constructing projections of curves, or of otherwise systematically transforming one set of relationships into another set. But if this special purpose is fulfilled, the correspondence in question is accomplished, and is said to hold true. But in any case, as you now see, correspondence does not necessarily imply, just as it does not exclude, any such common characters in the two corresponding objects, as makes you say that one of the two objects resembles the other in mere external appearance. A photograph looks like the man; a map may look, in outline, like the land mapped. But numbers and the symbols of an algebra no longer seem to our senses at all like the objects defined by these symbolic devices for establishing correspondence; and the accounts in the ledger, while very systematically corresponding, item for item, to the commercial transactions, are very unlike them in immediate interest and in sensible appearance. There is, then, no degree of unlikeness in appearance between two objects which excludes a correspondence — and even the most exact and instructive sort of correspondence — between one object and the other. What is involved in correspondence is the possession, on the part of the corresponding objects, of some system of ideally definable characters that is common to both of them, that is, for the purposes of our thought, the same in both of them, and that is such as to meet the systematic purpose for which the particular correspondence is established.
So much, then, for the relation of correspondence, viewed by itself. If we apply this consideration to the case of the definition of truth, we see that, for the first, a true idea, in corresponding to its object, need not in the
