# The World as Will and Representation/Appendix
## APPENDIX.

ABSTRACT.
SCHOPENHAUER'S ESSAY ON THE FOURFOLD ROOT OF THE PRINCIPLE OF SUFFICIENT REASON (Fourth Edition, Edited by FRAUENSTADT. The First Edition appeared in 1813).
This essay is divided into eight chapters. The first is introductory. The second contains an historical review of previous philosophical doctrines on the subject. The third deals with the insufficiency of the previous treatment of the principle, and prescribes the lines of the new departure. The fourth, fifth, sixth, and seventh treat of the four classes of objects for the subject, and the forms of the principle of sufficient reason which respectively characterise these classes. The eighth contains general remarks and results. It will be convenient to summarise these chapters severally.

### Chapter I.

Schopenhauer points out that Plato and Kant agree in recommending, as the method of all knowledge, obedience to two laws:—that of Homogeneity, and that of Specification. The former bids us, by attention to the points of resemblance and agreement in things, get at their kinds, and combine them into species, and these species again into genera, until we have arrived at the highest concept of all, that which embraces everything. This law being transcendental, or an essential in our faculty of reason, assumes that nature is in harmony with it, an assumption which is expressed in the old rule: Entia præter necessitatem non esse multiplicanda. The law of Specification, on the other hand, is stated by Kant in these words: Entium varietates non temere esse minuendas. That is to say, we must carefully distinguish the species which are united under a genus, and the lower kinds which in their turn are united under these species; taking care not to make a leap, and subsume the lower kinds and individuals under the concept of the genus, since this is always capable of division, but never descends to the object of pure perception. Plato and Kant agree that these laws are transcendental, and that they presuppose that things are in harmony with them.
The previous treatment of the principle of sufficient reason, even by Kant, has been a failure, owing to the neglect of the second of these laws. It may well be that we shall find that this principle is the common expression of more than one fundamental principle of knowledge, and that the necessity, to which it refers, is therefore of different kinds. It may be stated in these words: Nihil est sine ratione cur potius sit, quam non sit. This is the general expression for the different forms of the assumption which everywhere justifies that question “Why?” which is the mother of all science.

### Chapter II.

Schopenhauer in this chapter traces historically the forms in which the principle had been stated by his predecessors, and their influence. He points out that in Greek philosophy it appeared in two aspects—that of the necessity of a ground for a logical judgment, and that of a cause for every physical change—and that these two aspects were systematically confounded. The Aristotelian division, not of the forms of the principle itself, but of one of its aspects, the causal, exemplified a confusion which continued throughout the Scholastic period. Descartes succeeds no better. His proof of the existence of God that the immensity of His nature is a cause or reason beyond which no cause is needed for His existence, simply illustrates the gross confusion between cause and ground of knowledge which underlies every form of this ontological proof. “That a miserable fellow like Hegel, whose entire philosophy is nothing but a monstrous amplification of the ontological proof, should dare to defend this proof against Kant's criticism of it is an alliance of which the ontological proof itself, little as it knows of shame, might well feel ashamed. It is not to be expected I should speak respectfully of people who have brought philosophy into disrespect.” Spinoza made the same confusion when he laid it down that the cause of existence was either contained in the nature and definition of the thing as it existed, or was to be found outside that thing. It was through this confusion of the ground of knowledge with the efficient cause that he succeeded in identifying God with the world. The true picture of Spinoza's “Causa sui” is Baron Munchhausen encircling his horse with his legs, and raising himself and the horse upwards by means of his pigtail, with the inscription “Causa sui” written below. Leibnitz was the first to place the principle of sufficient reason in the position of a first principle, and to indicate the difference between its two meanings. But it was Wolff who first completely distinguished them, and divided the doctrine into three kinds: principium fiendi (cause), principium essendi (possibility), and principium cognoscendi. Baumgarten, Reimarus, Lambert, and Platner added nothing to the work of Wolff, and the next great step was Hume's question as to the validity of the principle. Kant's distinction of the logical or formal principle of knowledge—Every proposition must have its ground; from the transcendental or material principle, Every thing must have its ground—was followed out by his immediate successors. But when we come to Schelling we find the proposition that gravitation is the reason and light the cause of things, a proposition which is quoted simply as a curiosity, for such a piece of nonsense deserves no place among the opinions of earnest and honest inquirers. The chapter concludes by pointing out the futility of the attempts to prove the principle. Every proof is the exhibition of the ground of a judgment which has been expressed, and of which, just because that ground is exhibited, we predicate truth. The principle of sufficient reason is just this expression of the demand for such a ground, and he who seeks a proof, i.e., the exhibition of a ground for this principle itself, presupposes it as true, and so falls into the circle of seeking a proof of the justification of the demand for proof.

