The World as Will and Idea Volume I Part 3

As a third example taken from a different sphere we may mention that the so-called metaphysical truths, that is, such truths as those to which Kant a.s.signs the position of the metaphysical first principles of natural science, do not owe their evidence to demonstration. What is _a priori_ certain we know directly; as the form of all knowledge, it is known to us with the most complete necessity. For example, that matter is permanent, that is, can neither come into being nor pa.s.s away, we know directly as negative truth; for our pure intuition or perception of s.p.a.ce and time gives the possibility of motion; in the law of causality the understanding affords us the possibility of change of form and quality, but we lack powers of the imagination for conceiving the coming into being or pa.s.sing away of matter. Therefore that truth has at all times been evident to all men everywhere, nor has it ever been seriously doubted; and this could not be the case if it had no other ground of knowledge than the abstruse and exceedingly subtle proof of Kant. But besides this, I have found Kant's proof to be false (as is explained in the Appendix), and have shown above that the permanence of matter is to be deduced, not from the share which time has in the possibility of experience, but from the share which belongs to s.p.a.ce. The true foundation of all truths which in this sense are called metaphysical, that is, abstract expressions of the necessary and universal forms of knowledge, cannot itself lie in abstract principles; but only in the immediate consciousness of the forms of the idea communicating itself in apodictic a.s.sertions _a priori_, and fearing no refutation. But if we yet desire to give a proof of them, it can only consist in showing that what is to be proved is contained in some truth about which there is no doubt, either as a part of it or as a presupposition. Thus, for example, I have shown that all empirical perception implies the application of the law of causality, the knowledge of which is hence a condition of all experience, and therefore cannot be first given and conditioned through experience as Hume thought.

Demonstrations in general are not so much for those who wish to learn as for those who wish to dispute. Such persons stubbornly deny directly established insight; now only the truth can be consistent in all directions, and therefore we must show such persons that they admit under _one_ form and indirectly, what they deny under another form and directly; that is, the logically necessary connection between what is denied and what is admitted.

It is also a consequence of the scientific form, the subordination of everything particular under a general, and so on always to what is more general, that the truth of many propositions is only logically proved,-that is, through their dependence upon other propositions, through syllogisms, which at the same time appear as proofs. But we must never forget that this whole form of science is merely a means of rendering knowledge more easy, not a means to greater certainty. It is easier to discover the nature of an animal, by means of the species to which it belongs, and so on through the genus, family, order, and cla.s.s, than to examine on every occasion the animal presented to us: but the truth of all propositions arrived at syllogistically is always conditioned by and ultimately dependent upon some truth which rests not upon reasoning but upon perception. If this perception were always as much within our reach as a deduction through syllogisms, then it would be in every respect preferable. For every deduction from concepts is exposed to great danger of error, on account of the fact we have considered above, that so many spheres lie partly within each other, and that their content is often vague or uncertain. This is ill.u.s.trated by a mult.i.tude of demonstrations of false doctrines and sophisms of every kind. Syllogisms are indeed perfectly certain as regards form, but they are very uncertain on account of their matter, the concepts. For, on the one hand, the spheres of these are not sufficiently sharply defined, and, on the other hand, they intersect each other in so many ways that one sphere is in part contained in many others, and we may pa.s.s at will from it to one or another of these, and from this sphere again to others, as we have already shown. Or, in other words, the minor term and also the middle can always be subordinated to different concepts, from which we may choose at will the major and the middle, and the nature of the conclusion depends on this choice. Consequently immediate evidence is always much to be preferred to reasoned truth, and the latter is only to be accepted when the former is too remote, and not when it is as near or indeed nearer than the latter.

Accordingly we saw above that, as a matter of fact, in the case of logic, in which the immediate knowledge in each individual case lies nearer to hand than deduced scientific knowledge, we always conduct our thought according to our immediate knowledge of the laws of thought, and leave logic unused.(20)

-- 15. If now with our conviction that perception is the primary source of all evidence, and that only direct or indirect connection with it is absolute truth; and further, that the shortest way to this is always the surest, as every interposition of concepts means exposure to many deceptions; if, I say, we now turn with this conviction to mathematics, as it was established as a science by Euclid, and has remained as a whole to our own day, we cannot help regarding the method it adopts, as strange and indeed perverted. We ask that every logical proof shall be traced back to an origin in perception; but mathematics, on the contrary, is at great pains deliberately to throw away the evidence of perception which is peculiar to it, and always at hand, that it may subst.i.tute for it a logical demonstration. This must seem to us like the action of a man who cuts off his legs in order to go on crutches, or like that of the prince in the "_Triumph der Empfindsamkeit_" who flees from the beautiful reality of nature, to delight in a stage scene that imitates it. I must here refer to what I have said in the sixth chapter of the essay on the principle of sufficient reason, and take for granted that it is fresh and present in the memory of the reader; so that I may link my observations on to it without explaining again the difference between the mere ground of knowledge of a mathematical truth, which can be given logically, and the ground of being, which is the immediate connection of the parts of s.p.a.ce and time, known only in perception. It is only insight into the ground of being that secures satisfaction and thorough knowledge. The mere ground of knowledge must always remain superficial; it can afford us indeed rational knowledge _that_ a thing is as it is, but it cannot tell _why_ it is so.

