Knowledge A Priori

From the fact that we are able spontaneously to assign and determine the laws of relations in space without having recourse to experience, Plato concludes (Meno, p. 353, Bip.) that all learning is mere recollection. Kant, on the other hand, concludes that space is subjectively conditioned, and merely a form of the faculty of knowledge. How far, in this regard, does Kant stand above Plato!

Cogito, ergo sum, is an analytical judgment.

Indeed Parmenides held it to be an identical judgment: “Ä¿ 3±Á ±ÅÄ¿ 1⁄2¿μ11⁄2 μÃÄ1 Äμ o±1 μ11⁄2±1” (nam intelligere et esse idem est, Clem. Alex. Strom., vi. 2, § 23). As such, however, or indeed even as an analytical judgment, it cannot contain any special wisdom; nor yet if, to go still deeper, we seek to deduce it as a conclusion from the major premise, non-entis nulla sunt prædicata. But with this proposition what Descartes really wished to express was the great truth that immediate certainty belongs only to self-consciousness, to what is subjective. To what is objective, on the other hand, thus to everything else, only indirect certainty belongs; for it is arrived at through self-consciousness; and being thus merely at second hand, it is to be regarded as problematical. Upon this depends the value of this celebrated proposition. As its opposite we may set up, in the sense of the Kantian philosophy, cogito, ergo est, that is, exactly as I think certain relations in things (the mathematical), they must always occur in all possible experience;—this was an important, profound, and a late apperçu, which appeared in the form of the problem as to the possibility of synthetic judgments a priori, and has actually opened up the way to a deeper knowledge. This problem is the watchword of the Kantian philosophy, as the former proposition is that of the Cartesian, and shows μ3⁄4 ¿1É1⁄2 μ1à ¿1±. Kant very fitly places his investigations concerning time and space at the head of all the rest. For to the speculative mind [202]192 [203] The World As Will And Idea (Vol. 2 of 3) these questions present themselves before all others: what is time?—what is this that consists of mere movement, without anything that moves it?—and what is space? this omnipresent nothing, out of which nothing that exists can escape without ceasing to be anything at all? That time and space depend on the subject, are the mode in which the process of objective apperception is brought about in the brain, has already a sufficient proof in the absolute impossibility of thinking away time and space, while we can very easily think away everything that is presented in them. The hand can leave go of everything except itself. However, I wish here to illustrate by a few examples and deductions the more exact proofs of this truth which are given by Kant, not for the purpose of refuting stupid objections, but for the use of those who may have to expound Kant’s doctrine in future. “A right-angled equilateral triangle” contains no logical contradiction; for the predicates do not by any means cancel the subject, nor are they inconsistent with each other. It is only when their object is constructed in pure perception that the impossibility of their union in it appears. Now if on this account we were to regard this as a contradiction, then so would every physical impossibility, only discovered to be such after the lapse of centuries, be a contradiction; for example, the composition of a metal from its elements, or a mammal with more or fewer than seven cervical vertebra,14 or horns and upper incisors in the same animal. But only logical impossibility is a contradiction, not physical, and just as little mathematical. Equilateral and rectangled do not contradict each other (they coexist in the square), nor does either of them contradict a triangle. Therefore the incompatibility of the above conceptions can never be known by mere thinking, but is only discovered by perception—merely mental perception, however, which requires no experience, no 14 That the three-toed sloth has nine must be regarded as a mistake; yet Owen still states this, “Ostéologie Comp.,” p. 405.Chapter IV. On Knowledge A Priori. 193 real object. We should also refer here to the proposition of Giordano Bruno, which is also found in Aristotle: “An infinitely large body is necessarily immovable”—a proposition which cannot rest either upon experience or upon the principle of contradiction, since it speaks of things which cannot occur in any experience, and the conceptions “infinitely large” and “movable” do not contradict each other; but it is only pure perception that informs us that motion demands a space outside the body, while its infinite size leaves no space over. Suppose, now, it should be objected to the first mathematical example that it is only a question of how complete a conception of a triangle the person judging has: if the conception is quite complete it will also contain the impossibility of a triangle being rectangular and also equilateral. The answer to this is: assume that his conception is not so complete, yet without recourse to experience he can, by the mere construction of the triangle in his imagination, extend his conception of it and convince himself for ever of the impossibility of this combination of these conceptions. This process, however, is a synthetic judgment a priori, that is, a judgment through which, independently of all experience, and yet with validity for all experience, we form and perfect our conceptions. For, in general, whether a given judgment is analytical or synthetical can only be determined in the particular case according as the conception of the subject in the mind of the person judging is more or less complete. The conception “cat” contains in the mind of a Cuvier a hundred times more than in that of his servant; therefore the same judgments about it will be synthetical for the latter, and only analytical for the former. But if we take the conceptions objectively, and now wish to decide whether a given judgment is analytical or synthetical, we must change the predicate into its contradictory opposite, and apply this to the subject without a copula. If this gives a contradictio in adjecto, then the judgment was analytical; otherwise it was synthetical. That Arithmetic rests on the pure intuition or perception of [204]194 [205] The World As Will And Idea (Vol. 2 of 3) time is not so evident as that Geometry is based upon that of space.15 It can be proved, however, in the following manner. All counting consists in the repeated affirmation of unity. Only for the purpose of always knowing how often we have already affirmed unity do we mark it each time with another word: these are the numerals. Now repetition is only possible through succession. But succession, that is, being after one another, depends directly upon the intuition or perception of time. It is a conception which can only be understood by means of this; and thus counting also is only possible by means of time. This dependence of all counting upon time is also betrayed by the fact that in all languages multiplication is expressed by “time,” thus by a time-concept: sexies, 3⁄4±o1Â, six fois, sex mal. But simple counting is already a multiplication by one, and for this reason in Pestalozzi’s educational establishment the children are always made to multiply thus: “Two times two is four times one.” Aristotle already recognised the close relationship of number and time, and expounded it in the fourteenth chapter of the fourth book of the “Physics.” Time is for him “the number of motion” (“A 15 This, however, does not excuse a professor of philosophy who, sitting in Kant’s chair, expresses himself thus: “That mathematics as such contains arithmetic and geometry is correct. It is incorrect, however, to conceive arithmetic as the science of time, really for no other reason than to give a pendant (sic) to geometry as the science of space” (Rosenkranz in the “Deutschen Museum,” 1857, May 14, No. 20). This is the fruit of Hegelism. If the mind is once thoroughly debauched with its senseless jargon, serious Kantian philosophy will no longer enter it. The audacity to talk at random about what one does not understand has been inherited from the master, and one comes in the end to condemn without ceremony the fundamental teaching of a great genius in a tone of peremptory decision, just as if it were Hegelian foolery. We must not, however, fail to notice that these little people struggle to escape from the track of great thinkers. They would therefore have done better not to attack Kant, but to content themselves with giving their public full details about God, the soul, the actual freedom of the will, and whatever belongs to that sort of thing, and then to have indulged in a private luxury in their dark back-shop, the philosophical journal; there they may do whatever they like without constraint, for no one sees it.

