Finally, if this continuity of the operations of intelligence with other operations be essential to science, its relation to "practical" life is _ipso facto_ established. For science is "practical" life aware of its problems and aware of the part that experimental--i.e., creative--intelligence plays in the solution of those problems.
Herbart is said to have given the deathblow to faculty psychology. Man no longer appears endowed with volition, passion, desire, and reason; and logic, deprived of its hereditary right to elucidate the operations of inherent intelligence, has the new problem of investigating forms of intelligence in the making. This is no inconsequential task. "If man originally possesses only capacities which after a given amount of education will produce ideas and judgments" (Thorndike, _Educational Psychology_, Vol. I, p. 198), and if these ideas and judgments are to be substituted for a mythical intelligence it follows that tracing their development and observing their functioning renders clearer our conception of their nature and value and brings us nearer that exact knowledge of what we are talking about in which the philosopher at least aspires to equal the scientist, however much he may fall below his ideal.
For contemporary thought concerning the mathematical sciences this altered point of view generates peculiarly pressing problems. Mathematicians have weighed the old logic and found it wanting. They have builded themselves a new logic more adequate to their ends. But they have not whole-heartedly recognized the change that has come about in psychology; hence they have retained the faculty of intelligence knit into certain indefinables such as implication, relation, class, term, and the like, and have transported the faculty from the human soul to a mysterious realm of subsistence whence it radiates its ghostly light upon the realm of existence below. But while they reproach the old logic, often bitterly, their new logic merely furnishes a more adequate show-case in which already attained knowledge may be arranged to set off its charms for the observer in the same way that specimens in a museum are displayed before an admiring world. This statement is not a sweeping condemnation, however, for such a setting forth is not useless. It resembles the classificatory stage of science which, although not itself in the highest sense creative, often leads to higher stages by bringing under observation relations and facts that might otherwise have escaped notice. And in the realm of pure mathematics, the new logic has undoubtedly contributed in this manner to such discoveries. Danger appears when the logician attains Cartesian intoxication with the beauty of logico-mathematical form and tries to infer from the form itself the real nature of the formed material. The realm of subsistence too often has armed Indefinables with metaphysical myths whose attack is valiant when the doors of reflection are opened. It may be possible, however, to arrive at an understanding of mathematics without entering the kingdom of these warriors.