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?