ÇÁ¿1⁄2¿Â ±Á1 ̧1⁄4¿Â μÃÄ1 o11⁄2·ÃμÉ”). He very profoundly suggests the question whether time could be if the soul were not, and answers it in the negative. If arithmetic had not this pure intuition or perception of time at its foundation, it would be no science a priori, and therefore its propositions would not have infallible certainty.

Although time, like space, is the form of knowledge of the subject, yet, just like space, it presents itself as independent of the subject and completely objective. Against our will, or without our knowledge, it goes fast or slow. We ask what o’clock it is; we investigate time, as if it were something quite objective. And what is this objective existence? Not the progress of the stars, or of the clocks, which merely serve to measure the course of time itself, but it is something different from all things, and yet, like them, independent of our will and knowledge. It exists only in the heads of percipient beings, but the uniformity of its course and its independence of the will give it the authority of objectivity.

Time is primarily the form of inner sense. Anticipating the following book, I remark that the only object of inner sense is the individual will of the knowing subject. Time is therefore the form by means of which self-consciousness becomes possible for the individual will, which originally and in itself is without knowledge. In it the nature of the will, which in itself is simple and identical, appears drawn out into a course of life. But just on account of this original simplicity and identity of what thus exhibits itself, its character remains always precisely the same, and hence also the course of life itself retains throughout the same key-note, indeed its multifarious events and scenes are at bottom just like variations of one and the same theme. The a priori nature of the law of causality has, by Englishmen and Frenchmen, sometimes not been seen at all, sometimes not rightly conceived of; and therefore some of them still prosecute the earlier attempts to find for it an empirical origin. Maine de [206]196 [207] The World As Will And Idea (Vol. 2 of 3) Biran places this in the experience that the act of will as cause is followed by the movement of the body as effect. But this fact itself is untrue. We certainly do not recognise the really immediate act of will as something different from the action of the body, and the two as connected by the bond of causality; but both are one and indivisible. Between them there is no succession; they are simultaneous. They are one and the same thing, apprehended in a double manner. That which makes itself known to inner apprehension (self-consciousness) as the real act of will exhibits itself at once in external perception, in which the body exists objectively as an action of the body. That physiologically the action of the nerve precedes that of the muscle is here immaterial, for it does not come within self- consciousness; and we are not speaking here of the relation between muscle and nerve, but of that between the act of will and the action of the body. Now this does not present itself as a causal relation. If these two presented themselves to us as cause and effect their connection would not be so incomprehensible to us as it actually is; for what we understand from its cause we understand as far as there is an understanding of things generally. On the other hand, the movement of our limbs by means of mere acts of will is indeed a miracle of such common occurrence that we no longer observe it; but if we once turn our attention to it we become keenly conscious of the incomprehensibility of the matter, just because in this we have something before us which we do not understand as the effect of a cause. This apprehension, then, could never lead us to the idea of causality, for that never appears in it at all. Maine de Biran himself recognises the perfect simultaneousness of the act of will and the movement (Nouvelles Considérations des Rapports du Physique au Moral, p. 377, 378). In England Thomas Reid (On the First Principles of Contingent Truths, Essay IV. c. 5) already asserted that the knowledge of the causal relation has its ground in the nature of the faculty of knowledge itself. Quite recently Thomas Brown, inChapter IV. On Knowledge A Priori. 197 his very tediously composed book, “Inquiry into the Relation of Cause and Effect,” 4th edit., 1835, says much the same thing, that that knowledge springs from an innate, intuitive, and instinctive conviction; thus he is at bottom upon the right path. Quite unpardonable, however, is the crass ignorance on account of which in this book of 476 pages, of which 130 are devoted to the refutation of Hume, absolutely no mention is made of Kant, who cleared up the question more than seventy years ago. If Latin had remained the exclusive language of science such a thing would not have occurred. In spite of Brown’s exposition, which in the main is correct, a modification of the doctrine set up by Maine de Biran, of the empirical origin of the fundamental knowledge of the causal relation, has yet found acceptance in England; for it is not without a certain degree of plausibility. It is this, that we abstract the law of causality from the perceived effect of our own body upon other bodies. This was already refuted by Hume. I, however, have shown that it is untenable in my work, “Ueber den Willen in der Natur” (p. 75 of the second edition, p. 82 of the third), from the fact that since we apprehend both our own and other bodies objectively in spatial perception, the knowledge of causality must already be there, because it is a condition of such perception. The one genuine proof that we are conscious of the law of causality before all experience lies in the necessity of making a transition from the sensation, which is only empirically given, to its cause, in order that it may become perception of the external world. Therefore I have substituted this proof for the Kantian, the incorrectness of which I have shown. A most full and thorough exposition of the whole of this important subject, which is only touched on here, the a priori nature of the law of causality and the intellectual nature of empirical perception, will be found in my essay on the principle of sufficient reason, § 21, to which I refer, in order to avoid the necessity of repeating here what is said there. I have also shown there the enormous difference between the mere sensation of the [208]198 [209] The World As Will And Idea (Vol. 2 of 3) senses and the perception of an objective world, and discovered the wide gulf that lies between the two. The law of causality alone can bridge across this gulf, and it presupposes for its application the two other forms which are related to it, space and time. Only by means of these three combined is the objective idea attained to. Now whether the sensation from which we start to arrive at apprehension arises through the resistance which is suffered by our muscular exertion, or through the impression of light upon the retina, or of sound upon the nerves of the brain, &c. &c., is really a matter of indifference. The sensation always remains a mere datum for the understanding, which alone is capable of apprehending it as the effect of a cause different from itself, which the understanding now perceives as external, i.e., as something occupying and filling space, which is also a form inherent in the intellect prior to all experience. Without this intellectual operation, for which the forms must lie ready in us, the perception of an objective, external world could never arise from a mere sensation within our skin. How can it ever be supposed that the mere feeling of being hindered in intended motion, which occurs also in lameness, could be sufficient for this? We may add to this that before I attempt to affect external things they must necessarily have affected me as motives. But this almost presupposes the apprehension of the external world. According to the theory in question (as I have remarked in the place referred to above), a man born without arms and legs could never attain to the idea of causality, and consequently could never arrive at the apprehension of the external world. But that this is not the case is proved by a fact communicated in Froriep’s Notizen, July 1838, No. 133—the detailed account, accompanied by a likeness, of an Esthonian girl, Eva Lauk, then fourteen years old, who was born entirely without arms or legs. The account concludes with these words: “According to the evidence of her mother, her mental development had been quite as quick as that of her brothers and sisters; she attained just as soon as theyChapter IV. On Knowledge A Priori. 