Yet Herbart seeks by still another means to “bring about a mental science similar to the natural science: ... by quantitative methods and the application of mathematics.” We find here and there before this time the idea of advancing psychology by such means. The brilliant results produced in natural science by measurement and calculation readily suggested the idea that something similar might be done for psychology. But the philosophical thinkers interested in psychology did not find the right tools; they justified their inability by asserting that such an undertaking was impossible. The most famous is the denial by Kant that mathematics can be applied to the inner mental life and its laws, because time, within which the mental phenomena would have to be represented as occurring, has but one dimension. To be sure Herbart is not actually the pioneer in this field: he never gave a single example of how a measurement of a mental process was to be taken. However, he at least recognized that the mental life is open to quantitative treatment, not only with regard to time, but also in other respects. And in attempting to solve problems quantitatively, through the statement of numerical assumptions and their logical development to their consequences, he so strongly emphasized a side of the matter which had previously been wholly neglected, that more correct ways of clearing it up were soon found.

A strong and enduring influence was exerted by Herbart, yet the further progress of psychology did not occur along the path marked out by him. Many of his general assumptions, particularly those upon which his calculations are based, were entirely too vague to appear probable merely because a few of their consequences agreed with experience. Besides, a strong opposition had arisen against the intellectualism supported by him and by the associationists,—against the almost exclusive regard for the thinking and knowing activities of the mind. If mental life is really nothing but a machinery of ideas, a coöperation and opposition of masses of ideas, what is such a thing as religion? Is it a small complex of true and rational ideas, to which is added a large complex of superstitious fables, invented, or at any rate cultivated, by priests and princes, in order to keep men under their authority? So low a valuation of religion is scarcely possible. Or, what is art? Are the lyric poems of Goethe or the symphonies of Beethoven really only institutions for the conveyance of knowledge through the senses, as the name esthetics indicates, or for the unsuspected instilling of ideas which make men more virtuous or more patriotic?

Certainly one thing which stands in the center of all mental life seems entirely incomprehensible as the result of a mere mechanics of ideas, that is, that unity of mind without which we could not speak of personality, of character, of individuality, without which we could not call one man haughty and another humble, one good and another bad, one noble and another base. Because of this weakness in the theory numerous great thinkers, Rousseau, Kant, Fichte, Schopenhauer, raised their voices to insist upon the significance of the life of feeling and will as well as of the life of ideas, even to give to the former the first place, as the expression of mind’s most real inner being. Thus intellectualism was opposed by what we now call voluntarism.

This transferring of the conceptions of natural science to psychological research, in spite of the mighty impulse it gave to psychology, was not without its disadvantage. The first brilliant advances in natural science were in the province of physics, especially of mechanics. It is no wonder, then, that psychologists, in their gropings after something similar, turned first to mechanical-physical processes. Inertia, attraction, and repulsion, as we have seen, aggregation and chemical combination, were the categories with which they worked. No wonder, either, that facts were often distorted and their comprehension made difficult. For if mind is a machine, it is certainly not such a machine as even the most ingeniously constructed clock or as a galvanic battery. It is bound up with the organic body, especially with the nervous system, and on the structure and functions of the nervous system its own existence and activity somehow depend. So, if one wishes to use material analogies and to make them fruitful for the comprehension of mental structures, they must be taken from organic life, from biology rather than from physics and chemistry. We may find phenomena comparable to individuality and character, to the mind’s feeling and willing, in the unitary existence of every plant and animal organism, in the peculiar determination of its instinct of life and in the many special branches into which this instinct ceaselessly unfolds. And indeed the specifically mechanical categories gradually disappeared from psychology during the nineteenth century, and made way for the biological categories—reflex, inhibition, practice, assimilation, adaptation, and so on. Especially that great acquisition of modern biology, the theory of evolution, was at once seized upon by psychologists, and was utilized for gaining an understanding of the processes as well in the mind of the individual as in human society.

But side by side with such advances, springing from analogy and adaptation, there arose in the nineteenth century another and more direct influence of natural science, as previously mentioned. In its natural progress scientific research came to touch upon psychological problems at several points, and since it laid hold of them and followed them out for its own ends, it immediately became a pioneer for psychology.

