  In part, Bressan wanted to provide a logical foundation for physics. The connection with physics is this. When we say something has such-and-such a mass, for instance, we mean that if we had conducted certain experiments, we would have gotten certain results. This does not assume we did conduct those experiments, and thus alternate states (or cases, as Bressan calls them) arise. Hence there is a need for a rich modal language, with an ontology that includes numbers as well as physical objects. In Bressan 1972, an elaborate modal system was developed, with a full type hierarchy including numbers as in Principia Mathematica.