If we adhere strictly to Galileo's motivation, considering the way in which it in fact laid the foundation for the new idea of physics, we must make clear to ourselves the strangeness of his basic conception in the situation of his time; and we must ask, accordingly, how he could hit upon this conception, namely, that everything which manifests itself as real through the specific sense qualities must have its mathematical index in events belonging to the sphere of shapes which is, of course, already thought of as idealized and that there must arise from this the possibility of an indirect mathematization, in the fullest sense,.e., it must be possible (though indirectly and through a particular inductive method) to construct ex datis, and thus to determine objectively, all events in the sphere of the plena.