Let us first consider the etymology of the word. The root of “same” is found in almost all Indo-European languages; it is preserved in the first syllable of the Latin “similis” and “simul,” in the second syllable of the German “Zu_samm_en”; in the Greek “ἅμα” and “ὅμοιος,” and the Sanskrit “sama,” all of which denote a togetherness. Thus the etymological meaning seems to signify what is classed in one category. Accordingly, the present meaning as defined by the dictionaries, as being that which is “of one nature or not different in character,” has not changed; at any rate if there is any change, it is slight. Yet it is desirable to bring out and set in a clear light the purport of the word and its essence. What, then, is the economic service and function of the idea of “sameness” in the household of thought? “Sameness” is that feature in two things or states of things, in two processes or modes of action, which brings it to pass that the one may be replaced by the other without altering for a certain purpose the state of things or affecting the result of the entire process. Popularly expressed, sameness is the capability of one thing’s being substituted for another. There is no need of discussing or proving the truism, that, properly speaking, there is no absolute sameness, no identity in the strict sense of the term. This was the meaning of Heraclitus’s idea of the perpetual flux of things, expressed in his πάντα ῥεῖ. There are no two moments in time, no two points in space, no two atoms of matter actually identical, and we cannot enter into the identical river twice. Cratylus tried to outdo Heraclitus, by saying that we cannot even enter once into the identical river, for while entering, not only the river changes but also we ourselves; and Cratylus is perfectly right. We have purposely substituted in Heraclitus’s proposition “identical” for “same,” because this change is needed to bring out the truth of the idea. Heraclitus and Cratylus cease to be right if we use the word same as above defined. We enter indeed the same river twice. The river of to-day is, for a certain purpose, quite the same as the river of yesterday, in so far namely as the river of to-day and the river of yesterday serve a certain and the same purpose: for other purposes this same river will perhaps not be the same. The geographer and historian speak of the Rhine as that stream of water which since time immemorial has flowed down from the St. Gotthardt to the North Sea. Accordingly, if we stand on the bank of the Rhine, it is quite correct to say that this is the same river that was crossed by Cæsar. Let the purpose of our thoughts be changed, and we shall no longer be permitted to speak of sameness. Suppose we had seen the Rhine for the first time in its beautiful emerald coloring, and had come again after a rainy day to admire its beauty, should we not be justified in exclaiming: This is not the same river!