Euclid chose the latter way to the obvious detriment of the science. For just at the beginning, for example, when he ought to show once for all how in a triangle the angles and sides reciprocally determine each other, and stand to each other in the relation of reason and consequent, in accordance with the form which the principle of sufficient reason has in pure s.p.a.ce, and which there, as in every other sphere, always affords the necessity that a thing is as it is, because something quite different from it, is as it is; instead of in this way giving a thorough insight into the nature of the triangle, he sets up certain disconnected arbitrarily chosen propositions concerning the triangle, and gives a logical ground of knowledge of them, through a laborious logical demonstration, based upon the principle of contradiction. Instead of an exhaustive knowledge of these s.p.a.ce-relations we therefore receive merely certain results of them, imparted to us at pleasure, and in fact we are very much in the position of a man to whom the different effects of an ingenious machine are shown, but from whom its inner connection and construction are withheld. We are compelled by the principle of contradiction to admit that what Euclid demonstrates is true, but we do not comprehend _why_ it is so. We have therefore almost the same uncomfortable feeling that we experience after a juggling trick, and, in fact, most of Euclid's demonstrations are remarkably like such feats. The truth almost always enters by the back door, for it manifests itself _per accidens_ through some contingent circ.u.mstance. Often a _reductio ad absurdum_ shuts all the doors one after another, until only one is left through which we are therefore compelled to enter. Often, as in the proposition of Pythagoras, lines are drawn, we don't know why, and it afterwards appears that they were traps which close unexpectedly and take prisoner the a.s.sent of the astonished learner, who must now admit what remains wholly inconceivable in its inner connection, so much so, that he may study the whole of Euclid through and through without gaining a real insight into the laws of s.p.a.ce-relations, but instead of them he only learns by heart certain results which follow from them. This specially empirical and unscientific knowledge is like that of the doctor who knows both the disease and the cure for it, but does not know the connection between them. But all this is the necessary consequence if we capriciously reject the special kind of proof and evidence of one species of knowledge, and forcibly introduce in its stead a kind which is quite foreign to its nature. However, in other respects the manner in which this has been accomplished by Euclid deserves all the praise which has been bestowed on him through so many centuries, and which has been carried so far that his method of treating mathematics has been set up as the pattern of all scientific exposition. Men tried indeed to model all the sciences after it, but later they gave up the attempt without quite knowing why. Yet in our eyes this method of Euclid in mathematics can appear only as a very brilliant piece of perversity. But when a great error in life or in science has been intentionally and methodically carried out with universal applause, it is always possible to discover its source in the philosophy which prevailed at the time. The Eleatics first brought out the difference, and indeed often the conflict, that exists between what is perceived, fa???e???,(21) and what is thought, ???e???, and used it in many ways in their philosophical epigrams, and also in sophisms. They were followed later by the Megarics, the Dialecticians, the Sophists, the New-Academy, and the Sceptics; these drew attention to the illusion, that is to say, to the deception of the senses, or rather of the understanding which transforms the data of the senses into perception, and which often causes us to see things to which the reason unhesitatingly denies reality; for example, a stick broken in water, and such like. It came to be known that sense-perception was not to be trusted unconditionally, and it was therefore hastily concluded that only rational, logical thought could establish truth; although Plato (in the Parmenides), the Megarics, Pyrrho, and the New-Academy, showed by examples (in the manner which was afterwards adopted by s.e.xtus Empiricus) how syllogisms and concepts were also sometimes misleading, and indeed produced paralogisms and sophisms which arise much more easily and are far harder to explain than the illusion of sense-perception. However, this rationalism, which arose in opposition to empiricism, kept the upper hand, and Euclid constructed the science of mathematics in accordance with it.

He was compelled by necessity to found the axioms upon evidence of perception (fa???e???), but all the rest he based upon reasoning (???e???). His method reigned supreme through all the succeeding centuries, and it could not but do so as long as pure intuition or perception, _a priori_, was not distinguished from empirical perception.

Certain pa.s.sages from the works of Proclus, the commentator of Euclid, which Kepler translated into Latin in his book, "De Harmonia Mundi," seem to show that he fully recognised this distinction. But Proclus did not attach enough importance to the matter; he merely mentioned it by the way, so that he remained unnoticed and accomplished nothing. Therefore, not till two thousand years later will the doctrine of Kant, which is destined to make such great changes in all the knowledge, thought, and action of European nations, produce this change in mathematics also. For it is only after we have learned from this great man that the intuitions or perceptions of s.p.a.ce and time are quite different from empirical perceptions, entirely independent of any impression of the senses, conditioning it, not conditioned by it, _i.e._, are _a priori_, and therefore are not exposed to the illusions of sense; only after we have learned this, I say, can we comprehend that Euclid's logical method of treating mathematics is a useless precaution, a crutch for sound legs, that it is like a wanderer who during the night mistakes a bright, firm road for water, and carefully avoiding it, toils over the broken ground beside it, content to keep from point to point along the edge of the supposed water. Only now can we affirm with certainty that what presents itself to us as necessary in the perception of a figure, does not come from the figure on the paper, which is perhaps very defectively drawn, nor from the abstract concept under which we think it, but immediately from the form of all knowledge of which we are conscious _a priori_. This is always the principle of sufficient reason; here as the form of perception, _i.e._, s.p.a.ce, it is the principle of the ground of being, the evidence and validity of which is, however, just as great and as immediate as that of the principle of the ground of knowing, _i.e._, logical certainty. Thus we need not and ought not to leave the peculiar province of mathematics in order to put our trust only in logical proof, and seek to authenticate mathematics in a sphere which is quite foreign to it, that of concepts. If we confine ourselves to the ground peculiar to mathematics, we gain the great advantage that in it the rational knowledge _that_ something is, is one with the knowledge _why_ it is so, whereas the method of Euclid entirely separates these two, and lets us know only the first, not the second. Aristotle says admirably in the a.n.a.lyt., post. i. 27: "????este?a d? ep?st?? ep?st??? ?a? p??te?a, ?te t?? ?t? ?a? t?? d??t? ? a?t?, a??a ? ????? t?? ?t?, t?? t?? d??t?" (_Subtilior autem et praestantior ea est scientia, qua_ QUOD _aliquid sit, et_ CUR _sit una simulque intelligimus non separatim_ QUOD, _et_ CUR _sit_). In physics we are only satisfied when the knowledge that a thing is as it is is combined with the knowledge why it is so. To know that the mercury in the Torricellian tube stands thirty inches high is not really rational knowledge if we do not know that it is sustained at this height by the counterbalancing weight of the atmosphere. Shall we then be satisfied in mathematics with the _qualitas occulta_ of the circle that the segments of any two intersecting chords always contain equal rectangles? That it is so Euclid certainly demonstrates in the 35th Prop. of the Third Book; _why_ it is so remains doubtful. In the same way the proposition of Pythagoras teaches us a _qualitas occulta_ of the right-angled triangle; the stilted and indeed fallacious demonstration of Euclid forsakes us at the _why_, and a simple figure, which we already know, and which is present to us, gives at a glance far more insight into the matter, and firm inner conviction of that necessity, and of the dependence of that quality upon the right angle:-

[Ill.u.s.tration]

In the case of unequal catheti also, and indeed generally in the case of every possible geometrical truth, it is quite possible to obtain such a conviction based on perception, because these truths were always discovered by such an empirically known necessity, and their demonstration was only thought out afterwards in addition. Thus we only require an a.n.a.lysis of the process of thought in the first discovery of a geometrical truth in order to know its necessity empirically. It is the a.n.a.lytical method in general that I wish for the exposition of mathematics, instead of the synthetical method which Euclid made use of. Yet this would have very great, though not insuperable, difficulties in the case of complicated mathematical truths. Here and there in Germany men are beginning to alter the exposition of mathematics, and to proceed more in this a.n.a.lytical way. The greatest effort in this direction has been made by Herr Kosack, teacher of mathematics and physics in the Gymnasium at Nordhausen, who added a thorough attempt to teach geometry according to my principles to the programme of the school examination on the 6th of April 1852.

