"[W]hile we put number into objects, on the other hand we derive our idea of number only from the presence of the world external to the mind. We see a group of people, and we begin by making an abstraction ("people"), and we say, "Here are ten people"—thus calling them all by the one abstract name, even though the individuals be very different. "A careful observation shows us, however, that there are no objects exactly alike; but by a mental operation of which we are quite unconscious, although it holds within itself the entire secret of mathematical abstraction, we take in objects which seem to be alike, rejecting for the time being their differences. Here is to be found the source of calculation." So the idea of number is generated in the mind by the sense perception of a group of things supposed to be alike."