The World as Will and Idea Volume I Part 2

(Book II., ch. xi., ---- 10 and 11), very rightly refers to general concepts as the characteristic which distinguishes man from the brutes, and Leibnitz quotes this with full approval in the "Nouveaux Essais sur l'Entendement Humaine" (Book II., ch. xi., ---- 10 and 11.) But when Locke (in Book IV., ch. xvii., ---- 2 and 3) comes to the special explanation of reason he entirely loses sight of this simple, primary characteristic, and he also falls into a wavering, undetermined, incomplete account of mangled and derivative manifestations of it. Leibnitz also, in the corresponding part of his work, behaves in a similar manner, only with more confusion and indistinctness. In the Appendix, I have fully considered how Kant confused and falsified the conception of the nature of reason. But whoever will take the trouble to go through in this reference the ma.s.s of philosophical writing which has appeared since Kant, will find out, that just as the faults of princes must be expiated by whole nations, the errors of great minds extend their influence over whole generations, and even over centuries; they grow and propagate themselves, and finally degenerate into monstrosities. All this arises from the fact that, as Berkeley says, "Few men think; yet all will have opinions."

The understanding has only one function-immediate knowledge of the relation of cause and effect. Yet the perception of the real world, and all common sense, sagacity, and inventiveness, however multifarious their applications may be, are quite clearly seen to be nothing more than manifestations of that one function. So also the reason has one function; and from it all the manifestations of reason we have mentioned, which distinguish the life of man from that of the brutes, may easily be explained. The application or the non-application of this function is all that is meant by what men have everywhere and always called rational and irrational.(12)

-- 9. Concepts form a distinct cla.s.s of ideas, existing only in the mind of man, and entirely different from the ideas of perception which we have considered up till now. We can therefore never attain to a sensuous and, properly speaking, evident knowledge of their nature, but only to a knowledge which is abstract and discursive. It would, therefore, be absurd to demand that they should be verified in experience, if by experience is meant the real external world, which consists of ideas of perception, or that they should be brought before the eyes or the imagination like objects of perception. They can only be thought, not perceived, and only the effects which men accomplish through them are properly objects of experience. Such effects are language, preconceived and planned action and science, and all that results from these. Speech, as an object of outer experience, is obviously nothing more than a very complete telegraph, which communicates arbitrary signs with the greatest rapidity and the finest distinctions of difference. But what do these signs mean? How are they interpreted? When some one speaks, do we at once translate his words into pictures of the fancy, which instantaneously flash upon us, arrange and link themselves together, and a.s.sume form and colour according to the words that are poured forth, and their grammatical inflections? What a tumult there would be in our brains while we listened to a speech, or to the reading of a book? But what actually happens is not this at all. The meaning of a speech is, as a rule, immediately grasped, accurately and distinctly taken in, without the imagination being brought into play. It is reason which speaks to reason, keeping within its own province. It communicates and receives abstract conceptions, ideas that cannot be presented in perceptions, which are framed once for all, and are relatively few in number, but which yet encompa.s.s, contain, and represent all the innumerable objects of the actual world. This itself is sufficient to prove that the lower animals can never learn to speak or comprehend, although they have the organs of speech and ideas of perception in common with us. But because words represent this perfectly distinct cla.s.s of ideas, whose subjective correlative is reason, they are without sense and meaning for the brutes. Thus language, like every other manifestation which we ascribe to reason, and like everything which distinguishes man from the brutes, is to be explained from this as its one simple source-conceptions, abstract ideas which cannot be presented in perception, but are general, and have no individual existence in s.p.a.ce and time. Only in single cases do we pa.s.s from the conception to the perception, do we construct images as _representatives of concepts_ in perception, to which, however, they are never adequate. These cases are fully discussed in the essay on the principle of sufficient reason, -- 28, and therefore I shall not repeat my explanation here. It may be compared, however, with what is said by Hume in the twelfth of his "Philosophical Essays," p. 244, and by Herder in the "Metacritik," pt. i. p. 274 (an otherwise worthless book). The Platonic idea, the possibility of which depends upon the union of imagination and reason, is the princ.i.p.al subject of the third book of this work.

