To Reason as distinguished from Understanding, Schopenhauer assigns no such exalted function as was attributed to it in portions of his system by Kant, and still more by some of his successors. The name of 'reason,' he maintains, ought on etymological grounds to be restricted to the faculty of abstract concepts. This, and not understanding, is what distinguishes man from animals. It discovers and invents nothing, but it puts in a generalised and available form what the understanding has discovered in intuition. For the historical estimation of Schopenhauer, it is necessary to place him in relation to Kant, as he himself always insisted. Much also in his chief work is made clearer by knowledge of his dissertation _On the Fourfold Root of the Principle of Sufficient Reason_, to which he is constantly referring. Later, his manner of exposition became more independent; so that he can be read by the general reader with profit simply by himself, and without reference to antecedents. Still, it will always be advisable for an expositor to follow his directions, at least to the extent of giving some short account of the dissertation. This I proceed to give approximately in the place to which he has assigned it in his system. The name of the principle (_principium rationis sufficientis_) he took over from Leibniz and his successor Wolff, but gave it a new amplitude. With him, it stands as an inclusive term for four modes of connection by which the thoroughgoing relativity of phenomena to one another is constituted for our intelligence. The general statement adopted is, 'Nothing is without a reason why it should be rather than not be.' Its four forms are the principles of becoming (_fiendi_), of knowing (_cognoscendi_), of being (_essendi_), and of acting (_agendi_). (1) Under the first head come 'causes.' These are divided into 'cause proper,' for inorganic things; 'stimulus,' for the vegetative life both of plants and animals, and 'motive,' for animals and men. The law of causation is applicable only to changes; not to the forces of nature, to matter, or to the world as a whole, which are perdurable. Cause precedes effect in time. Not one thing, but one state of a thing, is the cause of another. From the law of causation there results an infinite series _a parte ante_ as well as _a parte post_. (2) The principle of sufficient reason of knowing is applicable to concepts, which are all derived from intuition, that is, from percepts. The laws of logic, which come under this head, can yield nothing original, but can only render explicit what was in the understanding. (3) Under the third head come arithmetical and geometrical relations. These are peculiar relations of presentations, distinct from all others, and only intelligible in virtue of a pure _a priori_ intuition. For geometry this is space; for arithmetic time, in which counting goes on. Scientifically, arithmetic is fundamental. (4)