199 did to a correct judgment of size and distance, yet without the assistance of hands.—Dorpat, 1st March 1838, Dr. A. Hueck.” Hume’s doctrine also, that the conception of causality arises from the custom of seeing two states constantly following each other, finds a practical refutation in the oldest of all successions, that of day and night, which no one has ever held to be cause and effect of each other. And the same succession also refutes Kant’s false assertion that the objective reality of a succession is only known when we apprehend the two succeeding events as standing in the relation of cause and effect to each other. Indeed the converse of this doctrine of Kant’s is true. We know which of the two connected events is the cause and which the effect, empirically, only in the succession. Again, on the other hand, the absurd assertion of several professors of philosophy in our own day that cause and effect are simultaneous can be refuted by the fact that in cases in which the succession cannot be perceived on account of its great rapidity, we yet assume it with certainty a priori, and with it the lapse of a certain time. Thus, for example, we know that a certain time must elapse between the falling of the flint and the projection of the bullet, although we cannot perceive it, and that this time must further be divided between several events that occur in a strictly determined succession—the falling of the flint, the striking of the spark, ignition, the spread of the fire, the explosion, and the projection of the bullet. No man ever perceived this succession of events; but because we know which is the cause of the others, we thereby also know which must precede the others in time, and consequently also that during the course of the whole series a certain time must elapse, although it is so short that it escapes our empirical apprehension; for no one will assert that the projection of the bullet is actually simultaneous with the falling of the flint. Thus not only the law of causality, but also its relation to time, and the necessity of the succession of cause and effect, is known to us a priori. If we know which of two events is the cause and which is the [210]200 [211] The World As Will And Idea (Vol. 2 of 3) effect, we also know which precedes the other in time; if, on the contrary, we do not know which is cause and which effect, but only know in general that they are causally connected, we seek to discover the succession empirically, and according to that we determine which is the cause and which the effect. The falseness of the assertion that cause and effect are simultaneous further appears from the following consideration. An unbroken chain of causes and effects fills the whole of time. (For if this chain were broken the world would stand still, or in order to set it in motion again an effect without a cause would have to appear.) Now if every effect were simultaneous with its cause, then every effect would be moved up into the time of its cause, and a chain of causes and effects containing as many links as before would fill no time at all, still less an infinite time, but would be all together in one moment. Thus, under the assumption that cause and effect are simultaneous, the course of the world shrinks up into an affair of a moment. This proof is analogous to the proof that every sheet of paper must have a certain thickness, because otherwise the whole book would have none. To say when the cause ceases and the effect begins is in almost all cases difficult, and often impossible. For the changes (i.e., the succession of states) are continuous, like the time which they fill, and therefore also, like it, they are infinitely divisible. But their succession is as necessarily determined and as unmistakable as that of the moments of time itself, and each of them is called, with reference to the one which precedes it, “effect,” and with reference to the one which follows it, “cause.” Every change in the material world can only take place because another has immediately preceded it: this is the true and the whole content of the law of causality. But no conception has been more misused in philosophy than that of cause, by means of the favourite trick or blunder of conceiving it too widely, taking it too generally, through abstract thinking. Since Scholasticism, indeed properly since Plato and Aristotle, philosophy has been forChapter IV. On Knowledge A Priori. 201 the most part a systematic misuse of general conceptions. Such, for example, are substance, ground, cause, the good, perfection, necessity, and very many others. A tendency of the mind to work with such abstract and too widely comprehended conceptions has shown itself almost at all times. It may ultimately rest upon a certain indolence of the intellect, which finds it too difficult a task to be constantly controlling thought by perception. By degrees such unduly wide conceptions come to be used almost like algebraical symbols, and tossed about like them, and thus philosophy is reduced to a mere process of combination, a kind of reckoning which (like all calculations) employs and demands only the lower faculties. Indeed there finally results from this a mere juggling with words, of which the most shocking example is afforded us by the mind-destroying Hegelism, in which it is carried to the extent of pure nonsense. But Scholasticism also often degenerated into word-juggling. Nay even the “Topi” of Aristotle—very abstract principles, conceived with absolute generality, which one could apply to the most different kinds of subjects, and always bring into the field in arguing either pro or contra—have also their origin in this misuse of general conceptions. We find innumerable examples of the way the Schoolmen worked with such abstractions in their writings, especially in those of Thomas Aquinas. But philosophy really pursued the path which was entered on by the Schoolmen down to the time of Locke and Kant, who at last bethought themselves as to the origin of conceptions. Indeed we find Kant himself, in his earlier years, still upon that path, in his “Proof of the Existence of God” (p. 191 of the first volume of Rosenkranz’s edition), where the conceptions substance, ground, reality, are used in such a way as would never have been possible if he had gone back to the source of these conceptions and to their true content which is determined thereby. For then he would have found as the source and content of substance