### Chapter III.

In the third chapter Schopenhauer points out that the two applications of the principle of sufficient reason distinguished by his predecessors, to judgments, which must have a ground, and to the changes of real objects, which must have a cause, are not exhaustive. The reason why the three sides of a certain triangle are equal is that the angles are equal, and this is neither a logical deduction nor a case of causation. With a view to stating exhaustively the various kinds into which the application of the principle falls it is necessary to determine the nature of the principle itself. All our ideas are objects of the subject, and all objects of the subject are our ideas. But our ideas stand to one another as a matter of fact in an orderly connection, which is always determinable a priori in point of form, and on account of which nothing that is in itself separate and wholly independent of other things can be the object of our consciousness. It is this connection which the principle of sufficient reason in its generality expresses. The relations which constitute it are what Schopenhauer calls its root, and they fall into four classes, which are discussed in the four following chapters.

### Chapter IV.

In the fourth chapter Schopenhauer deals with the first class of objects for the subject and the form of the principle of sufficient reason which obtains in it. This first class is that of those complete ideas of perception which form part of our experience, and which are referable to some sensation of our bodies. These ideas are capable of being perceived only under the forms of Space and Time. If time were the only form there would be no coexistence, and therefore no persistence. If space were their only form there would be no succession, and therefore no change. Time may therefore be defined as the possibility of mutually exclusive conditions of the same thing. But the union of these two forms of existence is the essential condition of reality, and this union is the work of the understanding (see “World as Will and Idea,” vol. i. § 4, and the table of predicables annexed to vol. ii., chap. 4). In this class of objects for the subject the principle of sufficient reason appears as the law of causality or the principle of sufficient reason of becoming, and it is through it that all objects which present themselves in perception are bound together through the changes of their states. When a new state of one or more objects makes its appearance it must have been preceded by another on which it regularly follows. This is causal sequence, and the first state is the cause, the second the effect. The law has thus to do exclusively with the changes of objects of external experience, and not with things themselves, a circumstance which is fatal to the validity of the cosmological proof of the existence of God. It follows also from the essential connection of causality with succession that the notion of reciprocity, with its contemporaneous existence of cause and effect, is a delusion. The chain of causes and effects does not affect either matter, which is that in which all changes take place, or the original forces of nature, through which causation becomes possible, and which exist apart from all change, and in this sense out of time, but which yet are everywhere present (e.g., chemical forces, see supra, vol. i., § 26). In nature causation assumes three different forms; that of cause in the narrow sense, of stimulus, and of motive, on which differences depend the true distinctions between inorganic bodies, plants, and animals. It is only of cause properly so called that Newton's third law of the equality of action and reaction is true, and only here do we find the degree of the effect proportionate to that of the cause. The absence of this feature characterises stimulation. Motive demands knowledge as its condition, and intelligence is therefore the true characteristic of the animal. The three forms are in principle identical, the difference being due to the degrees of receptivity in existence. What is called freedom of the will is therefore an absurdity, as is also Kant's “Practical Reason.” These results are followed by an examination of the nature of vision, which Schopenhauer sums up in these words: “I have examined all these visual processes in detail in order to show that the understanding is active in all of them, the understanding which, by apprehending every change as an effect and referring it to its cause, creates on the basis of the a priori and fundamental intuitions or perceptions of space and time, the objective world, that phenomenon of the brain, for which the sensations of the senses afford only certain data. And this task the understanding accomplishes only through its proper form, the law of causality, and accomplishes it directly without the aid of reflection, that is, of abstract knowledge through concepts and words, which are the material of secondary knowledge, of thought, thus of the Reason.” “What understanding knows aright is reality; what reason knows aright is truth, i.e., a judgment which has a ground; the opposite of the former being illusion (what is falsely perceived), of the latter error (what is falsely thought).” All understanding is an immediate apprehension of the causal relation, and this is the sole function of understanding, and not the complicated working of the twelve Kantian Categories, the theory of which is a mistaken one. A consequence of this conclusion is, that arithmetical processes do not belong to the understanding, concerned as they are with abstract conceptions. But it must not be forgotten that between volition and the apparently consequential action of the body there is no causal relation, for they are the same thing perceived in two different ways. Section 23 contains a detailed refutation of Kant's proof of the a priori nature of the causal relation in the “Second Analogy of Experience” of the Critique of Pure Reason, the gist of the objection being that the so-called subjective succession is as much objective in reality as what is called objective by Kant: “Phenomena may well follow one another, without following from one another.”

