To begin with, we can, without assuming anything that no one perceives, establish a common space and time in which we all live. (Our discussion is necessarily confined to people on the surface of the earth, since other people, if they exist,[Pg 208] have not succeeded in communicating with us; consequently the complications of relativity do not yet arise.) The usual methods of determining latitude and longitude can be applied, without assuming that the readings of clock and sextant have the physical meaning usually assigned to them. Altitudes, also, can be measured by the usual methods. By these means, observers can be arranged in a three-dimensional order. Of course the resulting space will not be a continuum, since it will contain only so many "points" as there are observers. But the motion of an observer can be sensibly continuous, so that we can construct "ideal" points of view with defined mathematical properties, and thus build up, for mathematical purposes, a continuous space. We can thus arrive at the laws of perspective, taken in a generalized sense; that is to say, we can correlate the differences between correlated perceptions with differences in the situations of the percipients. And in the space derived from "points of view" we can place physical objects. For, let and be two observers, and their correlated visual percepts, which, being correlated, are described as percepts of one physical object . If the angular dimensions of are larger than those of , we shall say (as a definition) that is nearer to than is. We can thus construct a number of routes converging on . We shall construct our geometry so that they intersect, and shall define their intersection as the place where is. If happens to be a human body, we shall find that the place of , so defined, is identical with the place of as an observer in the space of points of view.[45]