There are then ideal and inward relations amongst the objects of our thought which can in no intelligible sense whatever be interpreted as reproductions of the order of outer experience. In the æsthetic and ethical realms they conflict with its order—the early Christian with his kingdom of heaven, and the contemporary anarchist with his abstract dream of justice, will tell you that the existing order must perish, root and branch, ere the true order can come. Now the peculiarity of those relations among the objects of our thought which are dubbed 'scientific' is this, that although they no more are inward reproductions of the outer order than the ethical and æsthetic relations are, yet they do not conflict with that order, but, once having sprung up by the play of the inward forces, are found—some of them at least, namely the only ones which have survived long enough to be matters of record—to be congruent with the time- and space-relations which our impressions affect.
In other words, though nature's materials lend themselves slowly and discouragingly to our translation of them into ethical forms, but more readily into æsthetic forms; to translation into scientific forms they lend themselves with relative ease and completeness. The translation, it is true, will probably never be ended. The perceptive order does not give way, nor the right conceptive substitute for it arise, at our bare word of command.[535] It is often a deadly fight; and many a man of science can say, like Johannes Müller, after an investigation, 'Es klebt Blut an der Arbeit.' But victory after victory makes us sure that the essential doom of our enemy is defeat.[536]
THE GENESIS OF THE PURE SCIENCES.
I have now stated in general terms the relation of the natural sciences to experience strictly so called, and shall complete what I have to say by reverting to the subject on a later page. At present I will pass to the so-called pure or a priori sciences of Classification, Logic, and Mathematics. My thesis concerning these is that they are even less than the natural sciences effects of the order of the world as it comes to our experience. The pure sciences express results of comparison exclusively; comparison is not a conceivable effect of the order in which outer impressions are experienced—it is one of the house-born ([p. 627]) portions of our mental structure; therefore the pure sciences form a body of propositions with whose genesis experience has nothing to do.
First, consider the nature of comparison. The relations of resemblance and difference among things have nothing to do with the time- and space-order in which we may experience the latter. Suppose a hundred beings created by God and gifted with the faculties of memory and comparison. Suppose that upon each of them the same lot of sensations are imprinted, but in different orders. Let some of them have no single sensation more than once. Let some have this one and others that one repeated. Let every conceivable permutation prevail. And then let the magic-lantern show die out, and keep the creatures in a void eternity, with naught but their memories to muse upon. Inevitably in their long leisure they will begin to play with the items of their experience and rearrange them, make classificatory series of them, place gray between white and black, orange between red and yellow, and trace all other degrees of resemblance and difference. And this new construction will be absolutely identical in all the hundred creatures, the diversity of the sequence of the original experiences having no effect as regards this rearrangement. Any and every form of sequence will give the same result, because the result expresses the relation between the inward natures of the sensations; and to that the question of their outward succession is quite irrelevant. Black will differ from white just as much in a world in which they always come close together as in one in which they always come far apart; just as much in one in which they appear rarely as in one in which they appear all the time.
But the advocate of 'persistent outer relations' may still return to the charge: These are what make us so sure that white and black differ, he may say; for in a world where sometimes black resembled white and sometimes differed from it, we could never be so sure. It is because in this world black and white have always differed that the sense of their difference has become a necessary form of thought. The pair of colors on the one hand and the sense of difference on the other, inseparably experienced, not only by ourselves but by our ancestors, have become inseparably connected in the mind. Not through any essential structure of the mind, which made difference the only possible feeling which they could arouse; no, but because they simply did differ so often that at last they begat in us an impotency to imagine them doing anything else, and made us accept such a fabulous account as that just presented, of creatures to whom a single experience would suffice to make us feel the necessity of this relation.