In order to improve the method of mathematics, it is especially necessary to overcome the prejudice that demonstrated truth has any superiority over what is known through perception, or that logical truth founded upon the principle of contradiction has any superiority over metaphysical truth, which is immediately evident, and to which belongs the pure intuition or perception of s.p.a.ce.

That which is most certain, and yet always inexplicable, is what is involved in the principle of sufficient reason, for this principle, in its different aspects, expresses the universal form of all our ideas and knowledge. All explanation consists of reduction to it, exemplification in the particular case of the connection of ideas expressed generally through it. It is thus the principle of all explanation, and therefore it is neither susceptible of an explanation itself, nor does it stand in need of it; for every explanation presupposes it, and only obtains meaning through it. Now, none of its forms are superior to the rest; it is equally certain and incapable of demonstration as the principle of the ground of being, or of change, or of action, or of knowing. The relation of reason and consequent is a necessity in all its forms, and indeed it is, in general, the source of the concept of necessity, for necessity has no other meaning. If the reason is given there is no other necessity than that of the consequent, and there is no reason that does not involve the necessity of the consequent. Just as surely then as the consequent expressed in the conclusion follows from the ground of knowledge given in the premises, does the ground of being in s.p.a.ce determine its consequent in s.p.a.ce: if I know through perception the relation of these two, this certainty is just as great as any logical certainty. But every geometrical proposition is just as good an expression of such a relation as one of the twelve axioms; it is a metaphysical truth, and as such, just as certain as the principle of contradiction itself, which is a metalogical truth, and the common foundation of all logical demonstration. Whoever denies the necessity, exhibited for intuition or perception, of the s.p.a.ce-relations expressed in any proposition, may just as well deny the axioms, or that the conclusion follows from the premises, or, indeed, he may as well deny the principle of contradiction itself, for all these relations are equally undemonstrable, immediately evident and known _a priori_. For any one to wish to derive the necessity of s.p.a.ce-relations, known in intuition or perception, from the principle of contradiction by means of a logical demonstration is just the same as for the feudal superior of an estate to wish to hold it as the va.s.sal of another. Yet this is what Euclid has done. His axioms only, he is compelled to leave resting upon immediate evidence; all the geometrical truths which follow are demonstrated logically, that is to say, from the agreement of the a.s.sumptions made in the proposition with the axioms which are presupposed, or with some earlier proposition; or from the contradiction between the opposite of the proposition and the a.s.sumptions made in it, or the axioms, or earlier propositions, or even itself. But the axioms themselves have no more immediate evidence than any other geometrical problem, but only more simplicity on account of their smaller content.

When a criminal is examined, a _proces-verbal_ is made of his statement in order that we may judge of its truth from its consistency. But this is only a makeshift, and we are not satisfied with it if it is possible to investigate the truth of each of his answers for itself; especially as he might lie consistently from the beginning. But Euclid investigated s.p.a.ce according to this first method. He set about it, indeed, under the correct a.s.sumption that nature must everywhere be consistent, and that therefore it must also be so in s.p.a.ce, its fundamental form. Since then the parts of s.p.a.ce stand to each other in a relation of reason and consequent, no single property of s.p.a.ce can be different from what it is without being in contradiction with all the others. But this is a very troublesome, unsatisfactory, and roundabout way to follow. It prefers indirect knowledge to direct, which is just as certain, and it separates the knowledge that a thing is from the knowledge why it is, to the great disadvantage of the science; and lastly, it entirely withholds from the beginner insight into the laws of s.p.a.ce, and indeed renders him unaccustomed to the special investigation of the ground and inner connection of things, inclining him to be satisfied with a mere historical knowledge that a thing is as it is. The exercise of acuteness which this method is unceasingly extolled as affording consists merely in this, that the pupil practises drawing conclusions, _i.e._, he practises applying the principle of contradiction, but specially he exerts his memory to retain all those data whose agreement is to be tested. Moreover, it is worth noticing that this method of proof was applied only to geometry and not to arithmetic. In arithmetic the truth is really allowed to come home to us through perception alone, which in it consists simply in counting. As the perception of numbers is in _time alone_, and therefore cannot be represented by a sensuous schema like the geometrical figure, the suspicion that perception is merely empirical, and possibly illusive, disappeared in arithmetic, and the introduction of the logical method of proof into geometry was entirely due to this suspicion. As time has only one dimension, counting is the only arithmetical operation, to which all others may be reduced; and yet counting is just intuition or perception _a priori_, to which there is no hesitation in appealing here, and through which alone everything else, every sum and every equation, is ultimately proved. We prove, for example, not that (7 + 9 8 - 2)/3 = 42; but we refer to the pure perception in time, counting thus makes each individual problem an axiom. Instead of the demonstrations that fill geometry, the whole content of arithmetic and algebra is thus simply a method of abbreviating counting. We mentioned above that our immediate perception of numbers in time extends only to about ten. Beyond this an abstract concept of the numbers, fixed by a word, must take the place of the perception; which does not therefore actually occur any longer, but is only indicated in a thoroughly definite manner. Yet even so, by the important a.s.sistance of the system of figures which enables us to represent all larger numbers by the same small ones, intuitive or perceptive evidence of every sum is made possible, even where we make such use of abstraction that not only the numbers, but indefinite quant.i.ties and whole operations are thought only in the abstract and indicated as so thought, as [sqrt](r^b) so that we do not perform them, but merely symbolise them.