simply matter, of ground (if things of the real world are in question) simply cause, [212]202 [213] The World As Will And Idea (Vol. 2 of 3) that is, the prior change which brings about the later change, &c. It is true that in this case such an investigation would not have led to the intended result. But everywhere, as here, such unduly wide conceptions, under which, therefore, more was subsumed than their true content would have justified, there have arisen false principles, and from these false systems. Spinoza’s whole method of demonstration rests upon such uninvestigated and too widely comprehended conceptions. Now here lies the great merit of Locke, who, in order to counteract all that dogmatic unreality, insisted upon the investigation of the origin of the conceptions, and thus led back to perception and experience. Bacon had worked in a similar frame of mind, yet more with reference to Physics than to Metaphysics. Kant followed the path entered upon by Locke, but in a higher sense and much further, as has already been mentioned above. To the men of mere show who succeeded in diverting the attention of the public from Kant to themselves the results obtained by Locke and Kant were inconvenient. But in such a case they know how to ignore both the dead and the living. Thus without hesitation they forsook the only right path which had at last been found by those wise men, and philosophised at random with all kinds of indiscriminately collected conceptions, unconcerned as to their origin and content, till at last the substance of the Hegelian philosophy, wise beyond measure, was that the conceptions had no origin at all, but were rather themselves the origin and source of things. But Kant has erred in this respect. He has too much neglected empirical perception for the sake of pure perception—a point which I have fully discussed in my criticism of his philosophy. With me perception is throughout the source of all knowledge. I early recognised the misleading and insidious nature of abstractions, and in 1813, in my essay on the principle of sufficient reason, I pointed out the difference of the relations which are thought under this conception. General conceptions must indeed be the material in which philosophy deposits and stores up its knowledge, butChapter IV. On Knowledge A Priori. 203 not the source from which it draws it; the terminus ad quem, not a quo. It is not, as Kant defines it, a science drawn from conceptions, but a science in conceptions. Thus the conception of causality also, with which we are here concerned, has always been taken far too widely by philosophers for the furtherance of their dogmatic ends, and much was imported into it which does not belong to it at all. Hence arose propositions such as the following: “All that is has its cause”—“the effect cannot contain more than the cause, thus nothing that was not also in the cause”—“causa est nobilior suo effectu,” and many others just as unwarranted. The following subtilty of that insipid gossip Proclus affords an elaborate and specially lucid example of this. It occurs in his “Institutio Theologica,” § 76: “ ±1⁄2 Ä¿ ±À¿ ±o11⁄2·Ä¿Å 3131⁄2¿1⁄4μ1⁄2¿1⁄2 ±1Ä1±Â, ±1⁄4μı2»·Ä¿1⁄2 μÇμ1 Ä·1⁄2 QÀ±Á3⁄411⁄2; À±1⁄2 ́μ Ä¿ ±À¿ o11⁄2¿Å1⁄4μ1⁄2·Â, 1⁄4μı2»·Ä·1⁄2; μ1 3±Á ±o11⁄2·Ä¿1⁄2 μÃÄ1 À±1⁄2Äà Ŀ À¿1¿Å1⁄2, ¿Å ́1± o11⁄2·ÃμÉÂ, ±»»1⁄2 ±ÅÄó Äó μ11⁄2±1 À±Á±3μ1 Ä¿ ́μÅÄμÁ¿1⁄2 ±Æ1⁄2 ±ÅÄ¿Å.” (Quidquid ab immobili causa manat, immutabilem habet essentiam [substantiam]. Quidquid vero a mobili causa manat, essentiam habet mutabilem. Si enim illud, quod aliquid facit, est prorsus immobile, non per motum, sed per ipsum Esse producit ipsum secundum ex se ipso.) Excellent! But just show me a cause which is not itself set in motion: it is simply impossible. But here, as in so many cases, abstraction has thought away all determinations down to that one which it is desired to make use of without regard to the fact that the latter cannot exist without the former. The only correct expression of the law of causality is this: Every change has its cause in another change which immediately precedes it. If something happens, i.e., if a new state of things appears, i.e., if something is changed, then something else must have changed immediately before, and something else again before this, and so on ad infinitum, for a first cause is as impossible to conceive as a beginning of time or a limit of space. More than this the law of causality does not assert. Thus its claims only arise in the case of changes. So [214]204 [215] The World As Will And Idea (Vol. 2 of 3) long as nothing changes there can be no question of a cause. For there is no a priori ground for inferring from the existence of given things, i.e., states of matter, their previous non-existence, and from this again their coming into being, that is to say, there is no a priori ground for inferring a change. Therefore the mere existence of a thing does not justify us in inferring that it has a cause. Yet there may be a posteriori reasons, that is, reasons drawn from previous experience, for the assumption that the present state or condition did not always exist, but has only come into existence in consequence of another state, and therefore by means of a change, the cause of which is then to be sought, and also the cause of this cause. Here then we are involved in the infinite regressus to which the application of the law of causality always leads. We said above: “Things, i.e., states or conditions of matter,” for change and causality have only to do with states or conditions. It is these states which we understand by form, in the wider sense; and only the forms change, the matter is permanent. Thus it is only the form which is subject to the law of causality. But the form constitutes the thing, i.e., it is the ground of the difference of things; while matter must be thought as the same in all. Therefore the Schoolmen said, “Forma dat esse rei;” more accurately this proposition would run: Forma dat rei essentiam, materia existentiam. Therefore the question as to the cause of a thing always concerns merely its form, i.e., its state or quality, and not its matter, and indeed only the former so far as we have grounds for assuming that it has not always existed, but has come into being by means of a change. The union of form and matter, or of essentia and existentia, gives the concrete, which is always particular; thus, the thing. And it is the forms whose union with matter, i.e., whose appearance in matter by means of a change, are subject to the law of causality. By taking the conception too widely in the abstract the mistake slipped in of extending causality to the thing absolutely, that is, to its whole inner nature and existence, thus also to matter, and ultimately it was thoughtChapter IV. On Knowledge A Priori. 