The title of Schopenhauer's chief work is rendered in the English translation, The World as Will and Idea. Here the term 'idea' is used in the sense it had for Locke and Berkeley; namely, any object of mental activity. Thus it includes not merely imagery, but also perception. Since Hume distinguished ideas' from 'impressions,' it has tended to be specialised in the former sense. The German word, Vorstellung, which it is used to render, conveys the generalised meaning of the Lockian 'idea,' now frequently expressed in English and French philosophical works by the more technical term 'presentation' or 'representation.' By Schopenhauer himself the word 'Idea' was used exclusively in the sense of the Platonic Idea, which, as we shall see, plays an important part in his philosophy. The distinction is preserved in the translation by the use of a capital when Idea has the latter meaning; but in a brief exposition it seems convenient to adopt a more technical rendering of Vorstellung; and, from its common employment in psychological text-books, I have selected 'presentation' as the most suitable.

The first proposition of Schopenhauer's philosophical system is, 'The world is my presentation.' By this he means that it presents itself as appearance to the knowing subject. This appearance is in the forms of time, space and causality. Under these forms every phenomenon necessarily appears, because they are a priori forms of the subject. The world as it presents itself consists entirely of phenomena, that is, appearances, related according to these forms. The most fundamental form of all is the relation between object and subject, which is implied in all of them. Without a subject there can be no presented object.

Schopenhauer is therefore an idealist in the sense in which we call Berkeley's theory of the external world idealism; though the expressions used are to some extent different. The difference proceeds from his following of Kant. His Kantianism consists in the recognition of a priori forms by which the subject constructs for itself an 'objective' world of appearances. With Berkeley he agrees as against Kant in not admitting any residue whatever, in the object as such, that is not wholly appearance. But while he allows that Berkeley, as regards the general formulation of idealism, was more consistent than Kant, he finds him, in working out the principle, altogether inadequate. For the modern mind there is henceforth no way in philosophy except through Kant, from whom dates the revolution by which scholastic dualism was finally overthrown. Kant's systematic construction, however, he in effect reduces to very little. His is a much simplified 'Apriorism.' While accepting the 'forms of sensible intuition,' that is, time and space, just as Kant sets them forth, he clears away nearly all the superimposed mechanism. Kant's 'Transcendental Æsthetic,' he says, was a real discovery in metaphysics; but on the basis of this he for the most part only gave free play to his architectonic impulse. Of the twelve 'categories of the understanding,' which he professed to derive from the logical forms of judgment, all except causality are mere 'blind windows.' This alone, therefore, Schopenhauer adopts; placing it, however, not at a higher level but side by side with time and space, Kant's forms of intuition. These three forms, according to Schopenhauer, make up the understanding of men and animals. 'All intuition is intellectual.' It is not first mere appearance related in space and time, and waiting for understanding to organise it; but, in animals as in man, it is put in order at once under the three forms that suffice to explain the knowledge all have of the phenomenal world.

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) As the third form of causality was enumerated 'motive' for the will; but in that classification it was viewed from without, as belonging to the world of objects. Through the direct knowledge we have of our own will, we know also from within this determination by the presentation we call a motive. Hence emerges the fourth form of the principle of sufficient reason. This at a later stage makes possible the transition from physics to metaphysics.

All these forms alike are forms of necessary determination. Necessity has no clear and true sense but certainty of the consequence when the ground is posited. All necessity therefore is conditional. In accordance with the four expressions of the principle of sufficient reason, it takes the fourfold shape of physical, logical, mathematical, and moral necessity.

The sharp distinction between logical and mathematical truth, with the assignment of the former to conceptual and of the latter to intuitive relations, comes to Schopenhauer directly from Kant. So also does his view that the necessary form of causation is sequence; though here his points of contact with English thinkers, earlier and later, are very marked. Only in his statement of the 'law of motivation' as 'causality seen from within' does he hint at his own distinctive metaphysical doctrine. Meanwhile, it is evident that he is to be numbered with the group of modern thinkers who have arrived in one way or another at a complete scientific phenomenism. Expositors have noted that in his earlier statements of this he tends to lay more stress on the character of the visible and tangible world as mere appearance. The impermanence, the relativity, of all that exists in time and space, leads him to describe it, in a favourite term borrowed from Indian philosophy, as Maya, or illusion. Later, he dwells more on the relative reality of things as they appear. His position, however, does not essentially alter, but only finds varying expression as he turns more to the scientific or to the metaphysical side. From Hume's view on causation he differs not by opposing its pure phenomenism, but only by recognising, as Kant does, an a priori element in the form of its law. German critics have seen in his own formulation an anticipation of Mill, and this is certainly striking as regards the general conception of the causal order, although there is no anticipation of Mill's inductive logic. On the same side there is a close agreement with Malebranche and the Occasionalists, pointed out by Schopenhauer himself. The causal explanations of science, he is at one with them in insisting, give no ultimate account of anything. All its causes are no more than 'occasional causes,'—merely instances, as Mill expressed it afterwards, of 'invariable and unconditional sequence.' From Mill of course he differs in holding its form to be necessary and a priori, not ultimately derived from a summation of experiences; and, with the Occasionalists, he goes on to metaphysics in its sense of ontology, as Mill never did. The difference here is that he does not clothe his metaphysics in a theological dress.