### Chapter V.

The fifth chapter commences with an examination of the distinction between man and the brutes. Man possesses reason, that is to say, he has a class of ideas of which the brutes are not capable, abstract ideas as distinguished from those ideas of perception from which the former kind are yet derived. The consequence is, that the brute neither speaks nor laughs, and lacks all those qualities which make human life great. The nature of motives, too, is different where abstract ideas are possible. No doubt the actions of men follow of necessity from their causes, not less than is the case with the brutes, but the kind of sequence through thought which renders choice, i.e., the conscious conflict of motives, possible is different. Our abstract ideas, being incapable of being objects of perception, would be outside consciousness, and the operations of thought would be impossible, were it not that they are fixed for sense by arbitrary signs called words, which therefore always indicate general conceptions. It is just because the brutes are incapable of general conceptions that they have no faculty of speech. But thought does not consist in the mere presence of abstract ideas in consciousness, but in the union and separation of two or more of them, subject to the manifold restrictions and modifications which logic deals with. Such a clearly expressed conceptual relation is a judgment. In relation to judgments the principle of sufficient reason is valid in a new form: that of the ground of knowing. In this form it asserts that if a judgment is to express knowledge it must have a ground; and it is just because it has a ground that it has ascribed to it the predicate true. The grounds on which a judgment may depend are divisible into four kinds. A judgment may have another judgment as its ground, in which case its truth is formal or logical. There is no truth except in the relation of a judgment to something outside it, and intrinsic truth, which is sometimes distinguished from extrinsic logical truth, is therefore an absurdity. A judgment may also have its ground in sense-perception, and its truth is then material truth. Again, those forms of knowledge which lie in the understanding and in pure sensibility, as the conditions of the possibility of experience, may be the ground of a judgment which is then synthetical a priori. Finally, those formal conditions of all thinking which lie in the reason may be the ground of a judgment, which may in that case be called metalogically true. Of these metalogical judgments there are four, and they were long ago discovered and called laws of thought. (1.) A subject is equal to the sum of its predicates. (2.) A subject cannot at once have a given predicate affirmed and denied of it. (3.) Of two contradictorily opposed predicates one must belong to every subject. (4.) Truth is the relation of a judgment to something outside it as its sufficient reason. Reason, it may be remarked, has no material but only formal truth.

### Chapter VI.

The third class of objects for the subject is constituted by the formal element in perception, the forms of outer and inner sense, space and time. This class of ideas, in which time and space appear as pure intuitions, is distinguished from that other class in which they are objects of perception by the presence of matter which has been shown to be the perceptibility of time and space in one aspect, and causality which has become objective, in another. Space and time have this property, that all their parts stand to one another in a relation in which each is determined and conditioned by another. This relation is peculiar, and is intelligible to us neither through understanding nor through reason, but solely through pure intuition or perception a priori. And the law according to which the parts of space and time thus determine one another is called the law of sufficient reason of being. In space every position is determined with reference to every other position, so that the first stands to the second in the relation of a consequence to its ground. In time every moment is conditioned by that which precedes it. The ground of being, in the form of the law of sequence, is here very simple owing to the circumstance that time has only one dimension. On the nexus of the position of the parts of space depends the entire science of geometry. Ground of knowledge produces conviction only, as distinguished from insight into the ground of being. Thus it is that the attempt, which even Euclid at times makes, to produce conviction, as distinguished from insight into the ground of being, in geometry, is a mistake, and induces aversions to mathematics in many an admirable mind.

### Chapter VII.

The remaining class of objects for the subject is a very peculiar and important one. It comprehends only one object, the immediate object of inner sense, the subject in volition which becomes an object of knowledge, but only in inner sense, and therefore always in time and never in space; and in time only under limitations. There can be no knowledge of knowledge, for that would imply that the subject had separated itself from knowledge, and yet knew knowledge, which is impossible. The subject is the condition of the existence of ideas, and can never itself become idea or object. It knows itself therefore never as knowing, but only as willing. Thus what we know in ourselves is never what knows, but what wills, the will. The identity of the subject of volition with the subject of knowledge, through which the word “I” includes both, is the insoluble problem. The identity of the knowing with the known is inexplicable, and yet is immediately present. The operation of a motive is not, like that of all other causes, known only from without, and therefore indirectly, but also from within. Motivation is, in fact, causality viewed from within.

### Chapter VIII.

In this, the concluding chapter, Schopenhauer sums up his results. Necessity has no meaning other than that of the irresistible sequence of the effect where the cause is given. All necessity is thus conditioned, and absolute or unconditioned necessity is a contradiction in terms. And there is a fourfold necessity corresponding to the four forms of the principle of sufficient reason:—(1.) The logical form, according to the principle of the ground of knowledge; on account of which, if the premisses are given, the conclusion follows. (2.) The physical form, according to the law of causality; on account of which, if the cause is given, the effect must follow. (3.) The mathematical form, according to the law of being; on account of which every relation expressed by a true geometrical proposition is what it is affirmed to be, and every correct calculation is irrefutable. (4.) The moral form, on account of which every human being and every brute must, when the motive appears, perform the only act which accords with the inborn and unalterable character. A consequence of this is, that every department of science has one or other of the forms of the principle of sufficient reason as its basis. In conclusion, Schopenhauer points out that just because the principle of sufficient reason belongs to the a priori element in intelligence, it cannot be applied to the entirety of things, to the universe as inclusive of intelligence. Such a universe is mere phenomenon, and what is only true because it belongs to the form of intelligence can have no application to intelligence itself. Thus it is that it cannot be said that the universe and all things in it exist because of something else. In other words, the cosmological proof of the existence of God is inadmissible.