205 justifiable to ask for a cause of the world itself. This is the origin of the cosmological proof. This proof begins by inferring from the existence of the world its non-existence, which preceded its existence, and such an inference is quite unjustifiable; it ends, however, with the most fearful inconsistency, for it does away altogether with the law of causality, from which alone it derives all its evidencing power, for it stops at a first cause, and will not go further; thus ends, as it were, by committing parricide, as the bees kill the drones after they have served their end. All the talk about the absolute is referable to a shamefast, and therefore disguised cosmological proof, which, in the face of the “Critique of Pure Reason,” has passed for philosophy in Germany for the last sixty years. What does the absolute mean? Something that is, and of which (under pain of punishment) we dare not ask further whence and why it is. A precious rarity for professors of philosophy! In the case, however, of the honestly expressed cosmological proof, through the assumption of a first cause, and therefore of a first beginning in a time which has absolutely no beginning, this beginning is always pushed further back by the question: Why not earlier? And so far back indeed that one never gets down from it to the present, but is always marvelling that the present itself did not occur already millions of years ago. In general, then, the law of causality applies to all things in the world, but not to the world itself, for it is immanent in the world, not transcendent; with it it comes into action, and with it it is abolished. This depends ultimately upon the fact that it belongs to the mere form of our understanding, like the whole of the objective world, which accordingly is merely phenomenal, and is conditioned by the understanding. Thus the law of causality has full application, without any exception, to all things in the world, of course in respect of their form, to the variation of these forms, and thus to their changes. It is valid for the actions of men as for the impact of a stone, yet, as we have said always, merely with regard to events, to changes. But if we abstract [216]206 [217] The World As Will And Idea (Vol. 2 of 3) from its origin in the understanding and try to look at it as purely objective, it will be found in ultimate analysis to depend upon the fact that everything that acts does so by virtue of its original, and therefore eternal or timeless, power; therefore its present effect would necessarily have occurred infinitely earlier, that is, before all conceivable time, but that it lacked the temporal condition. This temporal condition is the occasion, i.e., the cause, on account of which alone the effect only takes place now, but now takes place necessarily; the cause assigns it its place in time. But in consequence of that unduly wide view in abstract thought of the conception cause, which was considered above, it has been confounded with the conception of force. This is something completely different from the cause, but yet is that which imparts to every cause its causality, i.e., the capability of producing an effect. I have explained this fully and thoroughly in the second book of the first volume, also in “The Will in Nature,” and finally also in the second edition of the essay on the principle of sufficient reason, § 20, p. 44 (third edition, p. 45). This confusion is to be found in its most aggravated form in Maine de Biran’s book mentioned above, and this is dealt with more fully in the place last referred to; but apart from this it is also very common; for example, when people seek for the cause of any original force, such as gravitation. Kant himself (Über den Einzig Möglichen Beweisgrund, vol. i. p. 211-215 of Rosenkranz’s edition) calls the forces of nature “efficient causes,” and says “gravity is a cause.” Yet it is impossible to see to the bottom of his thought so long as force and cause are not distinctly recognised as completely different. But the use of abstract conceptions leads very easily to their confusion if the consideration of their origin is set aside. The knowledge of causes and effects, always perceptive, which rests on the form of the understanding, is neglected in order to stick to the abstraction cause. In this way alone is the conception of causality, with all its simplicity, so very frequently wrongly apprehended. ThereforeChapter IV. On Knowledge A Priori. 207 even in Aristotle (“Metaph.,” iv. 2) we find causes divided into four classes which are utterly falsely, and indeed crudely conceived. Compare with it my classification of causes as set forth for the first time in my essay on sight and colour, chap. 1, and touched upon briefly in the sixth paragraph of the first volume of the present work, but expounded at full length in my prize essay on the freedom of the will, p. 30-33. Two things in nature remain untouched by that chain of causality which stretches into infinity in both directions; these are matter and the forces of nature. They are both conditions of causality, while everything else is conditioned by it. For the one (matter) is that in which the states and their changes appear; the other (forces of nature) is that by virtue of which alone they can appear at all. Here, however, one must remember that in the second book, and later and more thoroughly in “The Will in Nature,” the natural forces are shown to be identical with the will in us; but matter appears as the mere visibility of the will; so that ultimately it also may in a certain sense be regarded as identical with the will. On the other hand, not less true and correct is what is explained in § 4 of the first book, and still better in the second edition of the essay on the principle of sufficient reason at the end of § 21, p. 77 (third edition, p. 82), that matter is causality itself objectively comprehended, for its entire nature consists in acting in general, so that it itself is thus the activity (μ1⁄2μÁ3μ1± = reality) of things generally, as it were the abstraction of all their different kinds of acting. Accordingly, since the essence, essentia, of matter consists in action in general, and the reality, existentia, of things consists in their materiality, which thus again is one with action in general, it may be asserted of matter that in it existentia and essentia unite and are one, for it has no other attribute than existence itself in general and independent of all fuller definitions of it. On the other hand, all empirically given matter, thus all material or matter in the special sense (which our ignorant materialists at the present day confound with matter), has [218]208 [219] The World As Will And Idea (Vol. 2 of 3) already entered the framework of the forms and manifests itself only through their qualities and accidents, because in experience every action is of quite a definite and special kind, and is never merely general. Therefore pure matter is an object of thought alone, not of perception, which led Plotinus (Enneas II., lib. iv., c. 8 & 9) and Giordano Bruno (Della Causa, dial. 4) to make the paradoxical assertion that matter has no extension, for extension is inseparable from the form, and that therefore it is incorporeal. Yet Aristotle had already taught that it is not a body although it is corporeal: “ÃÉ1⁄4± 1⁄4μ1⁄2 ¿Åo ±1⁄2 μ1·, ÃÉ1⁄4±Ä1o· ́μ” (Stob. Ecl., lib. i., c. 12, § 5). In reality we think under pure matter only action, in the abstract, quite independent of the kind of action, thus pure causality itself; and as such it is not an object but a condition of experience, just like space and time. This is the reason why in the accompanying table of our pure a priori knowledge matter is able to take the place of causality, and therefore appears along with space and time as the third pure form, and therefore as dependent on our intellect. This table contains all the fundamental truths which are rooted in our perceptive or intuitive knowledge a priori, expressed as first principles independent of each other. What is special, however, what forms the content of arithmetic and geometry, is not given here, nor yet what only results from the union and application of those formal principles of knowledge. This is the subject of the “Metaphysical First Principles of Natural Science” expounded by Kant, to which this table in some measure forms the propædutic and introduction, and with which it therefore stands in direct connection. In this table I have primarily had in view the very remarkable parallelism of those a priori principles of knowledge which form the framework of all experience, but specially also the fact that, as I have explained in § 4 of the first volume, matter (and also causality) is to be regarded as a combination, or if it is preferred, an amalgamation, of space and time. In agreement with this, we find that what geometryChapter IV. On Knowledge A Priori. 