VI. Our Knowledge of the World

Let me make myself clearer by another example. If I throw a stone horizontally through the air, I perceive it in different places at different times. I connect these places so as to form a line. Mathematics teaches me to distinguish various kinds of lines, one of which is the parabola. I know a parabola to be a line which is produced by a point moving according to a certain well-defined law. If I analyze the conditions under which the stone thrown by me moves, I find that the line of its flight is identical with the line I know as a parabola. That the stone moves exactly in a parabola is a result of the given conditions and follows necessarily from them. The form of the parabola belongs to the whole phenomenon as much as any other feature of it. The hypothetical mind described above which has no need of the roundabout way of thought, would find itself presented, not only with a sequence of visual percepts at different points, but, as part and parcel of these phenomena, also with the parabolic form of the line of flight, which we can add to the phenomenon only by an act of thought.