Although concepts are fundamentally different from ideas of perception, they stand in a necessary relation to them, without which they would be nothing. This relation therefore const.i.tutes the whole nature and existence of concepts. Reflection is the necessary copy or repet.i.tion of the originally presented world of perception, but it is a special kind of copy in an entirely different material. Thus concepts may quite properly be called ideas of ideas. The principle of sufficient reason has here also a special form. Now we have seen that the form under which the principle of sufficient reason appears in a cla.s.s of ideas always const.i.tutes and exhausts the whole nature of the cla.s.s, so far as it consists of ideas, so that time is throughout succession, and nothing more; s.p.a.ce is throughout position, and nothing more; matter is throughout causation, and nothing more. In the same way the whole nature of concepts, or the cla.s.s of abstract ideas, consists simply in the relation which the principle of sufficient reason expresses in them; and as this is the relation to the ground of knowledge, the whole nature of the abstract idea is simply and solely its relation to another idea, which is its ground of knowledge.

This, indeed, may, in the first instance, be a concept, an abstract idea, and this again may have only a similar abstract ground of knowledge; but the chain of grounds of knowledge does not extend _ad infinitum_; it must end at last in a concept which has its ground in knowledge of perception; for the whole world of reflection rests on the world of perception as its ground of knowledge. Hence the cla.s.s of abstract ideas is in this respect distinguished from other cla.s.ses; in the latter the principle of sufficient reason always demands merely a relation to another idea of the _same_ cla.s.s, but in the case of abstract ideas, it at last demands a relation to an idea of _another_ cla.s.s.

Those concepts which, as has just been pointed out, are not immediately related to the world of perception, but only through the medium of one, or it may be several other concepts, have been called by preference _abstracta_, and those which have their ground immediately in the world of perception have been called _concreta_. But this last name is only loosely applicable to the concepts denoted by it, for they are always merely _abstracta_, and not ideas of perception. These names, which have originated in a very dim consciousness of the distinctions they imply, may yet, with this explanation, be retained. As examples of the first kind of concepts, _i.e._, _abstracta_ in the fullest sense, we may take "relation," "virtue," "investigation," "beginning," and so on. As examples of the second kind, loosely called _concreta_, we may take such concepts as "man," "stone," "horse," &c. If it were not a somewhat too pictorial and therefore absurd simile, we might very appropriately call the latter the ground floor, and the former the upper stories of the building of reflection.(13)

It is not, as is commonly supposed, an essential characteristic of a concept that it should contain much under it, that is to say, that many ideas of perception, or it may be other abstract ideas, should stand to it in the relation of its ground of knowledge, _i.e._, be thought through it.

This is merely a derived and secondary characteristic, and, as a matter of fact, does not always exist, though it must always exist potentially. This characteristic arises from the fact that a concept is an idea of an idea, _i.e._, its whole nature consists in its relation to another idea; but as it is not this idea itself, which is generally an idea of perception and therefore belongs to quite a different cla.s.s, the latter may have temporal, s.p.a.cial, and other determinations, and in general many relations which are not thought along with it in the concept. Thus we see that several ideas which are different in unessential particulars may be thought by means of one concept, _i.e._, may be brought under it. Yet this power of embracing several things is not an essential but merely an accidental characteristic of the concept. There may be concepts through which only one real object is thought, but which are nevertheless abstract and general, by no means capable of presentation individually and as perceptions. Such, for example, is the conception which any one may have of a particular town which he only knows from geography; although only this one town is thought under it, it might yet be applied to several towns differing in certain respects. We see then that a concept is not general because of being abstracted from several objects; but conversely, because generality, that is to say, non-determination of the particular, belongs to the concept as an abstract idea of the reason, different things can be thought by means of the same one.

It follows from what has been said that every concept, just because it is abstract and incapable of presentation in perception, and is therefore not a completely determined idea, has what is called extension or sphere, even in the case in which only one real object exists that corresponds to it.