209 is for the pure perception or intuition of space, and arithmetic for that of time, Kant’s phoronomy is for the pure perception or intuition of the two united. For matter is primarily that which is movable in space. The mathematical point cannot even be conceived as movable, as Aristotle has shown (“Physics,” vi. 10). This philosopher also himself provided the first example of such a science, for in the fifth and sixth books of his “Physics” he determined a priori the laws of rest and motion. Now this table may be regarded at pleasure either as a collection of the eternal laws of the world, and therefore as the basis of our ontology, or as a chapter of the physiology of the brain, according as one assumes the realistic or the idealistic point of view; but the second is in the last instance right. On this point, indeed, we have already come to an understanding in the first chapter; yet I wish further to illustrate it specially by an example. Aristotle’s book “De Xenophane,” &c., commences with these weighty words of Xenophanes: “‘Ê ́1¿1⁄2 μ11⁄2±1 Æ·Ã11⁄2, μ1 Ä1 μÃÄ11⁄2, μ1ÀμÁ 1⁄4· μ1⁄2 ́μÇμı1 3μ1⁄2μà ̧±1 1⁄4· ́μ1⁄2 μo 1⁄4· ́μ1⁄2¿Â.” (Æternum esse, inquit, quicquid est, siquidem fieri non potest, ut ex nihilo quippiam existat.) Here, then, Xenophanes judges as to the origin of things, as regards its possibility, and of this origin he can have had no experience, even by analogy; nor indeed does he appeal to experience, but judges apodictically, and therefore a priori. How can he do this if as a stranger he looks from without into a world that exists purely objectively, that is, independently of his knowledge? How can he, an ephemeral being hurrying past, to whom only a hasty glance into such a world is permitted, judge apodictically, a priori and without experience concerning that world, the possibility of its existence and origin? The solution of this riddle is that the man has only to do with his own ideas, which as such are the work of his brain, and the constitution of which is merely the manner or mode in which alone the function of his brain can be fulfilled, i.e., the form of his perception. He thus judges only as to the phenomena of his [220]210 [221] The World As Will And Idea (Vol. 2 of 3) own brain, and declares what enters into its forms, time, space, and causality, and what does not. In this he is perfectly at home and speaks apodictically. In a like sense, then, the following table of the Prædicabilia a priori of time, space, and matter is to be taken:— Prædicabilia A Priori. Of Time. (1) There is only one Time, and all different times are parts of it.Of Space. (1) There is only one Space, and all different spaces are parts of it. (2) Different times are not simultaneous but successive.(2) Different spaces are not successive but simultaneous. (3) Time can- not be thought away, but ev- erything can be thought away from it.(3) Space can- not be thought away, but ev- erything can be thought away from it. Of Matter. (1) There is only one Matter, and all different ma- terials are dif- ferent states of matter; as such it is called Sub- stance. (2) Different matters (mate- rials) are not so through substance but through accidents. (3) Annihilation of matter is in- conceivable, but annihilation of all its forms and qualities is con- ceivable.Chapter IV. On Knowledge A Priori. (4) Time has three divisions, the past, the present, and the future, which constitute two directions and a centre of indif- ference.(4) Space has three dimen- sions—height, breadth, and length. (5) Time is in- finitely divisi- ble.(5) Space is in- finitely divisi- ble. 211 (4) Matter ex- ists, i.e., acts in all the dimen- sions of space and throughout the whole length of time, and thus these two are united and thereby filled. In this consists the true nature of matter; thus it is through and through causal- ity. (5) Matter is infinitely divisi- ble.212 The World As Will And Idea (Vol. 2 of 3) (6) Time is ho- mogeneous and a Continuum, i.e., no one of its parts is dif- ferent from the rest, nor sepa- rated from it by anything that is not time.(6) Space is ho- mogeneous and a Continuum, i.e., no one of its parts is dif- ferent from the rest, nor sepa- rated from it by anything that is not space. (7) Time has no beginning and no end, but all beginning and end is in it.(7) Space has no limits, but all limits are in it. (8) By reason of time we count.(8) By reason of space we mea- sure. (9) Symmetry is only in space. (9) Rhythm is only in time. (6) Matter is ho- mogeneous and a Continuum, i.e., it does not consist of orig- inally different (homoiomeria) or originally separated parts (atoms); it is therefore not composed of parts, which would necessar- ily be separated by something that was not matter. (7) Matter has no origin and no end, but all coming into be- ing and passing away are in it. (8) By reason of matter we weigh. (9) Equilibrium is only in matter.Chapter IV. On Knowledge A Priori. (10) We know the laws of time a priori.(10) We know the laws of space a priori. (11) Time can be perceived a priori, although only in the form of a line. (12) Time has no permanence, but passes away as soon as it is there. (13) Time never rests.(11) Space is immediately perceptible a priori. (14) Everything that exists in time has dura- tion.(14) Everything that exists in space has a po- sition. (12) Space can never pass away, but en- dures through all time. (13) Space is immovable. 213 (10) We know the laws of the substance of all accidents a pri- ori. (11) Matter can only be thought a priori. (12) The ac- cidents change; the substance remains. (13) Matter is indifferent to rest and motion, i.e., it is orig- inally disposed towards neither of the two. (14) Everything material has the capacity for ac- tion.214 The World As Will And Idea (Vol. 2 of 3) (15) Time has no duration, but all duration is in it, and is the per- sistence of what is permanent in contrast with its restless course.(15) Space has no motion, but all motion is in it, and it is the change of posi- tion of what is moved, in con- trast with its un- broken rest. (16) All motion is only possible in time. (17) Velocity is, in equal spaces, in inverse pro- portion to the time.(16) All motion is only possible in space. (17) Velocity is, in equal times, in direct propor- tion to the space. (15) Matter is what is perma- nent in time and movable in space; by the comparison of what rests with what is moved we measure du- ration. (16) All motion is only possible to matter. (17) The magni- tude of the mo- tion, the veloc- ity being equal, is in direct geo- metrical propor- tion to the mat- ter (mass).Chapter IV. On Knowledge A Priori. (18) Time is not measurable directly through itself, but only indirectly through motion, which is in space and time together: thus the motion of the sun and of the clock measure time. (19) Time is omnipresent. Every part of time is every- where, i.e., in all space, at once. (18) Space is measurable directly through itself, and indi- rectly through motion, which is in time and space together; hence, for ex- ample, an hour’s journey, and the distance of the fixed stars expressed as the travelling of light for so many years. (19) Space is eternal. Every part of it exists always. 