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Robert W. Batterman 《Synthese》2009,169(3):427-446
This paper examines the role of mathematical idealization in describing and explaining various features of the world. It examines
two cases: first, briefly, the modeling of shock formation using the idealization of the continuum. Second, and in more detail,
the breaking of droplets from the points of view of both analytic fluid mechanics and molecular dynamical simulations at the
nano-level. It argues that the continuum idealizations are explanatorily ineliminable and that a full understanding of certain
physical phenomena cannot be obtained through completely detailed, nonidealized representations. 相似文献
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Robert W. Batterman 《Synthese》1995,103(2):171-201
This paper addresses a relatively common scientific (as opposed to philosophical) conception of intertheoretic reduction between physical theories. This is the sense of reduction in which one (typically newer and more refined) theory is said to reduce to another (typically older and coarser) theory in the limit as some small parameter tends to zero. Three examples of such reductions are discussed: First, the reduction of Special Relativity (SR) to Newtonian Mechanics (NM) as (v/c)20; second, the reduction of wave optics to geometrical optics as 0; and third, the reduction of Quantum Mechanics (QM) to Classical Mechanics (CM) as0. I argue for the following two claims. First, the case of SR reducing to NM is an instance of a genuine reductive relationship while the latter two cases are not. The reason for this concerns the nature of the limiting relationships between the theory pairs. In the SR/NM case, it is possible to consider SR as a regular perturbation of NM; whereas in the cases of wave and geometrical optics and QM/CM, the perturbation problem is singular. The second claim I wish to support is that as a result of the singular nature of the limits between these theory pairs, it is reasonable to maintain that third theories exist describing the asymptotic limiting domains. In the optics case, such a theory has been called catastrophe optics. In the QM/CM case, it is semiclassical mechanics. Aspects of both theories are discussed in some detail.I wish to thank Roger Jones and Joe Mendola for valuable comments on this and related work. Discussions with Bill Wimsatt also helped me get clear about certain issues related to intertheoretic reductions. Of course, they are not responsible for any mistakes and misinterpretations that still remain. 相似文献
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Robert W. Batterman 《Synthese》1991,89(2):189-227
Work on this paper was supported by the National Science Foundation under grant No. DIR-9012010. 相似文献
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Robert W. Batterman 《Synthese》2014,191(13):2973-2992
This paper discusses a conception of physics as a collection of theories that, from a logical point of view, is inconsistent. It is argued that this logical conception of the relations between physical theories is too crude. Mathematical subtleties allow for a much more nuanced and sophisticated understanding of the relations between different physical theories. 相似文献
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