Now we always find that the sphere of one concept has something in common with the sphere of other concepts. That is to say, part of what is thought under one concept is the same as what is thought under other concepts; and conversely, part of what is thought under these concepts is the same as what is thought under the first; although, if they are really different concepts, each of them, or at least one of them, contains something which the other does not contain; this is the relation in which every subject stands to its predicate. The recognition of this relation is called judgment. The representation of these spheres by means of figures in s.p.a.ce, is an exceedingly happy idea. It first occurred to Gottfried Plouquet, who used squares for the purpose. Lambert, although later than him, used only lines, which he placed under each other. Euler carried out the idea completely with circles. Upon what this complete a.n.a.logy between the relations of concepts, and those of figures in s.p.a.ce, ultimately rests, I am unable to say. It is, however, a very fortunate circ.u.mstance for logic that all the relations of concepts, according to their possibility, _i.e._, _a priori_, may be made plain in perception by the use of such figures, in the following way:-

(1.) The spheres of two concepts coincide: for example the concept of necessity and the concept of following from given grounds, in the same way the concepts of _Ruminantia_ and _Bisulca_ (ruminating and cloven-hoofed animals), also those of vertebrate and red-blooded animals (although there might be some doubt about this on account of the annelida): they are convertible concepts. Such concepts are represented by a single circle which stands for either of them.

(2.) The sphere of one concept includes that of the other.

[Ill.u.s.tration: Category "horse" within category "animal".]

(3.) A sphere includes two or more spheres which exclude each other and fill it.

[Ill.u.s.tration: Circle divided into thirds "right", "acute", and "obtuse".]

(4.) Two spheres include each a part of the other.

[Ill.u.s.tration: Two overlapping circles, one "flower" and one "red".]

(5.) Two spheres lie in a third, but do not fill it.

[Ill.u.s.tration: A large circle, "matter", within which are two other circles, "water" and "earth".]

This last case applies to all concepts whose spheres have nothing immediately in common, for there is always a third sphere, often a much wider one, which includes both.

To these cases all combinations of concepts may be referred, and from them the entire doctrine of the judgment, its conversion, contraposition, equipollence, disjunction (this according to the third figure) may be deduced. From these also may be derived the properties of the judgment, upon which Kant based his pretended categories of the understanding, with the exception however of the hypothetical form, which is not a combination of concepts, but of judgments. A full account is given in the Appendix of "Modality," and indeed of every property of judgments on which the categories are founded.

With regard to the possible combinations of concepts which we have given, it has only further to be remarked that they may also be combined with each other in many ways. For example, the fourth figure with the second.

