Idealization as prescriptions and the Role of Fiction in Science: Towards a Formal Semantics

One important feature of Poincaré’s conventionalism of geometry is linked to the relation between the abstract notion of space geometry and the representations of the free mobility of our bodies where the first is an idealization of the second. Furthermore, since Poincaré thinks that the only adequate candidates for physical geometry – the geometries of constant curvature – are equivalent from a mathematical point of view (they are homeomorphic), we can choose any one of these. In this context, conventionalism assumes idealization. The first main aim of this paper is to study the relation between idealization and idealized in a more general way. More precisely we will discuss the recent theories of models in science as games of make believe, where models are conceived not as /descriptions of facts/ but as /prescriptions/ to imagine or to build a determinate situation in analogous way to the games of pretence involved in literary fiction. According to this view, idealizations are not descriptions but prescriptions. Now, the applications of make believe to models of science is usually linked with an irrealist approach: the objects prescribed by idealizations do not exist, or more bluntly, the prescriptions do not denote any object at all. This presents some difficulties when we would like to compare the models with nature: how should we compare if the one of terms of the relation is lacking? The second main aim of the paper is to defend that the artifactual theory of fictions provides a plausible ontology compatible with the theory of models as prescriptions. The version of the artifactual theory, developed in collaboration with Tero Tulenheimo, makes use of Amie Thomasson’s reconstruction of ontological dependence of Roman Ingarden. The very point of the paper is not to describe the process of idealization but rather to explore the formal semantics of a notion of idealization conceived as a prescription to imagine.