In this paper I discuss the relationship between model, theories, and laws in the practice of experimental scale modeling. The methodology of experimental scale modeling, also known as physical similarity, differs markedly from that of other kinds of models in ways that are important to issues in philosophy of science. Scale models are not discussed in much depth in mainstream philosophy of science. In this paper, I examine how scale models are used in making inferences. The main question I address (...) in this talk is ``How are fundamental laws involved in the construction of, and inferences drawn from, experimental scale models?'' We shall see that there is a refreshing alternative to the mainstream view that models can serve only as intermediaries between theory and experiment. Using the methodology of scale models, one can use observations on one piece of the world to make inferences about another piece of the world, without involving an intermediate abstract model about which one reasons. The philosophical significance of that point to philosophy of science is that the method of physical similarity, which provides the basis for inferences based upon scale models, is a qualitatively different way in which fundamental laws can be used in analogical reasoning that is truly informative. Finally, as this method provides a formal basis for case-based reasoning, it may be helpful in formalizing methods used in some of the so-called ``special sciences''. (shrink)

Experimental engineering models have been used both to model general phenomena, such as the onset of turbulence in fluid flow, and to predict the performance of machines of particular size and configuration in particular contexts. Various sorts of knowledge are involved in the method - logical consistency, general scientific principles, laws of specific sciences, and experience. I critically examine three different accounts of the foundations of the method of experimental engineering models (scale models), and examine how theory, practice, and experience (...) are involved in employing the method to obtain practical results. Models of machines and mechanisms can be (and generally are) involved in establishing criteria for similar phenomena, which provide guidance in using events to model other events. Conversely, models of phenomena such as events that model other events can be (and generally are) involved in experimentation on models of machines. I conclude that often it is not more detailed models or the more precise equations they engender that leads to better understanding, but rather an insightful use of knowledge at hand to determine which similarity principles are appropriate in allowing us to infer what we do not know from what we are able to observe. (shrink)

An introduction to the developments of nonstandard models. Beginning with Godel's incompleteness theorem, it covers the prime models, cofinal extensions, and extensions, Gaifman's construction of a definable type, Tennenbaum's theorem and Friedman's theorem on indicators, ending with a chapter on recursive saturation and resplendency.