215 (18) Matter as such (mass) is measurable, i.e., determinable as regards its quantity only indirectly, only through the amount of the motion which it receives and imparts when it is repelled or attracted. (19) Matter is absolute. That is, it neither comes into be- ing nor passes away, and thus its quantity can neither be in- creased nor di- minished.216 The World As Will And Idea (Vol. 2 of 3) (20) In time taken by it- self everything would be in suc- cession.(20) In space taken by it- self everything would be simul- taneous. (21) Time makes the change of acci- dents possible.(21) Space makes the permanence of substance possible. (22) No part of space contains the same matter as another. (23) Space is the principium indi- viduationis. (22) Every part of time contains all parts of mat- ter. (23) Time is the principium indi- viduationis. (20, 21) Mat- ter unites the ceaseless flight of time with the rigid immo- bility of space; therefore it is the permanent substance of the changing acci- dents. Causality determines this change for every place at every time, and thereby combines time and space, and constitutes the whole nature of matter. (22) For matter is both perma- nent and impen- etrable. (23) Individuals are material.Chapter IV. On Knowledge A Priori. (24) The now has no duration. (25) Time in itself is empty and without properties.(24) The point has no exten- sion. (25) Space in itself is empty and without properties. (26) Every mo- ment is condi- tioned by the preceding mo- ment, and is only because the latter has ceased to be. (Principle of sufficient rea- son of existence in time.—See my essay on the principle of suf- ficient reason.)(26) By the po- sition of every limit in space with reference to any other limit, its posi- tion with refer- ence to every possible limit is precisely deter- mined. (Princi- ple of sufficient reason of exis- tence in space.) 217 (24) The atom has no reality. (25) Matter in it- self is without form and qual- ity, and likewise inert, i.e., in- different to rest or motion, thus without proper- ties. (26) Every change in mat- ter can take place only on account of another change which preceded it; and therefore a first change, and thus also a first state of matter, is just as inconceivable as a beginning of time or a limit of space. (Principle of sufficient reason of becoming.)218 The World As Will And Idea (Vol. 2 of 3) (27) Time makes arith- metic possible.(27) Space makes geome- try possible. (28) The simple element in arith- metic is unity.(28) The sim- ple element in geometry is the point. (27) Matter, as that which is movable in space, makes phoronomy possible. (28) The sim- ple element in phoronomy is the atom. [224] Notes to the Annexed Table. (1) To No. 4 of Matter. The essence of matter is acting, it is acting itself, in the abstract, thus acting in general apart from all difference of the kind of action: it is through and through causality. On this account it is itself, as regards its existence, not subject to the law of causality, and thus has neither come into being nor passes away, for otherwise the law of causality would be applied to itself. Since now causality is known to us a priori, the conception of matter, as the indestructible basis of all that exists, can so far take its place in the knowledge we possess a priori, inasmuch as it is only the realisation of an a priori form of our knowledge. For as soon as we see anything that acts or is causally efficient it presents itself eo ipso as material, and conversely anything material presents itself as necessarily active or causally efficient. They are in fact interchangeable conceptions. Therefore the word “actual” is used as synonymous with “material;” and also the Greek o±Ä1⁄2 μ1⁄2μÁ3μ1±1⁄2, in opposition to o±Ä± ́Å1⁄2±1⁄411⁄2, reveals the same source, for μ1⁄2μÁ3μ1± signifies action in general; so also

Chapter IV. On Knowledge A Priori. 219 with actu in opposition to potentia, and the English “actually” for “wirklich.” What is called space-occupation, or impenetrability, and regarded as the essential predicate of body (i.e. of what is material), is merely that kind of action which belongs to all bodies without exception, the mechanical. It is this universality alone, by virtue of which it belongs to the conception of body, and follows a priori from this conception, and therefore cannot be thought away from it without doing away with the conception itself—it is this, I say, that distinguishes it from any other kind of action, such as that of electricity or chemistry, or light or heat. Kant has very accurately analysed this space-occupation of the mechanical mode of activity into repulsive and attractive force, just as a given mechanical force is analysed into two others by means of the parallelogram of forces. But this is really only the thoughtful analysis of the phenomenon into its two constituent parts. The two forces in conjunction exhibit the body within its own limits, that is, in a definite volume, while the one alone would diffuse it into infinity, and the other alone would contract it to a point. Notwithstanding this reciprocal balancing or neutralisation, the body still acts upon other bodies which contest its space with the first force, repelling them, and with the other force, in gravitation, attracting all bodies in general. So that the two forces are not extinguished in their product, as, for instance, two equal forces acting in different directions, or +E and -E, or oxygen and hydrogen in water. That impenetrability and gravity really exactly coincide is shown by their empirical inseparableness, in that the one never appears without the other, although we can separate them in thought. I must not, however, omit to mention that the doctrine of Kant referred to, which forms the fundamental thought of the second part of his “Metaphysical First Principles of Natural Science,” thus of the Dynamics, was distinctly and fully expounded before Kant by Priestley, in his excellent “Disquisitions on Matter and Spirit,” § 1 and 2, a book which appeared in 1777, and the [225]220 The World As Will And Idea (Vol. 2 of 3) second edition in 1782, while Kant’s work was published in 1786. Unconscious recollection may certainly be assumed in the case of subsidiary thoughts, flashes of wit, comparisons, &c., but not in the case of the principal and fundamental thought. Shall we then believe that Kant silently appropriated such important thoughts of another man? and this from a book which at that time was new? Or that this book was unknown to him, and that the same thoughts sprang up in two minds within a short time? The explanation, also, which Kant gives, in the “Metaphysical First Principles of Natural Science” (first edition, p. 88; Rosenkranz’s edition, p. 384), of the real difference between fluids and solids, is in substance already to be found in Kaspar Freidr. Wolff’s “Theory of Generation,” Berlin 1764, p. 132. But what are we to say if we find Kant’s most important and brilliant doctrine, that of the ideality of space and the merely phenomenal existence of the corporeal world, already expressed by Maupertuis thirty years earlier? This will be found more fully referred to in Frauenstädt’s letters on my philosophy, Letter 14. Maupertuis expresses this paradoxical doctrine so decidedly, and yet without adducing any proof of it, that one must suppose that he also took it from somewhere else.