We might establish truth in geometry also, through pure _a priori_ perception, with the same right and certainty as in arithmetic. It is in fact always this necessity, known through perception in accordance with the principle of sufficient reason of being, which gives to geometry its princ.i.p.al evidence, and upon which in the consciousness of every one, the certainty of its propositions rests. The stilted logical demonstration is always foreign to the matter, and is generally soon forgotten, without weakening our conviction. It might indeed be dispensed with altogether without diminishing the evidence of geometry, for this is always quite independent of such demonstration, which never proves anything we are not convinced of already, through another kind of knowledge. So far then it is like a cowardly soldier, who adds a wound to an enemy slain by another, and then boasts that he slew him himself.(22)

After all this we hope there will be no doubt that the evidence of mathematics, which has become the pattern and symbol of all evidence, rests essentially not upon demonstration, but upon immediate perception, which is thus here, as everywhere else, the ultimate ground and source of truth. Yet the perception which lies at the basis of mathematics has a great advantage over all other perception, and therefore over empirical perception. It is _a priori_, and therefore independent of experience, which is always given only in successive parts; therefore everything is equally near to it, and we can start either from the reason or from the consequent, as we please. Now this makes it absolutely reliable, for in it the consequent is known from the reason, and this is the only kind of knowledge that has necessity; for example, the equality of the sides is known as established by the equality of the angles. All empirical perception, on the other hand, and the greater part of experience, proceeds conversely from the consequent to the reason, and this kind of knowledge is not infallible, for necessity only attaches to the consequent on account of the reason being given, and no necessity attaches to the knowledge of the reason from the consequent, for the same consequent may follow from different reasons. The latter kind of knowledge is simply induction, _i.e._, from many consequents which point to one reason, the reason is accepted as certain; but as the cases can never be all before us, the truth here is not unconditionally certain. But all knowledge through sense-perception, and the great bulk of experience, has only this kind of truth. The affection of one of the senses induces the understanding to infer a cause of the effect, but, as a conclusion from the consequent to the reason is never certain, illusion, which is deception of the senses, is possible, and indeed often occurs, as was pointed out above. Only when several of the senses, or it may be all the five, receive impressions which point to the same cause, the possibility of illusion is reduced to a minimum; but yet it still exists, for there are cases, for example, the case of counterfeit money, in which all the senses are deceived. All empirical knowledge, and consequently the whole of natural science, is in the same position, except only the pure, or as Kant calls it, metaphysical part of it. Here also the causes are known from the effects, consequently all natural philosophy rests upon hypotheses, which are often false, and must then gradually give place to more correct ones. Only in the case of purposely arranged experiments, knowledge proceeds from the cause to the effect, that is, it follows the method that affords certainty; but these experiments themselves are undertaken in consequence of hypotheses. Therefore, no branch of natural science, such as physics, or astronomy, or physiology could be discovered all at once, as was the case with mathematics and logic, but required and requires the collected and compared experiences of many centuries. In the first place, repeated confirmation in experience brings the induction, upon which the hypothesis rests, so near completeness that in practice it takes the place of certainty, and is regarded as diminishing the value of the hypothesis, its source, just as little as the incommensurability of straight and curved lines diminishes the value of the application of geometry, or that perfect exactness of the logarithm, which is not attainable, diminishes the value of arithmetic. For as the logarithm, or the squaring of the circle, approaches infinitely near to correctness through infinite fractions, so, through manifold experience, the induction, _i.e._, the knowledge of the cause from the effects, approaches, not infinitely indeed, but yet so near mathematical evidence, _i.e._, knowledge of the effects from the cause, that the possibility of mistake is small enough to be neglected, but yet the possibility exists; for example, a conclusion from an indefinite number of cases to all cases, _i.e._, to the unknown ground on which all depend, is an induction. What conclusion of this kind seems more certain than that all men have the heart on the left side? Yet there are extremely rare and quite isolated exceptions of men who have the heart upon the right side. Sense-perception and empirical science have, therefore, the same kind of evidence. The advantage which mathematics, pure natural science, and logic have over them, as _a priori_ knowledge, rests merely upon this, that the formal element in knowledge upon which all that is _a priori_ is based, is given as a whole and at once, and therefore in it we can always proceed from the cause to the effect, while in the former kind of knowledge we are generally obliged to proceed from the effect to the cause. In other respects, the law of causality, or the principle of sufficient reason of change, which guides empirical knowledge, is in itself just as certain as the other forms of the principle of sufficient reason which are followed by the _a priori_ sciences referred to above. Logical demonstrations from concepts or syllogisms have the advantage of proceeding from the reason to the consequent, just as much as knowledge through perception _a priori_, and therefore in themselves, _i.e._, according to their form, they are infallible. This has greatly a.s.sisted to bring demonstration in general into such esteem. But this infallibility is merely relative; the demonstration merely subsumes under the first principles of the science, and it is these which contain the whole material truth of science, and they must not themselves be demonstrated, but must be founded on perception. In the few _a priori_ sciences we have named above, this perception is pure, but everywhere else it is empirical, and is only raised to universality through induction. If, then, in the empirical sciences also, the particular is proved from the general, yet the general, on the other hand, has received its truth from the particular; it is only a store of collected material, not a self-const.i.tuted foundation.

So much for the foundation of truth. Of the source and possibility of error many explanations have been tried since Plato's metaphorical solution of the dove-cot where the wrong pigeons are caught, &c.