Only if one sphere, which partly or wholly contains another, is itself contained in a third sphere, do these together exemplify the syllogism in the first figure, _i.e._, that combination of judgments, by means of which it is known that a concept which is partly or wholly contained in another concept, is also contained in a third concept, which again contains the first: and also, conversely, the negation; the pictorial representation of which can, of course, only be two connected spheres which do not lie within a third sphere. If many spheres are brought together in this way we get a long train of syllogisms. This schematism of concepts, which has already been fairly well explained in more than one textbook, may be used as the foundation of the doctrine of the judgment, and indeed of the whole syllogistic theory, and in this way the treatment of both becomes very easy and simple. Because, through it, all syllogistic rules may be seen in their origin, and may be deduced and explained. It is not necessary, however, to load the memory with these rules, as logic is never of practical use, but has only a theoretical interest for philosophy. For although it may be said that logic is related to rational thinking as thorough-ba.s.s is to music, or less exactly, as ethics is to virtue, or aesthetics to art; we must yet remember that no one ever became an artist by the study of aesthetics; that a n.o.ble character was never formed by the study of ethics; that long before Rameau, men composed correctly and beautifully, and that we do not need to know thorough-ba.s.s in order to detect discords: and just as little do we need to know logic in order to avoid being misled by fallacies. Yet it must be conceded that thorough-ba.s.s is of the greatest use in the practice of musical composition, although it may not be necessary for the understanding of it; and indeed aesthetics and even ethics, though in a much less degree, and for the most part negatively, may be of some use in practice, so that we cannot deny them all practical worth, but of logic even this much cannot be conceded. It is nothing more than the knowledge in the abstract of what every one knows in the concrete. Therefore we call in the aid of logical rules, just as little to enable us to construct a correct argument as to prevent us from consenting to a false one, and the most learned logician lays aside the rules of logic altogether in his actual thought. This may be explained in the following way. Every science is a system of general and therefore abstract truths, laws, and rules with reference to a special cla.s.s of objects. The individual case coming under these laws is determined in accordance with this general knowledge, which is valid once for all; because such application of the general principle is far easier than the exhaustive investigation of the particular case; for the general abstract knowledge which has once been obtained is always more within our reach than the empirical investigation of the particular case. With logic, however, it is just the other way. It is the general knowledge of the mode of procedure of the reason expressed in the form of rules. It is reached by the introspection of reason, and by abstraction from all content. But this mode of procedure is necessary and essential to reason, so that it will never depart from it if left to itself. It is, therefore, easier and surer to let it proceed itself according to its nature in each particular case, than to present to it the knowledge abstracted from this procedure in the form of a foreign and externally given law. It is easier, because, while in the case of all other sciences, the general rule is more within our reach than the investigation of the particular case taken by itself; with the use of reason, on the contrary, its necessary procedure in a given case is always more within our reach than the general rule abstracted from it; for that which thinks in us is reason itself. It is surer, because a mistake may more easily occur in such abstract knowledge, or in its application, than that a process of reason should take place which would run contrary to its essence and nature. Hence arises the remarkable fact, that while in other sciences the particular case is always proved by the rule, in logic, on the contrary, the rule must always be proved from the particular case; and even the most practised logician, if he remark that in some particular case he concludes otherwise than the rule prescribes, will always expect to find a mistake in the rule rather than in his own conclusion. To desire to make practical use of logic means, therefore, to desire to derive with unspeakable trouble, from general rules, that which is immediately known with the greatest certainty in the particular case. It is just as if a man were to consult mechanics as to the motion of his body, and physiology as to his digestion; and whoever has learnt logic for practical purposes is like him who would teach a beaver to make its own dam. Logic is, therefore, without practical utility; but it must nevertheless be retained, because it has philosophical interest as the special knowledge of the organisation and action of reason. It is rightly regarded as a definite, self-subsisting, self-contained, complete, and thoroughly safe discipline; to be treated scientifically for itself alone and independently of everything else, and therefore to be studied at the universities. But it has its real value, in relation to philosophy as a whole, in the inquiry into the nature of knowledge, and indeed of rational and abstract knowledge. Therefore the exposition of logic should not have so much the form of a practical science, should not contain merely naked arbitrary rules for the correct formation of the judgment, the syllogism, &c., but should rather be directed to the knowledge of the nature of reason and the concept, and to the detailed investigation of the principle of sufficient reason of knowing. For logic is only a paraphrase of this principle, and, more exactly, only of that exemplification of it in which the ground that gives truth to the judgment is neither empirical nor metaphysical, but logical or metalogical. Besides the principle of sufficient reason of knowing, it is necessary to take account of the three remaining fundamental laws of thought, or judgments of metalogical truth, so nearly related to it; and out of these the whole science of reason grows. The nature of thought proper, that is to say, of the judgment and the syllogism, must be exhibited in the combination of the spheres of concepts, according to the a.n.a.logy of the special schema, in the way shown above; and from all this the rules of the judgment and the syllogism are to be deduced by construction. The only practical use we can make of logic is in a debate, when we can convict our antagonist of his intentional fallacies, rather than of his actual mistakes, by giving them their technical names. By thus throwing into the background the practical aim of logic, and bringing out its connection with the whole scheme of philosophy as one of its chapters, we do not think that we shall make the study of it less prevalent than it is just now. For at the present day every one who does not wish to remain uncultured, and to be numbered with the ignorant and incompetent mult.i.tude, must study speculative philosophy. For the nineteenth century is a philosophical age, though by this we do not mean either that it has philosophy, or that philosophy governs it, but rather that it is ripe for philosophy, and, therefore, stands in need of it. This is a sign of a high degree of civilisation, and indeed, is a definite stage in the culture of the ages.(14)

