Scientific representation, denotation, and explanatory power

Abstract

In the last few decades, various debates in philosophy of science over how scientific theories relate (referentially or not) to the world has strengthened the view that if this quest is to lead to any fruitful results then three intertwined concepts must be understood: model, representation, idealization. That these concepts are intertwined is evident. A model is meant to represent something, whether an actual or an ideal state, whether a physical or an ideal system. For instance, a model of a building is a representation of an actual (or actualizable) building. Moreover, a model represents a physical system in an abstract and idealized way. That is, a model of a building is not meant as an exact replica but as an idealized and abstract representation of an actual building because, for instance, it represents only certain features of the actual system, e.g. some spatial relations, and ignores others, e.g. the plumbing system. In science one encounters several kinds of models, such as iconic or scale models, analogical models, and mathematical models. In this chapter, my discussion is restricted to mathematical models, to which I shall refer as scientific models. Representation seems to be a primary function of scientific models, and idealization (and abstraction) seems to be the steering thought process by which this function is achieved. By highlighting this point I mean to suggest that a better understanding of ‘scientific representation’ could be achieved if we examine it in relation to ‘scientific models’ and to ‘idealization’.