The following article treats the 'applicational turn' of modern fluid dynamics as it set in at the beginning of the 20th century with Ludwig Prandtl's concept of the boundary layer. It seeks to show that there is much more to applying a theory in a highly mathematical field like fluid dynamics than deriving a special case from a general explanatory theory under particular antecedent conditions. In Prandtl's case, the decisive move was to introduce a model that provided a physical/causal conception (...) of viscous flow at high Reynolds numbers. It facilitated an approximate solution to the Navier-Stokes equations, which in turn gave rise to many special applications. After a detailed account of Prandtl's achievement, the article discusses the role of the physical model and its experimental and mathematical significance. It is shown that the mathematical simplification provided by the physical model greatly expanded the explanatory capacity of the theory which the Navier-Stokes equations alone could not provide. (shrink)

The notion of reduction in the natural sciences has been assimilated to the notion of inter-theoretical explanation. Many philosophers of science (following Nagel) have held that the apparently ontological issues involved in reduction should be replaced by analyses of the syntactic and semantic connections involved in explaining one theory on the basis of another. The replacement does not seem to have been especially successful, for we still lack a plausible account of inter-theoretical explanation. I attempt to provide one.

In The Foundations of Space-Time Theories Friedman argues for a literal realistic interpretation about theoretical structures that participate in theory unification. His account of the relationship between observational and theoretical structure is characterized as that of model to submodel and involves a reductivist strategy that allows for the conjunction of certain theoretical structures with other structures which, taken together, form a truly unified theory. Friedman criticizes the representational account for its failure to allow for a literal interpretation and conjunction of (...) theoretical structure. I argue that contra Friedman the representationalist account can sanction a literal interpretation and in fact presents a more accurate account of scientific practice than the model-submodel account. The strict reductivism characteristic of the model submodel approach can in some cases be seen to prevent rather than facilitate a literal account of theoretical structure. Because of the dependence Friedman places on reduction for his account of conjunction, and because the former cannot be sustained, it would appear that Friedman's own account fails to achieve what it was designed to do. (shrink)