Though logic is of so little practical use, it cannot be denied that it was invented for practical purposes. It appears to me to have originated in the following way:-As the love of debating developed among the Eleatics, the Megarics, and the Sophists, and by degrees became almost a pa.s.sion, the confusion in which nearly every debate ended must have made them feel the necessity of a method of procedure as a guide; and for this a scientific dialectic had to be sought. The first thing which would have to be observed would be that both the disputing parties should always be agreed on some one proposition, to which the disputed points might be referred. The beginning of the methodical procedure consisted in this, that the propositions admitted on both sides were formally stated to be so, and placed at the head of the inquiry. But these propositions were at first concerned only with the material of the inquiry. It was soon observed that in the process of going back to the truth admitted on both sides, and of deducing their a.s.sertions from it, each party followed certain forms and laws about which, without any express agreement, there was no difference of opinion. And from this it became evident that these must const.i.tute the peculiar and natural procedure of reason itself, the form of investigation. Although this was not exposed to any doubt or difference of opinion, some pedantically systematic philosopher hit upon the idea that it would look well, and be the completion of the method of dialectic, if this formal part of all discussion, this regular procedure of reason itself, were to be expressed in abstract propositions, just like the substantial propositions admitted on both sides, and placed at the beginning of every investigation, as the fixed canon of debate to which reference and appeal must always be made. In this way what had formerly been followed only by tacit agreement, and instinctively, would be consciously recognised and formally expressed. By degrees, more or less perfect expressions were found for the fundamental principles of logic, such as the principles of contradiction, sufficient reason, excluded middle, the _dictum de omni et nullo_, as well as the special rules of the syllogism, as for example, _ex meris particularibus aut negativis nihil sequitur, a rationato ad rationem non valet consequentia_, and so on. That all this was only brought about slowly, and with great pains, and up till the time of Aristotle remained very incomplete, is evident from the awkward and tedious way in which logical truths are brought out in many of the Platonic dialogues, and still more from what s.e.xtus Empiricus tells us of the controversies of the Megarics, about the easiest and simplest logical rules, and the laborious way in which they were brought into a definite form (s.e.xt. Emp. adv. Math. l. 8, p. 112). But Aristotle collected, arranged, and corrected all that had been discovered before his time, and brought it to an incomparably greater state of perfection. If we thus observe how the course of Greek culture had prepared the way for, and led up to the work of Aristotle, we shall be little inclined to believe the a.s.sertion of the Persian author, quoted by Sir William Jones with much approval, that Kallisthenes found a complete system of logic among the Indians, and sent it to his uncle Aristotle (Asiatic Researches, vol. iv.

p. 163). It is easy to understand that in the dreary middle ages the Aristotelian logic would be very acceptable to the controversial spirit of the schoolmen, which, in the absence of all real knowledge, spent its energy upon mere formulas and words, and that it would be eagerly adopted even in its mutilated Arabian form, and presently established as the centre of all knowledge. Though its authority has since declined, yet up to our own time logic has retained the credit of a self-contained, practical, and highly important science. Indeed, in our own day, the Kantian philosophy, the foundation-stone of which is taken from logic, has excited a new interest in it; which, in this respect, at any rate, that is, as the means of the knowledge of the nature of reason, it deserves.

Correct and accurate conclusions may be arrived at if we carefully observe the relation of the spheres of concepts, and only conclude that one sphere is contained in a third sphere, when we have clearly seen that this first sphere is contained in a second, which in its turn is contained in the third. On the other hand, the art of sophistry lies in casting only a superficial glance at the relations of the spheres of the concepts, and then manipulating these relations to suit our purposes, generally in the following way:-When the sphere of an observed concept lies partly within that of another concept, and partly within a third altogether different sphere, we treat it as if it lay entirely within the one or the other, as may suit our purpose. For example, in speaking of pa.s.sion, we may subsume it under the concept of the greatest force, the mightiest agency in the world, or under the concept of the irrational, and this again under the concept of impotency or weakness. We may then repeat the process, and start anew with each concept to which the argument leads us. A concept has almost always several others, which partially come under it, and each of these contains part of the sphere of the first, but also includes in its own sphere something more, which is not in the first. But we draw attention only to that one of these latter concepts, under which we wish to subsume the first, and let the others remain un.o.bserved, or keep them concealed. On the possession of this skill depends the whole art of sophistry and all finer fallacies; for logical fallacies such as _mentiens_, _velatus_, _cornatus_, &c., are clearly too clumsy for actual use. I am not aware that hitherto any one has traced the nature of all sophistry and persuasion back to this last possible ground of its existence, and referred it to the peculiar character of concepts, _i.e._, to the procedure of reason itself. Therefore, as my exposition has led me to it, though it is very easily understood, I will ill.u.s.trate it in the following table by means of a schema. This table is intended to show how the spheres of concepts overlap each other at many points, and so leave room for a pa.s.sage from each concept to whichever one we please of several other concepts. I hope, however, that no one will be led by this table to attach more importance to this little explanation, which I have merely given in pa.s.sing, than ought to belong to it, from the nature of the subject. I have chosen as an ill.u.s.tration the concept of travelling. Its sphere partially includes four others, to any of which the sophist may pa.s.s at will; these again partly include other spheres, several of them two or more at once, and through these the sophist takes whichever way he chooses, always as if it were the only way, till at last he reaches, in good or evil, whatever end he may have in view. In pa.s.sing from one sphere to another, it is only necessary always to follow the direction from the centre (the given chief concept) to the circ.u.mference, and never to reverse this process. Such a piece of sophistry may be either an unbroken speech, or it may a.s.sume the strict syllogistic form, according to what is the weak side of the hearer. Most scientific arguments, and especially philosophical demonstrations, are at bottom not much more than this, for how else would it be possible, that so much, in different ages, has not only been falsely apprehended (for error itself has a different source), but demonstrated and proved, and has yet afterwards been found to be fundamentally wrong, for example, the Leibnitz-Wolfian Philosophy, Ptolemaic Astronomy, Stahl's Chemistry, Newton's Theory of Colours, &c.

