be as mysterious as you please, would, in one respect, present to an observer who understood the one purpose of the whole series, no mystery at all. For one who understood the purpose of the making within England a map of England, and the purpose of making this map absolutely accurate, would see precisely why the map must be contained within the map, and why, in the series of maps within maps, there could be no end consistently with the original requirement. Mathematically regarded, the endless series of maps within maps, if made according to such a projection as we have indicated, would cluster about a limiting point whose position could be exactly determined. Logically speaking, their variety would be a mere expression of the single plan, “Let us make within England, and upon the surface thereof, a precise map, with all the details of the contour of its surface.” Then the One and the Many would become, in one respect, clear as to their relations, even when all else was involved in mystery. We should see, namely, why the one purpose, if it could be carried out, would involve the endless series of maps.
But so far we have dealt with our illustration as involving a certain progressive process of map making, occurring in stages. We have seen that this process never could be ended without a confession that the original purpose had failed. But now suppose that we change our manner of speech. Whatever our theory of the meaning of the verb to be, suppose that some one, depending upon any authority you please, — say upon the authority of a revelation, — assured us of this as a truth about existence, viz., “Upon and within the surface of England there exists somehow (no matter how or when made) an absolutely perfect map of the whole of England.” Suppose that, for an instance, we had accepted this assertion as true. Suppose that we then attempted to discover the meaning implied in this one assertion. We should at once observe that in this one assertion, “A part of England perfectly maps all England, on a smaller scale,” there would be implied the assertion, not now of a process of trying to draw maps, but of the contemporaneous presence, in England, of an infinite number of
