This paper utilizes Scott domains (continuous lattices) to provide a mathematical model for the use of idealized and approximately true data in the testing of scientific theories. Key episodes from the history of science can be understood in terms of this model as attempts to demonstrate that theories are monotonic, that is, yield better predictions when fed better or more realistic data. However, as we show, monotonicity and truth of theories are independent notions. A formal description is given of the (...) pragmatic virtues of theories which are monotonic. We also introduce the stronger concept of continuity and show how it relates to the finite nature of scientific computations. Finally, we show that the space of theories also has the structure of a Scott domain. This result provides an analysis of how one theory can be said to approximate another. (shrink)

One of the things I attempted to do in my paper on independent testability was to illustrate convincingly the very real difficulties of distinguishing between the accidental and essential features of a scientific experiment. The importance of this distinction is that independent testability presumably requires differences that are essential and telling and not merely accidental reflections of existing experimental technique or of the procedural preferences of the experimenter. In the case of the Michelson-Morley and Kennedy-Thorndike experiments, I showed, following a (...) suggestion of M. G. Evans, that Grünbaum's attempt to distinguish these two experiments does not work. I also showed that certain obvious and natural variations of Grünbaum's approach do not adequately distinguish these experiments. So, for example, it will not do simply to claim that MM is characterized by equal arms and KT by unequal arms, since equal arms are required for MM only in the absence of adequate photographic registration methods. But if these methods are not available then KT is not possible. Conversely, if these methods are available, then while both MM and KT are experimentally possible, MM need not be restricted to equal arms. (shrink)