&c.(15)

-- 10. Through all this, the question presses ever more upon us, how _certainty_ is to be attained, how _judgments __ are to be established_, what const.i.tutes _rational knowledge_, (_wissen_), and _science_, which we rank with language and deliberate action as the third great benefit conferred by reason.

Reason is feminine in nature; it can only give after it has received. Of itself it has nothing but the empty forms of its operation. There is no absolutely pure rational knowledge except the four principles to which I have attributed metalogical truth; the principles of ident.i.ty, contradiction, excluded middle, and sufficient reason of knowledge. For even the rest of logic is not absolutely pure rational knowledge. It presupposes the relations and the combinations of the spheres of concepts.

But concepts in general only exist after experience of ideas of perception, and as their whole nature consists in their relation to these, it is clear that they presuppose them. No special content, however, is presupposed, but merely the existence of a content generally, and so logic as a whole may fairly pa.s.s for pure rational science. In all other sciences reason has received its content from ideas of perception; in mathematics from the relations of s.p.a.ce and time, presented in intuition or perception prior to all experience; in pure natural science, that is, in what we know of the course of nature prior to any experience, the content of the science proceeds from the pure understanding, _i.e._, from the _a priori_ knowledge of the law of causality and its connection with those pure intuitions or perceptions of s.p.a.ce and time. In all other sciences everything that is not derived from the sources we have just referred to belongs to experience. Speaking generally, _to know rationally_ (_wissen_) means to have in the power of the mind, and capable of being reproduced at will, such judgments as have their sufficient ground of knowledge in something outside themselves, _i.e._, are true.

Thus only abstract cognition is _rational knowledge_ (_wissen_), which is therefore the result of reason, so that we cannot accurately say of the lower animals that they _rationally __ know_ (_wissen_) anything, although they have apprehension of what is presented in perception, and memory of this, and consequently imagination, which is further proved by the circ.u.mstance that they dream. We attribute consciousness to them, and therefore although the word (_bewusstsein_) is derived from the verb to know rationally (_wissen_), the conception of consciousness corresponds generally with that of idea of whatever kind it may be. Thus we attribute life to plants, but not consciousness. _Rational knowledge_ (_wissen_) is therefore abstract consciousness, the permanent possession in concepts of the reason, of what has become known in another way.