(Theaetetus, p. 167, _et seq._) Kant's vague, indefinite explanation of the source of error by means of the diagram of diagonal motion, will be found in the "Critique of Pure Reason," p. 294 of the first edition, and p. 350 of the fifth. As truth is the relation of a judgment to its ground of knowledge, it is always a problem how the person judging can believe that he has such a ground of knowledge and yet not have it; that is to say, how error, the deception of reason, is possible. I find this possibility quite a.n.a.logous to that of illusion, or the deception of the understanding, which has been explained above. My opinion is (and this is what gives this explanation its proper place here) that _every error is an inference from the consequent to the reason_, which indeed is valid when we know that the consequent has that reason and can have no other; but otherwise is not valid. The person who falls into error, either attributes to a consequent a reason which it cannot have, in which case he shows actual deficiency of understanding, _i.e._, deficiency in the capacity for immediate knowledge of the connection between the cause and the effect, or, as more frequently happens, he attributes to the effect a cause which is possible, but he adds to the major proposition of the syllogism, in which he infers the cause from the effect, that this effect _always_ results only from this cause. Now he could only be a.s.sured of this by a complete induction, which, however, he a.s.sumes without having made it. This "always" is therefore too wide a concept, and instead of it he ought to have used "sometimes" or "generally." The conclusion would then be problematical, and therefore not erroneous. That the man who errs should proceed in this way is due either to haste, or to insufficient knowledge of what is possible, on account of which he does not know the necessity of the induction that ought to be made. Error then is quite a.n.a.logous to illusion. Both are inferences from the effect to the cause; the illusion brought about always in accordance with the law of causality, and by the understanding alone, thus directly, in perception itself; the error in accordance with all the forms of the principle of sufficient reason, and by the reason, thus in thought itself; yet most commonly in accordance with the law of causality, as will appear from the three following examples, which may be taken as types or representatives of the three kinds of error. (1.) The illusion of the senses (deception of the understanding) induces error (deception of the reason); for example, if one mistakes a painting for an alto-relief, and actually takes it for such; the error results from a conclusion from the following major premise: "If dark grey pa.s.ses regularly through all shades to white; the cause is _always_ the light, which strikes differently upon projections and depressions, _ergo_-." (2.) "If there is no money in my safe, the cause is _always_ that my servant has got a key for it: _ergo_-." (3.) "If a ray of sunlight, broken through a prism, _i.e._, bent up or down, appears as a coloured band instead of round and white as before, the cause must always be that light consists of h.o.m.ogeneous rays, differently coloured and refrangible to different degrees, which, when forced asunder on account of the difference of their refrangibility, give an elongated and variously-coloured spectrum: _ergo-bibamus!_"-It must be possible to trace every error to such a conclusion, drawn from a major premise which is often only falsely generalised, hypothetical, and founded on the a.s.sumption that some particular cause is that of a certain effect. Only certain mistakes in counting are to be excepted, and they are not really errors, but merely mistakes. The operation prescribed by the concepts of the numbers has not been carried out in pure intuition or perception, in counting, but some other operation instead of it.

As regards the _content_ of the sciences generally, it is, in fact, always the relation of the phenomena of the world to each other, according to the principle of sufficient reason, under the guidance of the _why_, which has validity and meaning only through this principle. _Explanation_ is the establishment of this relation. Therefore explanation can never go further than to show two ideas standing to each other in the relation peculiar to that form of the principle of sufficient reason which reigns in the cla.s.s to which they belong. If this is done we cannot further be asked the question, _why_: for the relation proved is that one which absolutely cannot be imagined as other than it is, _i.e._, it is the form of all knowledge. Therefore we do not ask why 2 + 2 = 4; or why the equality of the angles of a triangle determines the equality of the sides; or why its effect follows any given cause; or why the truth of the conclusion is evident from the truth of the premises. Every explanation which does not ultimately lead to a relation of which no "why" can further be demanded, stops at an accepted _qualitas occulta_; but this is the character of every original force of nature. Every explanation in natural science must ultimately end with such a _qualitas occulta_, and thus with complete obscurity. It must leave the inner nature of a stone just as much unexplained as that of a human being; it can give as little account of the weight, the cohesion, the chemical qualities, &c., of the former, as of the knowing and acting of the latter. Thus, for example, weight is a _qualitas occulta_, for it can be thought away, and does not proceed as a necessity from the form of knowledge; which, on the contrary, is not the case with the law of inertia, for it follows from the law of causality, and is therefore sufficiently explained if it is referred to that law.

There are two things which are altogether inexplicable,-that is to say, do not ultimately lead to the relation which the principle of sufficient reason expresses. These are, first, the principle of sufficient reason itself in all its four forms, because it is the principle of all explanation, which has meaning only in relation to it; secondly, that to which this principle does not extend, but which is the original source of all phenomena; the thing-in-itself, the knowledge of which is not subject to the principle of sufficient reason. We must be content for the present not to understand this thing-in-itself, for it can only be made intelligible by means of the following book, in which we shall resume this consideration of the possible achievements of the sciences. But at the point at which natural science, and indeed every science, leaves things, because not only its explanation of them, but even the principle of this explanation, the principle of sufficient reason, does not extend beyond this point; there philosophy takes them up and treats them after its own method, which is quite distinct from the method of science. In my essay on the principle of sufficient reason, -- 51, I have shown how in the different sciences the chief guiding clue is one or other form of that principle; and, in fact, perhaps the most appropriate cla.s.sification of the sciences might be based upon this circ.u.mstance. Every explanation arrived at by the help of this clue is, as we have said, merely relative; it explains things in relation to each other, but something which indeed is presupposed is always left unexplained. In mathematics, for example, this is s.p.a.ce and time; in mechanics, physics, and chemistry it is matter, qualities, original forces and laws of nature; in botany and zoology it is the difference of species, and life itself; in history it is the human race with all its properties of thought and will: in all it is that form of the principle of sufficient reason which is respectively applicable. It is peculiar to _philosophy_ that it presupposes nothing as known, but treats everything as equally external and a problem; not merely the relations of phenomena, but also the phenomena themselves, and even the principle of sufficient reason to which the other sciences are content to refer everything. In philosophy nothing would be gained by such a reference, as one member of the series is just as external to it as another; and, moreover, that kind of connection is just as much a problem for philosophy as what is joined together by it, and the latter again is just as much a problem after its combination has been explained as before it. For, as we have said, just what the sciences presuppose and lay down as the basis and the limits of their explanation, is precisely and peculiarly the problem of philosophy, which may therefore be said to begin where science ends. It cannot be founded upon demonstrations, for they lead from known principles to unknown, but everything is equally unknown and external to philosophy. There can be no principle in consequence of which the world with all its phenomena first came into existence, and therefore it is not possible to construct, as Spinoza wished, a philosophy which demonstrates _ex firmis principiis_. Philosophy is the most general rational knowledge, the first principles of which cannot therefore be derived from another principle still more general. The principle of contradiction establishes merely the agreement of concepts, but does not itself produce concepts. The principle of sufficient reason explains the connections of phenomena, but not the phenomena themselves; therefore philosophy cannot proceed upon these principles to seek a _causa efficiens_ or a _causa finalis_ of the whole world. My philosophy, at least, does not by any means seek to know _whence_ or _wherefore_ the world exists, but merely _what_ the world is. But the _why_ is here subordinated to the _what_, for it already belongs to the world, as it arises and has meaning and validity only through the form of its phenomena, the principle of sufficient reason. We might indeed say that every one knows what the world is without help, for he is himself that subject of knowledge of which the world is the idea; and so far this would be true. But that knowledge is empirical, is in the concrete; the task of philosophy is to reproduce this in the abstract to raise to permanent rational knowledge the successive changing perceptions, and in general, all that is contained under the wide concept of feeling and merely negatively defined as not abstract, distinct, rational knowledge. It must therefore consist of a statement in the abstract, of the nature of the whole world, of the whole, and of all the parts. In order then that it may not lose itself in the endless mult.i.tude of particular judgments, it must make use of abstraction and think everything individual in the universal, and its differences also in the universal. It must therefore partly separate and partly unite, in order to present to rational knowledge the whole manifold of the world generally, according to its nature, comprehended in a few abstract concepts. Through these concepts, in which it fixes the nature of the world, the whole individual must be known as well as the universal, the knowledge of both therefore must be bound together to the minutest point. Therefore the capacity for philosophy consists just in that in which Plato placed it, the knowledge of the one in the many, and the many in the one. Philosophy will therefore be a sum-total of general judgments, whose ground of knowledge is immediately the world itself in its entirety, without excepting anything; thus all that is to be found in human consciousness; it will be _a complete recapitulation, as it were, a reflection, of the world in abstract concepts_, which is only possible by the union of the essentially identical in _one_ concept and the relegation of the different to another.

