26/27 What the mathematician tells us about real points and real lines has no bearing on the constitution of the single experience and its parts. Thus, when he tells us that between any two points on a line there are an infinite number of other points, he only means that we may expand the line indefinitely by the system of substitutions described above. We do this for ourselves within limits every time that we approach from a distance a line drawn on a blackboard. The mathematician has generalized our experience for us, and that is all he has done. We should try to get at his real meaning, and not quote him as supporting an absurdity. |