The first and at the same time the strongest of these impulses came from the advance of the physiology of the senses. In the fourth decade of the nineteenth century remarkably active and fruitful work in this field began. Physiologists and physicists vied with each other in accurate study of the structure and functions of sense organs. Naturally they were not able to stop at the material functions in which they were most directly interested. They could not forbear to draw into the circle of their investigations those mental functions mediated by the physiological functions and explainable on a physiological basis. The eye, especially, attracted scores of investigators, both because it is very richly endowed with dioptric and mechanical auxiliary apparatus and because it is particularly important on account of the delicacy and diversity of its functions. Yet cutaneous sensations and hearing were not neglected.

Johannes Müller, E. H. Weber, Brewster, and above all—especially versatile, far-seeing, and inventive—the somewhat younger Helmholtz, are only a few of the most noteworthy representatives of this class of research. They brought to psychology results such as it had never known before—results resting on well-conceived and original questions as to the nature of things, and on skillful attempts at arranging the circumstances for an answer, that is, on experiment and when possible on exact measurement of the effects and their causes. When Weber in 1828 had the seemingly petty curiosity to want to know at what distances apart two touches on the skin could be just perceived as two, and later, with what accuracy he could distinguish between two weights laid on the hand, or how he could distinguish between the perception received through the muscles in lifting the weights and the perception received through the skin, his curiosity resulted in more real progress in psychology than all the combined distinctions, definitions, and classifications of the time from Aristotle to Hobbes. The surprising discovery of hitherto unknown sense organs, the muscles and the semicircular canals, was made at that time, although not thoroughly verified until later. That discovery meant not only an increase of knowledge, but also a widening of the horizon, since the most conspicuous peculiarity of these organs is that they do not, like the others, bring to our consciousness external stimuli in the ordinary sense, but processes on the inside of the body.

One result in particular of these investigations in the physiology of the senses became the starting point of a strong new movement. The course of biology in the second quarter of the nineteenth century was toward methodical and exact study of empirical facts, and away from speculation in the philosophy of nature. But for some time this exact study and this speculation were often to be found combined in the same men. Fechner was one of these. On the one hand he was a speculative philosopher, a follower of Schelling’s philosophy of nature, a disciple of Herbart in his attempt at applying mathematics to psychology. So we find him speculating as to what might be the exact relations between body and soul, seeking for a mathematical formulation of the dependence of the corresponding mental and nervous processes. One October morning in 1850, while lying in bed, he conceived a formula which seemed to him plausible. In spite of this speculative tendency he was a physicist of scientific exactness, accustomed to demand a support of facts for such plausible formulas, ready to attack problems not only with his mind, but also with his hands. In following up his speculations he came across some of the results of the work of Weber. By the use of more exact methods and by long-continued series of experiments he carried Weber’s investigations farther, at the same time utilizing the observations of others to which no one had before paid any attention. He succeeded in formulating the first mathematical law of mental life, Weber’s law as he called it, according to which an increase of the external stimulus in geometrical progression corresponds to the increase of the mental process in arithmetical progression. (We shall discuss this law in [§ 4.]) He classed together all of his speculations, investigations, formulations, and conclusions as a new branch of knowledge, Psychophysics, “the scientific doctrine of the relations obtaining between body and mind.”

Fechner’s work called forth numberless books and articles, confirming, opposing, discussing it, or carrying its conclusions still further. The chief question which they discussed, the question whether the law formulated by Fechner was correct or not, has gradually lost its importance, and made way for other problems. Quite aside from this question, which originally formed the center of interest, Fechner’s work has made itself felt in three different ways. Herbart’s mathematical fiction of the combat among ideas had made such an impression upon the thinkers of the time, that—incredible as it may seem—as late as 1852 Lotze confessed that he would prefer it to formulas found by experiment. For this fiction Fechner substituted a scientific law derived from actual measurement of physical forces. Further, he gave to these facts their proper place in a broad system, showed their significance for the deepest psychological problems, and thus compelled even those psychologists who had affiliated themselves with philosophy and had previously remained unaffected by the physiology of the senses, to take notice of the new movement in their science. And finally, he worked out a methodical procedure for all psychophysical investigations, which was far superior to the methods then employed by psychologists and which continues to be of great use for the study of sensation and perception.

At about the same time, in the sixties, psychology received a third kind of impulse. Although weaker than the two just mentioned, it contributed not a little toward increasing the number of psychological problems to which experimental methods could be applied.