This task was already prescribed to philosophy by Bacon of Verulam when he said: _ea demum vera est philosophia, quae mundi ipsius voces fidelissime reddit, et veluti dictante mundo conscripta est, et nihil aliud est, quam ejusdem_ SIMULACRUM ET REFLECTIO, _neque addit quidquam de proprio, sed tantum iterat et resonat_ (De Augm. Scient., L. 2, c. 13). But we take this in a wider sense than Bacon could then conceive.

The agreement which all the sides and parts of the world have with each other, just because they belong to a whole, must also be found in this abstract copy of it. Therefore the judgments in this sum-total could to a certain extent be deduced from each other, and indeed always reciprocally so deduced. Yet to make the first judgment possible, they must all be present, and thus implied as prior to it in the knowledge of the world in the concrete, especially as all direct proof is more certain than indirect proof; their harmony with each other by virtue of which they come together into the unity of _one_ thought, and which arises from the harmony and unity of the world of perception itself, which is their common ground of knowledge, is not therefore to be made use of to establish them, as that which is prior to them, but is only added as a confirmation of their truth. This problem itself can only become quite clear in being solved.(23)

-- 16. After this full consideration of reason as a special faculty of knowledge belonging to man alone, and the results and phenomena peculiar to human nature brought about by it, it still remains for me to speak of reason, so far as it is the guide of human action, and in this respect may be called _practical_. But what there is to say upon this point has found its place elsewhere in the appendix to this work, where I controvert the existence of the so-called practical reason of Kant, which he (certainly very conveniently) explained as the immediate source of virtue, and as the seat of an absolute (_i.e._, fallen from heaven) imperative. The detailed and thorough refutation of this Kantian principle of morality I have given later in the "Fundamental Problems of Ethics." There remains, therefore, but little for me to say here about the actual influence of reason, in the true sense of the word, upon action. At the commencement of our treatment of reason we remarked, in general terms, how much the action and behaviour of men differs from that of brutes, and that this difference is to be regarded as entirely due to the presence of abstract concepts in consciousness. The influence of these upon our whole existence is so penetrating and significant that, on account of them, we are related to the lower animals very much as those animals that see are related to those that have no eyes (certain larvae, worms, and zoophytes). Animals without eyes know only by touch what is immediately present to them in s.p.a.ce, what comes into contact with them; those which see, on the contrary, know a wide circle of near and distant objects. In the same way the absence of reason confines the lower animals to the ideas of perception, _i.e._, the real objects which are immediately present to them in time; we, on the contrary, on account of knowledge in the abstract, comprehend not only the narrow actual present, but also the whole past and future, and the wide sphere of the possible; we view life freely on all its sides, and go far beyond the present and the actual. Thus what the eye is in s.p.a.ce and for sensuous knowledge, reason is, to a certain extent, in time and for inner knowledge. But as the visibility of objects has its worth and meaning only in the fact that it informs us of their tangibility, so the whole worth of abstract knowledge always consists in its relation to what is perceived.

Therefore men naturally attach far more worth to immediate and perceived knowledge than to abstract concepts, to that which is merely thought; they place empirical knowledge before logical. But this is not the opinion of men who live more in words than in deeds, who have seen more on paper and in books than in actual life, and who in their greatest degeneracy become pedants and lovers of the mere letter. Thus only is it conceivable that Leibnitz and Wolf and all their successors could go so far astray as to explain knowledge of perception, after the example of Duns Scotus, as merely confused abstract knowledge! To the honour of Spinoza, I must mention that his truer sense led him, on the contrary, to explain all general concepts as having arisen from the confusion of that which was known in perception (Eth. II., prop. 40, Schol. 1). It is also a result of perverted opinion that in mathematics the evidence proper to it was rejected, and logical evidence alone accepted; that everything in general which was not abstract knowledge was comprehended under the wide name of feeling, and consequently was little valued; and lastly that the Kantian ethics regarded the good will which immediately a.s.serts itself upon knowledge of the circ.u.mstances, and guides to right and good action as mere feeling and emotion, and consequently as worthless and without merit, and would only recognise actions which proceed from abstract maxims as having moral worth.

The many-sided view of life as a whole which man, as distinguished from the lower animals, possesses through reason, may be compared to a geometrical, colourless, abstract, reduced plan of his actual life. He, therefore, stands to the lower animals as the navigator who, by means of chart, compa.s.s, and quadrant, knows accurately his course and his position at any time upon the sea, stands to the uneducated sailors who see only the waves and the heavens. Thus it is worth noticing, and indeed wonderful, how, besides his life in the concrete, man always lives another life in the abstract. In the former he is given as a prey to all the storms of actual life, and to the influence of the present; he must struggle, suffer, and die like the brute. But his life in the abstract, as it lies before his rational consciousness, is the still reflection of the former, and of the world in which he lives; it is just that reduced chart or plan to which we have referred. Here in the sphere of quiet deliberation, what completely possessed him and moved him intensely before, appears to him cold, colourless, and for the moment external to him; he is merely the spectator, the observer. In respect of this withdrawal into reflection he may be compared to an actor who has played his part in one scene, and who takes his place among the audience till it is time for him to go upon the stage again, and quietly looks on at whatever may happen, even though it be the preparation for his own death (in the piece), but afterwards he again goes on the stage and acts and suffers as he must. From this double life proceeds that quietness peculiar to human beings, so very different from the thoughtlessness of the brutes, and with which, in accordance with previous reflection, or a formed determination, or a recognised necessity, a man suffers or accomplishes in cold blood, what is of the utmost and often terrible importance to him; suicide, execution, the duel, enterprises of every kind fraught with danger to life, and, in general, things against which his whole animal nature rebels. Under such circ.u.mstances we see to what an extent reason has mastered the animal nature, and we say to the strong: s?d??e??? ?? t??

