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A live interest springs most easily out of knowledge subjects like history and natural science. Formal studies like grammar and arithmetic awaken it less easily. Herbart has classified the chief kinds and sources of interest as follows: Interest in nature apart from man, and interest in man, society, etc.

Herbart maintains that these are entirely independent of each other, so that aesthetics, since it presupposes nothing of metaphysics, may be discussed before metaphysics, while the philosophy of nature and psychology depend throughout on ontological principles. Together with natural theology the two latter sciences constitute "applied" metaphysics.

Schopenhauer is in all respects the antipodes of Herbart. If in Herbart philosophy breaks up into a number of distinct special inquiries, Schopenhauer has but one fundamental thought to communicate, in the carrying out of which, as he is convinced, each part implies the whole and is implied by the whole. The former operates with sober concepts where the latter follows the lead of gifted intuition.

There is no doubt that under good teaching the principle of the concentric circles produces some excellent fruits, a mastery of the subject, and a concentration of ideas within the limits of a single study. The disciples of Herbart, while admitting the merits of the concentric circles, have subjected the plan to a severe criticism.

On the arrest of partially or totally opposed representations Herbart bases his psychological calculus. Let there be given simultaneously in consciousness three opposed representations of different intensities, the strongest to be called a, the weakest c, the intermediate one b. What happens? They arrest one another, i.e. a part of each is forced to sink below the threshold of consciousness.