The generality of scientific models: a measure theoretic approach

Scientific models are often said to be more or less general depending on how many cases they cover. In this paper we argue that the cardinality of cases is insufficient as a metric of generality, and we present a novel account based on measure theory. This account overcomes several problems with the cardinality approach, and additionally provides some insight into the nature of assessments of generality. Specifically, measure theory affords a natural and quantitative way of describing local spaces of possibility. The generality of models can be understood as the measure of possibilities to which the models apply. In order to illustrate our view, we consider the example of structural genomics, the ongoing project of building three-dimensional models of biological macromolecules like proteins. Using measure theory, we interpret the practice of homology modeling, where such models are understood to apply widely but imperfectly to the space of possible proteins.