?t??! (_ferreum certe tibi cor_), Il. 24, 521. Here we can say truly that reason manifests itself practically, and thus wherever action is guided by reason, where the motives are abstract concepts, wherever we are not determined by particular ideas of perception, nor by the impression of the moment which guides the brutes, there _practical reason_ shows itself. But I have fully explained in the Appendix, and ill.u.s.trated by examples, that this is entirely different from and unrelated to the ethical worth of actions; that rational action and virtuous action are two entirely different things; that reason may just as well find itself in connection with great evil as with great good, and by its a.s.sistance may give great power to the one as well as to the other; that it is equally ready and valuable for the methodical and consistent carrying out of the n.o.ble and of the bad intention, of the wise as of the foolish maxim; which all results from the const.i.tution of its nature, which is feminine, receptive, retentive, and not spontaneous; all this I have shown in detail in the Appendix, and ill.u.s.trated by examples. What is said there would have been placed here, but on account of my polemic against Kant's pretended practical reason I have been obliged to relegate it to the Appendix, to which I therefore refer.

The ideal explained in the _Stoical philosophy_ is the most complete development of _practical reason_ in the true and genuine sense of the word; it is the highest summit to which man can attain by the mere use of his reason, and in it his difference from the brutes shows itself most distinctly. For the ethics of Stoicism are originally and essentially, not a doctrine of virtue, but merely a guide to a rational life, the end and aim of which is happiness through peace of mind. Virtuous conduct appears in it as it were merely by accident, as the means, not as the end.

Therefore the ethical theory of Stoicism is in its whole nature and point of view fundamentally different from the ethical systems which lay stress directly upon virtue, such as the doctrines of the Vedas, of Plato, of Christianity, and of Kant. The aim of Stoical ethics is happiness: te???

t? e?da? ??e?? (_virtutes omnes finem habere beat.i.tudinem_) it is called in the account of the Stoa by Stobaeus (Ecl., L. ii. c. 7, p. 114, and also p. 138). Yet the ethics of Stoicism teach that happiness can only be attained with certainty through inward peace and quietness of spirit (ata?a??a), and that this again can only be reached through virtue; this is the whole meaning of the saying that virtue is the highest good. But if indeed by degrees the end is lost sight of in the means, and virtue is inculcated in a way which discloses an interest entirely different from that of one's own happiness, for it contradicts this too distinctly; this is just one of those inconsistencies by means of which, in every system, the immediately known, or, as it is called, felt truth leads us back to the right way in defiance of syllogistic reasoning; as, for example, we see clearly in the ethical teaching of Spinoza, which deduces a pure doctrine of virtue from the egoistical _suum utile quaerere_ by means of palpable sophisms. According to this, as I conceive the spirit of the Stoical ethics, their source lies in the question whether the great prerogative of man, reason, which, by means of planned action and its results, relieves life and its burdens so much, might not also be capable of freeing him at once, directly, _i.e._, through mere knowledge, completely, or nearly so, of the sorrows and miseries of every kind of which his life is full. They held that it was not in keeping with the prerogative of reason that the nature given with it, which by means of it comprehends and contemplates an infinity of things and circ.u.mstances, should yet, through the present, and the accidents that can be contained in the few years of a life that is short, fleeting, and uncertain, be exposed to such intense pain, to such great anxiety and suffering, as arise from the tempestuous strain of the desires and the antipathies; and they believed that the due application of reason must raise men above them, and can make them invulnerable. Therefore Antisthenes says: ?e?

?tas?a? ????, ? ????? (_aut mentem parandam, aut laqueum._ Plut. de stoic. repugn., c. 14), _i.e._, life is so full of troubles and vexations, that one must either rise above it by means of corrected thoughts, or leave it. It was seen that want and suffering did not directly and of necessity spring from not having, but from desiring to have and not having; that therefore this desire to have is the necessary condition under which alone it becomes a privation not to have and begets pain. ??

pe??a ??p?? e??a?eta?, a??a ep????a (_non paupertas dolorem efficit, sed cupiditas_), Epict., fragm. 25. Men learned also from experience that it is only the hope of what is claimed that begets and nourishes the wish; therefore neither the many unavoidable evils which are common to all, nor unattainable blessings, disquiet or trouble us, but only the trifling more or less of those things which we can avoid or attain; indeed, not only what is absolutely unavoidable or unattainable, but also what is merely relatively so, leaves us quite undisturbed; therefore the ills that have once become joined to our individuality, or the good things that must of necessity always be denied us, are treated with indifference, in accordance with the peculiarity of human nature that every wish soon dies and can no more beget pain if it is not nourished by hope. It followed from all this that happiness always depends upon the proportion between our claims and what we receive. It is all one whether the quant.i.ties thus related be great or small, and the proportion can be established just as well by diminishing the amount of the first as by increasing the amount of the second; and in the same way it also follows that all suffering proceeds from the want of proportion between what we demand and expect and what we get. Now this want of proportion obviously lies only in knowledge, and it could be entirely abolished through fuller insight.(24) Therefore Chrysippus says: de? ??? ?at? epe???a? t?? f?se? s?a????t?? (Stob.

