MODELS

Although all of the above kinds of models in science are philosophically interesting, one kind sticks out: mathematical models. Representation with iconic or scale models, for instance, has a local character. It is local either in the sense that it applies only to a particular situation at a particular time or in the sense that it requires the mediation of a mathematical (or abstract) model in order to relate to other modes of scientific discourse and scientific representation, like theories. Representation via mathematical models, on the other hand, is of utmost interest because it has a global character. It is global because it is closely related to scientific theories and because it applies to types of target systems, but also because it can be used to draw inferences about the time-evolution of systems. Moreover, since mathematical language is the principal scientific mode of describing aspects of the world, philosophical analyses have centered, by and large, on the notion of scientific model as a mathematical entity. For these reasons it is on this notion that I focus here. It is not just philosophers who focus their attention primarily on mathematical models. Physicists, for example, consider material and other kinds of models as auxiliary devices that help visualize or understand the propositions of theoretical physics and not as a central part of the latter. The construction of mathematical models, on the other hand, is considered central to their work, and in their meta-theoretical moments they go as far as to make – epistemological and methodological – distinctions among them. They commonly divide mathematical models roughly into two categories: theory-driven models and phenomenological models. The distinction is based on the consideration that theory-driven models are constructed in a systematic, theory-regulated way by supplementing the theoretical calculus with locally operative hypotheses. Phenomenological models, on the other hand, are constructed by the deployment of semi-empirical results, by the use of ad hoc hypotheses, or by the use of a conceptual apparatus that is not directly related to the fundamental concepts of a theory. In other words, physicists distinguish these two kinds of models on the grounds that the latter are not in any straightforward sense deductive consequences of a theory, whereas the former seem to be. The distinction provides valuable insight into the processes of construction of mathematical models in science that a philosophical analysis of “model” cannot ignore.