which we shall here consider, may be taken, in a measure, from that world “external to thought” whose variety we still find a matter of “mere conjunction” and so opaque. For, despite the use of such a basis, our illustration will interest us not by reason of this aspect, but by reason of the opportunity thereby furnished for carrying out a certain recurrent process of thought, whose internal meaning we want to follow.
We are familiar with maps, and with similar constructions, such as representative diagrams, in which the elements of which a certain artificial or ideal object is composed, are intended to correspond, one to one, to certain elements in an external object.[1] A map is usually intended to resemble the contour of the region mapped in ways which seem convenient, and which have a decidedly manifold sensuous interest to the user of the map; but, in the nature of the case, there is no limit to the outward diversity of form which would be consistent with a perfectly exact and mathematically definable correspondence between map and region mapped. If our power to draw map contours were conceived as perfectly exact, the ideal map, made in accordance with a given system of projection, could be defined as involving absolutely the aforesaid one to one correspondence, point for point, of the surface mapped and the representation. And even if one conceived space or matter as made up of indivisible parts, still an ideally perfect map upon some scale could be conceived, if one supposed it made up of ultimate space units, or of the ultimate material corpuscles, so arranged as to correspond, one by one, to the ultimate parts that a perfect observation would then distinguish in the surface mapped. In general, if A be the object mapped, and A’ be the map, the latter could be conceived as perfect if, while always possessing the desired degree of visible similarity of contours, it actually stood in such correspondence to A that for every elementary detail of A, namely, ɑ, b, c, d (be these details conceived as points or merely as physically smallest parts; as relations amongst the
- ↑ Compare the general discussion of “Correspondence” in the course of Lecture VII.