It is very desirable that the matter should be further investigated, and as this would demand tiresome and extensive researches, some German Academy might very well make the question the subject of a prize essay. Now in the same relation as that in which Kant here stands to Priestley, and perhaps also to Kaspar Wolff, and Maupertuis or his predecessor, Laplace stands to Kant. For the principal and fundamental thought of Laplace’s admirable and certainly correct theory of the origin of the planetary system, which is set forth in his “Exposition du Système du Monde,” liv. v. c. 2, was expressed by Kant nearly fifty years before, in 1755, in his “Naturgeschichte und Theorie des Himmels,” and more fully in 1763 in his “Einzig möglichen Beweisgrund des Daseyns Gottes,” ch. 7. Moreover, in the later work he gives us to understand that Lambert in his “Kosmologischen Briefen,” 1761, tacitly adopted that doctrine from him, and these letters at the same time also appeared in French (Lettres Cosmologiques sur la Constitution de l’Univers). We are therefore obliged to assume that Laplace knew that Kantian doctrine. Certainly he expounds the matter more thoroughly, strikingly, and fully, and at the same time more simply than Kant, as is natural from his more profound astronomical knowledge; yet in the main it is to be found clearly expressed in Kant, and on account of the importance of the matter, would alone have been sufficient to make his name immortal. It cannot but disturb us very much if we find minds of the first order under suspicion of dishonesty, which would be a scandal to those of the lowest order. For we feel that theft is even more inexcusable in a rich man than in a poor one. We dare not, however, be silent; for here we are posterity, and must be just, as we hope that posterity will some day be just to us. Therefore, as a third example, I will add to these cases, that the fundamental thoughts of the “Metamorphosis of Plants,” by Goethe, were already expressed by Kaspar Wolff in 1764 in his “Theory of Generation,” p. 148, 229, 243, &c. Indeed, is it otherwise with the system of gravitation? the discovery of which is on the Continent of Europe always ascribed to Newton, while in England the learned at least know very well that it belongs to Robert Hooke, who in the year 1666, in a “Communication to the Royal Society,” expounds it quite distinctly, although only as an hypothesis and without proof. The principal passage of this communication is quoted in Dugald Stewart’s “Philosophy of the Human Mind,” and is probably taken from Robert Hooke’s Posthumous Works. The history of the matter, and how Newton got into difficulty by it, is also to be found in the “Biographie Universelle,” article Newton. Hooke’s priority is treated as an established fact in a short history of astronomy, Quarterly Review, August 1828. Further details on this subject are to be found in my “Parerga,” vol. ii., § 86 (second edition, § 88).

The story of the fall of an apple is a fable as groundless as it is popular, and is quite without authority.

(2) To No. 18 of Matter. The quantity of a motion (quantitas motus, already in Descartes) is the product of the mass into the velocity. This law is the basis not only of the doctrine of impact in mechanics, but also of that of equilibrium in statics. From the force of impact which two bodies with the same velocity exert the relation of their masses to each other may be determined. Thus of two hammers striking with the same velocity, the one which has the greater mass will drive the nail deeper into the wall or the post deeper into the earth. For example, a hammer weighing six pounds with a velocity = 6 effects as much as a hammer weighing three pounds with a velocity = 12, for in both cases the quantity of motion or the momentum = 36. Of two balls rolling at the same pace, the one which has the greater mass will impel a third ball at rest to a greater distance than the ball of less mass can. For the mass of the first multiplied by the same velocity gives a greater quantity of motion, or a greater momentum. The cannon carries further than the gun, because an equal velocity communicated to a much greater mass gives a much greater quantity of motion, which resists longer the retarding effect of gravity. For the same reason, the same arm will throw a lead bullet further than a stone one of equal magnitude, or a large stone further than quite a small one. And therefore also a case-shot does not carry so far as a ball-shot. The same law lies at the foundation of the theory of the lever and of the balance. For here also the smaller mass, on the longer arm of the lever or beam of the balance, has a greater velocity in falling; and multiplied by this it may be equal to, or indeed exceed, the quantity of motion or the momentum of the greater mass at the shorter arm of the lever. In the state of rest broughtChapter IV. On Knowledge A Priori. 223 about by equilibrium this velocity exists merely in intention or virtually, potentiâ, not actu; but it acts just as well as actu, which is very remarkable. The following explanation will be more easily understood now that these truths have been called to mind. The quantity of a given matter can only be estimated in general according to its force, and its force can only be known in its expression. Now when we are considering matter only as regards its quantity, not its quality, this expression can only be mechanical, i.e., it can only consist in motion which it imparts to other matter. For only in motion does the force of matter become, so to speak, alive; hence the expression vis viva for the manifestation of force of matter in motion. Accordingly the only measure of the quantity of a given matter is the quantity of its motion, or its momentum. In this, however, if it is given, the quantity of matter still appears in conjunction and amalgamated with its other factor, velocity. Therefore if we want to know the quantity of matter (the mass) this other factor must be eliminated. Now the velocity is known directly; for it is S/T. But the other factor, which remains when this is eliminated, can always be known only relatively in comparison with other masses, which again can only be known themselves by means of the quantity of their motion, or their momentum, thus in their combination with velocity. We must therefore compare one quantity of motion with the other, and then subtract the velocity from both, in order to see how much each of them owed to its mass. This is done by weighing the masses against each other, in which that quantity of motion is compared which, in each of the two masses, calls forth the attractive power of the earth that acts upon both only in proportion to their quantity. Therefore there are two kinds of weighing. Either we impart to the two masses to be compared equal velocity, in order to find out which of the two now communicates motion to the other, thus itself has a greater quantity of motion, which, since the velocity is the same on both sides, is to be ascribed to the other factor of the quantity of motion or the momentum, thus to the mass (common balance).

Or we weigh, by investigating how much more velocity the one mass must receive than the other has, in order to be equal to the latter in quantity of motion or momentum, and therefore allow no more motion to be communicated to itself by the other; for then in proportion as its velocity must exceed that of the other, its mass, i.e., the quantity of its matter, is less than that of the other (steelyard). This estimation of masses by weighing depends upon the favourable circumstance that the moving force, in itself, acts upon both quite equally, and each of the two is in a position to communicate to the other directly its surplus quantity of motion or momentum, so that it becomes visible. The substance of these doctrines has long ago been expressed by Newton and Kant, but through the connection and the clearness of this exposition I believe I have made it more intelligible, so that that insight is possible for all which I regarded as necessary for the justification of proposition No. 18. [228]Second Half. The Doctrine of the Abstract Idea, or Thinking.