In the later development of his thought, Schopenhauer dealt more expressly with the question, how this kind of phenomenism is reconcilable with a scientific cosmogony. On one side the proposition, 'No object without subject,' makes materialism for ever impossible; for the materialist tries to explain from relations among presentations what is the condition of all presentation. On the other side, we are all compelled to agree with the materialists that knowledge of the object comes late in a long series of material events. Inorganic things existed in time before life; vegetative life before animal life; and only with animal life does knowledge emerge. Reasoned knowledge of the whole series comes only at the end of it in the human mind. This apparent contradiction he solves by leaving a place for metaphysics. Our representation of the world as it existed before the appearance of life was indeed non-existent at the time to which we assign it; but the real being of the world had a manifestation not imaginable by us. For this, we substitute a picture of a world such as we should have been aware of had our 'subject,' with its a priori forms of time, space, and causality, been then present. What the reality is, is the problem of the thing-in-itself (to use the Kantian term). This problem remains over; but we know that the metaphysical reality cannot be matter; for matter, with all its qualities, is phenomenal. It exists only 'for understanding, through understanding, in understanding.' These discriminations made, Schopenhauer offers us a scientific cosmogony beginning with the nebular hypothesis and ending with an outline of organic evolution. This last differs from the Darwinian theory in supposing a production of species by definite steps instead of by accumulation of small individual variations. At a certain time, a form that has all the characters of a new species appears among the progeny of an existing species. Man is the last and highest form to be evolved. From Schopenhauer's metaphysics, as we shall see, it follows that no higher form of life will ever appear.

A word may be said here on a materialistic-sounding phrase which is very prominent in Schopenhauer's later expositions, and has been remarked on as paradoxical for an idealist. The world as presentation, he often says, is 'in the brain.' This, it must be allowed, is not fully defensible from his own point of view, except with the aid of a later distinction. The brain as we know it is of course only a part of the phenomenon of the subject,—a grouping of possible perceptions. How then, since it is itself only appearance, can it be the bearer of the whole universe as appearance? The answer is that Schopenhauer meant in reality 'the being of the brain,' and not the brain as phenomenon. He had a growing sense of the importance of physiology for the investigation of mind; and his predilection led him to adopt a not quite satisfactory shorthand expression for the correspondence we know scientifically to exist between our mental processes and changes capable of objective investigation in the matter of the brain.

In science his distinctive bent was to the borderland between psychology and physiology. Hence came the attraction exercised on him by Goethe's theory of colours. To his own theory, though, unlike his philosophical system, it has always failed to gain the attention he predicted for it, the merit must be allowed of treating the problem as essentially one of psychophysics. What he does is to attempt to ascertain the conditions in the sensibility of the retina that account for our actual colour-sensations. This problem was untouched by the Newtonian theory; but Schopenhauer followed Goethe in the error of trying to overthrow this on its own ground. He had no aptitude for the special inquiries of mathematics and physics, though he had gained a clear insight into their general nature as sciences. On the psycho-physical side there is to-day no fully authorised theory. The problem indeed has become ever more complex. Schopenhauer's attempt, by combination of sensibilities to 'light' and 'darkness,' to explain the phenomena of complementary colours, deserves at least a record in the long series of essays of which the best known are the 'Young-Helmholtz theory' and that of Hering. It marks an indubitable advance on Goethe in the clear distinction drawn between the mixture, in the ordinary sense, that can only result in dilution to different shades of grey, and the kinds of mixture from which, in their view, true colours arise.

A characteristic position in Schopenhauer's theory of knowledge, and one that is constantly finding new expression in his writings, is the distinction between abstract and intuitive knowledge already touched on. Intuitive knowledge of the kind that is common to men and animals, as we have seen, makes up, in his terminology, the 'understanding'; while 'reason' is the distinctively human faculty of concepts. When he depreciates this, as he often does, in comparison with 'intuition,' it must be remembered that he does not limit this term to perception of particulars, but ascribes to what he calls the 'Platonic Idea' a certain kind of union between reason and 'phantasy,' which gives it an intuitive character of its own. Thus intuition can stand, though not in every case for what is higher, yet always for that which is wider and greater and more immediate. Whatever may be done with reflective reason and its abstractions, every effectual process of thought must end, alike for knowledge and art and virtue, in some intuitive presentation. The importance of reason for practice is due to its generality. Its function is subordinate. It does not furnish the ground of virtuous action any more than Æsthetic precepts can enable any one to produce a work of art; but it can help to preserve constancy to certain maxims, as also in art a reasoned plan is necessary because the inspiration of genius is not every moment at command. Virtue and artistic genius alike, however, depend ultimately on intuition: and so also does every true discovery in science. The nature of pedantry is to try to be guided everywhere by concepts, and to trust nothing to perception in the particular case. Philosophy also Schopenhauer regards as depending ultimately on a certain intuitive view; but he allows that it has to translate this into abstractions. Its problem is to express the what of the world in abstract form: science dealing only with the why of phenomena related within the world. This character of philosophy as a system of abstract concepts deprives it of the immediate attractiveness of art; so that, as he says in one place, it is more fortunate to be a poet than a philosopher.