Ecl., L. ii. c. 7, p. 134), that is, one ought to live with a due knowledge of the transitory nature of the things of the world. For as often as a man loses self-command, or is struck down by a misfortune, or grows angry, or becomes faint-hearted, he shows that he finds things different from what he expected, consequently that he was caught in error, and did not know the world and life, did not know that the will of the individual is crossed at every step by the chance of inanimate nature and the antagonism of aims and the wickedness of other individuals: he has therefore either not made use of his reason in order to arrive at a general knowledge of this characteristic of life, or he lacks judgment, in that he does not recognise in the particular what he knows in general, and is therefore surprised by it and loses his self-command.(25) Thus also every keen pleasure is an error and an illusion, for no attained wish can give lasting satisfaction; and, moreover, every possession and every happiness is but lent by chance for an uncertain time, and may therefore be demanded back the next hour. All pain rests on the pa.s.sing away of such an illusion; thus both arise from defective knowledge; the wise man therefore holds himself equally aloof from joy and sorrow, and no event disturbs his ata?a??a.

In accordance with this spirit and aim of the Stoa, Epictetus began and ended with the doctrine as the kernel of his philosophy, that we should consider well and distinguish what depends upon us and what does not, and therefore entirely avoid counting upon the latter, whereby we shall certainly remain free from all pain, sorrow, and anxiety. But that which alone is dependent upon us is the will; and here a transition gradually takes place to a doctrine of virtue, for it is observed that as the outer world, which is independent of us, determines good and bad fortune, so inner contentment with ourselves, or the absence of it, proceeds from the will. But it was then asked whether we ought to apply the words _bonum_ and _malum_ to the two former or to the two latter? This was indeed arbitrary and a matter of choice, and did not make any real difference, but yet the Stoics disputed everlastingly with the Peripatetics and Epicureans about it, and amused themselves with the inadmissible comparison of two entirely incommensurable quant.i.ties, and the ant.i.thetical, paradoxical judgments which proceeded from them, and which they flung at each other. The _Paradoxa_ of Cicero afford us an interesting collection of these from the Stoical side.

Zeno, the founder, seems originally to have followed a somewhat different path. The starting-point with him was that for the attainment of the highest good, _i.e._, blessedness and spiritual peace, one must live in harmony with oneself (???????e???? ???; d? est? ?a?? ??a ????? ?a?

s?f???? ???.-_Consonanter vivere: hoc est secundum unam rationem et concordem sibi vivere._ Stob. Ecl. eth. L. ii., c. 7, p. 132. Also: ??et??

d?a?es?? e??a? ????? s?f???? ?a?t? pe?? ???? t?? ???. _Virtutem esse animi affectiomem sec.u.m per totam vitam consentientem_, _ibid._, p. 104.) Now this was only possible for a man if he determined himself entirely rationally, according to concepts, not according to changing impressions and moods; since, however, only the maxims of our conduct, not the consequences nor the outward circ.u.mstances, are in our power, in order to be always consistent we must set before us as our aim only the maxims and not the consequences and circ.u.mstances, and thus again a doctrine of virtue is introduced.

But the ethical principle of Zeno-to live in harmony with oneself-appeared even to his immediate successors to be too formal and empty. They therefore gave it material content by the addition-"to live in harmony with nature" (???????e??? t? f?se? ???), which, as Stobaeus mentions in another place, was first added by Kleanthes, and extended the matter very much on account of the wide sphere of the concept and the vagueness of the expression. For Kleanthes meant the whole of nature in general, while Chrysippus meant human nature in particular (Diog. Laert., 7, 89). It followed that what alone was adapted to the latter was virtue, just as the satisfaction of animal desires was adapted to animal natures; and thus ethics had again to be forcibly united to a doctrine of virtue, and in some way or other established through physics. For the Stoics always aimed at unity of principle, as for them G.o.d and the world were not dissevered.

The ethical system of Stoicism, regarded as a whole, is in fact a very valuable and estimable attempt to use the great prerogative of man, reason, for an important and salutary end; to raise him above the suffering and pain to which all life is exposed, by means of a maxim-

"_Qua ratione queas traducere leniter vum:_ _Ne te semper inops agitet vexetque cupido,_ _Ne pavor et rerum mediocriter utilium spes,_"

and thus to make him partake, in the highest degree, of the dignity which belongs to him as a rational being, as distinguished from the brutes; a dignity of which, in this sense at any rate, we can speak, though not in any other. It is a consequence of my view of the ethical system of Stoicism that it must be explained at the part of my work at which I consider what reason is and what it can do. But although it may to a certain extent be possible to attain that end through the application of reason, and through a purely rational system of ethics, and although experience shows that the happiest men are those purely rational characters commonly called practical philosophers,-and rightly so, because just as the true, that is, the theoretical philosopher carries life into the concept, they carry the concept into life,-yet it is far from the case that perfection can be attained in this way, and that the reason, rightly used, can really free us from the burden and sorrow of life, and lead us to happiness. Rather, there lies an absolute contradiction in wishing to live without suffering, and this contradiction is also implied in the commonly used expression, "blessed life." This will become perfectly clear to whoever comprehends the whole of the following exposition. In this purely rational system of ethics the contradiction reveals itself thus, the Stoic is obliged in his doctrine of the way to the blessed life (for that is what his ethical system always remains) to insert a recommendation of suicide (as among the magnificent ornaments and apparel of Eastern despots there is always a costly vial of poison) for the case in which the sufferings of the body, which cannot be philosophised away by any principles or syllogistic reasonings, are paramount and incurable; thus its one aim, blessedness, is rendered vain, and nothing remains as a mode of escape from suffering except death; in such a case then death must be voluntarily accepted, just as we would take any other medicine. Here then a marked antagonism is brought out between the ethical system of Stoicism and all those systems referred to above which make virtue in itself directly, and accompanied by the most grievous sorrows, their aim, and will not allow a man to end his life in order to escape from suffering.

Not one of them, however, was able to give the true reason for the rejection of suicide, but they laboriously collected illusory explanations from all sides: the true reason will appear in the Fourth Book in the course of the development of our system. But the antagonism referred to reveals and establishes the essential difference in fundamental principle between Stoicism, which is just a special form of endaemonism, and those doctrines we have mentioned, although both are often at one in their results, and are apparently related. And the inner contradiction referred to above, with which the ethical system of Stoicism is affected even in its fundamental thought, shows itself further in the circ.u.mstance that its ideal, the Stoic philosopher, as the system itself represents him, could never obtain life or inner poetic truth, but remains a wooden, stiff lay-figure of which nothing can be made. He cannot himself make use of his wisdom, and his perfect peace, contentment, and blessedness directly contradict the nature of man, and preclude us from forming any concrete idea of him. When compared with him, how entirely different appear the overcomers of the world, and voluntary hermits that Indian philoso