Functions and Shapes in the Light of the International System of Units

Famously, Galilei made the ontological claim that the book of nature is written in the language of mathematics. Probably, if only implicitly, most contemporary natural scientists share his view. This paper, in contradistinction, argues that nature is only partly written in the language of mathematics; partly, it is written in the language of functions and partly in a very simple purely qualitative language, too. During the argumentation, three more specific but in themselves interesting theses are put forward: first (in Section 3), there are more shapes than real numbers; second (in Section 4), the metrological notion ‘amount of substance’ can profitably be exchanged for ‘number of entities’; third (in Section 5), prototypical concepts will always be scientifically important.