V/N)! the Vlasov equation is no approximation at all. Instead, the Boltzmann equation provides a much better approximate description of the system.
Eberle, 1971 ,"Replacing one theory by another under preservation of a given feature", Philosophy·of Science 38, pp. 486-501. L. 22, p. 107. Math. 49, pp. 35-92. Kreisel, S. Grundlagenf. 6, pp. 52-63. Lindstrom, 1983, On faithful interpretability, Colloquium 1983, Aachen, mimeographed. Oppenheim, 1956, "On reduction", Philosophical Studies 7, pp. 6-19. math. Logik u. Grundlagen d. Math. 7, pp. 146-153. Mayr, 1976, "Investigations of the concept of reduction I" Erkenntnis 10, pp. 275-294. Mayr,1981.
Global links between different theories of the kind structuralism is now considering are normally composed of some partial links that connect some terms of each theory in specific ways. ) What I suggest for the present case is that, among all other requirements put on a reductive link , it be viewed as composed of some partial links between some of the base sets of each theory. That this is a reasonable requirement on reduction appears to be something that not even critics of Nagel's approach would like to deny.
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