VI. When a man thinks of two other men as perceiving the same object, he must recognize, if he reflect, that he has in mind a picture of the object, of two human bodies in a peculiar relation to it, and two images of the object somehow connected with these bodies. He need not think of these images as wholly resembling his picture of the object or each other. He does, indeed, make them more or less like his picture of the object, but what is prominent in his mind is the thought of them as representatives, as related to and giving information concerning the object. I say concerning the object, but this phrase is ambiguous. If the man under discussion believes in "real" objects in an extra-consciousness world, he will look upon the images as representing such a "real" object; though, of course, his guarantee for this "real" object, and all his information concerning, it must be found in his picture of the object, and this, or its copy, will stand for the "real" object in any mental complex he may construct. If the man be an Idealist, accepting only what can be found in a consciousness, he will look upon the two images as related to his picture of the object and representative of that. In any case he must regard them as representatives, and in this sense the same with the thing they represent. The notion of similarity which is at the bottom of this idea of representative and thing represented is then implied in sameness of the sixth kind also. VII. And since those who distinguish between the immediate and the mediate objects of knowledge make the former representative of the latter, we have evidently this implied notion of similarity in the seventh kind of sameness as well as in the sixth. The mediate object is said to be known _through_ the immediate: that is, the qualities and relations of the one are made to stand for and serve in place of the qualities and relations of the other. This they can do, of course, only in so far as the two sets of qualities and relations are similar. It is easy enough to see that this notion of similarity is present when we think of an idea or complex of ideas as representing a "real" thing beyond consciousness, and giving information concerning it. When, however, we sublimate our "real" thing into a noumenon and strip it of the determinations which, taken together, make up our idea of a thing, we destroy, if we are consistent and thorough-going, all notion of similarity between the two; but in doing this we destroy our noumenon altogether. If, for instance, we refuse to allow to our notion of a thing "any qualitative or quantitative expression whatever," we cannot think of the thing as having reality or existence, or any mark by which it is to be distinguished from nothing at all. In this case the idea is no longer representative, for it has nothing to represent. If, on the other hand, we do not wholly destroy the noumenon, but still allow it a diluted existence of an indefinite kind, in so far as it has this, and