become clear enough that we cannot regard the 'thought' as a separate product in addition to the material phenomena, but that the subjective state of the sentient individual is at the same time to external observation an objective one, a molecular movement. This objective state must, on the law of the conservation of energy, fit into the unbroken causal series. Let this series be fully exhibited to us! This must be possible, without any regard to the subjective state, as this is not a special link in the chain. of organic phenomena, but as it were merely the aspect of some of these phenomena from another side. We stumble here, indeed, upon a limit to Materialism, but only in carrying it out with the most rigid consistency. We are, in fact, of opinion that there is hardly anything to look for in sensation over and above the nerve processes above spoken of; only these processes have themselves a quite different mode of appearing, namely, that which the individual calls sensation. It is quite conceivable that some time we shall succeed in determining more precisely that portion of the physical processes which coincides in point of time with the origin of a sensation in the individual. This would be extremely interesting, and we certainly could offer no objection if this particular portion of the circuit of nerve processes were then described absolutely as the sensation.' A more exact definition of the relation of the subjective phenomenon of sensation to the objectively observed nervous phenomenon would, on the contrary, be impossible.

But now, as to the intellectual value of the content of sensation, this, too, can hardly be completely separated from the physical phenomenon. A masterpiece of sculpture and a rough copy of it present to the retina of the observer a similar crowd of light-stimuli; but so soon as the eye follows the lines, there arise in the muscles of the eye quite different sensations of movement. That these continue to act not according to the absolute mass of the movement, but according to the most delicate numerical

relations between the individual motory impulses cannot appear unnatural if we reflect what a part is played by numerical relations even in the first forming of sensations. It is true, indeed, that this very point will be one of the last and most difficult riddles of nature, but we have not the slightest occasion, therefore, to seek for that which is intellectually significant, the artistically moulded sensation or the ingenious thought, outside the ordinary processes of sensation. Only, of course, let us not proceed like a man who should try to discover the melodies that an organ can play in the individual pipes.

The co-operation of very many, and, individually considered, extraordinarily feeble nerve impulses, must give us the key to the physiological understanding of thinking, and the form of this co-operation is the characteristic feature of each individual function. What in this remains unexplained-the manner, the external, natural phenomenon-is at the same time an internal one for the thinking subject: that is the point which altogether overpasses the limits of the knowledge of nature.

VOL. III.

L

CHAPTER III.

SCIENTIFIC PSYCHOLOGY.

BUT what, then, will psychology say if we for the present remove quite into the background the inner subjective side of human nature? And yet we have had given us in this century not only a scientific, but even a mathematical psychology too, and there are a number of sensible and excellent people who quite seriously believe that Herbart with his differential equations has as thoroughly mastered the world of ideas, as Kopernikus and Kepler the world of the planets. This is indeed as thorough a delusion as phrenology, and as to psychology as a natural science, so much mischief has been worked by this pretty name, that we might easily run the risk of pouring away bath and child together. We shall, however, be able to give their full value to the beginnings of a really scientific and, in parts, even mathematical treatment of psychological questions, without abandoning the standpoint we have already taken up.

First of all, we must point out that the notion of psychology can only be a rigidly determined and completely clear one to the scholastic or the ignorant pedant. It is true that even able and sagacious men have begun their supposed scientific investigations with a section 'Of the Nature of the Soul;' but it was merely a reaction of the hollow scholastic metaphysic when they imagined that they could thus gain a firm basis for their investigations. Those cases, of course, must be excepted where the notion of the soul is only historically or critically treated.

But the man who begins with positive principles as to the soul, as, e.g., of its simplicity, extensionlessness, and so on, or who feels bound to carefully hedge in the field of his inquiry into the soul before he begins to build, can hardly be expected to give us a scientific treatment of the subject. What should we say of a physicist who began by explaining the nature of Nature, and who would only consider his inquiries as likely to be of service when he had first made it quite clear what Nature is? It is still more obvious if we think of special departments. Had Gilbert not rubbed his bits of amber until he was clear as to the nature of electricity, he would probably never have taken a great step towards the knowledge of its nature. What inquirer could to-day exactly define magnetism? The idea becomes transformed in the hands of inquirers. From the power of the magnet to attract iron there comes a more general power. The earth is perceived to be a magnet. The connexion with electricity is discovered. Diamagnetism is traced through a mass of the most surprising phenomena. Where would have remained the brilliant discoveries of Oersted, Faraday, Plücker, if they had first sounded metaphysically the notion of magnetism and then proposed to begin their scientific investigations?

It is a remarkable monument of the philosophical fermentation in Germany that so subtle a thinker as Herbart, a man of admirable critical acuteness and great mathematical skill, could have come upon so adventurous an idea as that of finding by speculation the principle of the statics and mechanics of ideas. It is still more striking that so enlightened a mind, with a genuinely philosophical tendency to practical life, could lose himself in the laborious and thankless task of working out a whole system of mental statics and mechanics from his principle, without having any voucher whatever in experience for its truth. We see here how peculiar are the relations between a man's gifts and achievements. That Gall should not be

protected by his great experience, his extensive and special knowledge, from the invention of phrenology is, with his imaginative and ardently creative character, easily intelligible; but that Herbart could invent a mathematical psychology, while he was pre-eminent in the very qualities which are calculated to protect men against such courses, must always be regarded as a highly remarkable testimony to the violence of the metaphysical whirlpool, which in our country at that time mastered even him who struggled against it, and hurled him out into the intellectual comet-orbit of visionary discoveries.

Nevertheless, Herbart's powerful effort deserves a better refutation than that of mere disregard. But the previous attempts at a worthy critical disproof of mathematical psychology have the defect of losing themselves in miscellaneous discussions, and partly do not at all indicate, partly do not indicate precisely enough, the elementary logical fallacy in the deduction of the fundamental formula. We have attempted in a separate essay 40 to fill this gap in our philosophical literature, because our rejection of mathematical psychology shall not go into the world without proofs: but here the troublesome task of demonstration would disturb the connexion and confuse the clearness of our criticism, so far as it concerns Materialism. If there were a mathematical psychology, we should have to take it into account even on this ground-that it would be the surest proof for that regularity of all psychical processes which Materialism rightly maintains, and at the same time the most complete refutation of the reduction

40 Die Grundlegung d. mathemat. Psychol., Duisb. 1865. Cornelius has attempted a refutation in the Zeits. f. ex. Phil., Bd. vii., H. 3, which, despite its dogmatic tone, seems to demand no answer. A calm comparison of the grounds and countergrounds would be enough to show the untenableness of mathematical psychology. Wittstein has attempted a new foundation of mathe

matical psychology, which avoids the errors pointed out by me in Herbart's foundation, but at the same time leads also to quite other results than those of Herbart. It is, however, easy to see that if once the pretension to rigid metaphysical deduction of the principle is given up, in point of method there is as yet no occasion for propounding such a theory at all.