-- 11. In this regard the direct opposite of _rational knowledge_ is feeling, and therefore we must insert the explanation of feeling here. The concept which the word feeling denotes has merely a negative content, which is this, that something which is present in consciousness, _is not a concept_, _is not abstract rational knowledge_. Except this, whatever it may be, it comes under the concept of _feeling_. Thus the immeasurably wide sphere of the concept of feeling includes the most different kinds of objects, and no one can ever understand how they come together until he has recognised that they all agree in this negative respect, that they are not _abstract concepts_. For the most diverse and even antagonistic elements lie quietly side by side in this concept; for example, religious feeling, feeling of sensual pleasure, moral feeling, bodily feeling, as touch, pain, sense of colour, of sounds and their harmonies and discords, feeling of hate, of disgust, of self-satisfaction, of honour, of disgrace, of right, of wrong, sense of truth, aesthetic feeling, feeling of power, weakness, health, friendship, love, &c. &c. There is absolutely nothing in common among them except the negative quality that they are not abstract rational knowledge. But this diversity becomes more striking when the apprehension of s.p.a.ce relations presented _a priori_ in perception, and also the knowledge of the pure understanding is brought under this concept, and when we say of all knowledge and all truth, of which we are first conscious only intuitively, and have not yet formulated in abstract concepts, we _feel_ it. I should like, for the sake of ill.u.s.tration, to give some examples of this taken from recent books, as they are striking proofs of my theory. I remember reading in the introduction to a German translation of Euclid, that we ought to make beginners in geometry draw the figures before proceeding to demonstrate, for in this way they would already feel geometrical truth before the demonstration brought them complete knowledge. In the same way Schleiermacher speaks in his "Critique of Ethics" of logical and mathematical feeling (p. 339), and also of the feeling of the sameness or difference of two formulas (p. 342). Again Tennemann in his "History of Philosophy" (vol. I., p. 361) says, "One _felt_ that the fallacies were not right, but could not point out the mistakes." Now, so long as we do not regard this concept "_feeling_" from the right point of view, and do not recognise that one negative characteristic which alone is essential to it, it must constantly give occasion for misunderstanding and controversy, on account of the excessive wideness of its sphere, and its entirely negative and very limited content which is determined in a purely one-sided manner. Since then we have in German the nearly synonymous word _empfindung_ (sensation), it would be convenient to make use of it for bodily feeling, as a sub-species. This concept "feeling," which is quite out of proportion to all others, doubtless originated in the following manner. All concepts, and concepts alone, are denoted by words; they exist only for the reason, and proceed from it. With concepts, therefore, we are already at a one-sided point of view; but from such a point of view what is near appears distinct and is set down as positive, what is farther off becomes mixed up and is soon regarded as merely negative. Thus each nation calls all others foreign: to the Greek all others are barbarians; to the Englishman all that is not England or English is continent or continental; to the believer all others are heretics, or heathens; to the n.o.ble all others are _roturiers_; to the student all others are Philistines, and so forth. Now, reason itself, strange as it may seem, is guilty of the same one-sidedness, indeed one might say of the same crude ignorance arising from vanity, for it cla.s.ses under the one concept, "_feeling_," every modification of consciousness which does not immediately belong to its own mode of apprehension, that is to say, which is _not an abstract concept_. It has had to pay the penalty of this. .h.i.therto in misunderstanding and confusion in its own province, because its own procedure had not become clear to it through thorough self-knowledge, for a special faculty of feeling has been set up, and new theories of it are constructed.

-- 12. _Rational knowledge_ (_wissen_) is then all abstract knowledge,-that is, the knowledge which is peculiar to the reason as distinguished from the understanding. Its contradictory opposite has just been explained to be the concept "feeling." Now, as reason only reproduces, for knowledge, what has been received in another way, it does not actually extend our knowledge, but only gives it another form. It enables us to know in the abstract and generally, what first became known in sense-perception, in the concrete. But this is much more important than it appears at first sight when so expressed. For it depends entirely upon the fact that knowledge has become rational or abstract knowledge (_wissen_), that it can be safely preserved, that it is communicable and susceptible of certain and wide-reaching application to practice. Knowledge in the form of sense-perception is valid only of the particular case, extends only to what is nearest, and ends with it, for sensibility and understanding can only comprehend one object at a time. Every enduring, arranged, and planned activity must therefore proceed from principles,-that is, from abstract knowledge, and it must be conducted in accordance with them.

Thus, for example, the knowledge of the relation of cause and effect arrived at by the understanding, is in itself far completer, deeper and more exhaustive than anything that can be thought about it in the abstract; the understanding alone knows in perception directly and completely the nature of the effect of a lever, of a pulley, or a cog-wheel, the stability of an arch, and so forth. But on account of the peculiarity of the knowledge of perception just referred to, that it only extends to what is immediately present, the mere understanding can never enable us to construct machines and buildings. Here reason must come in; it must subst.i.tute abstract concepts for ideas of perception, and take them as the guide of action; and if they are right, the antic.i.p.ated result will happen. In the same way we have perfect knowledge in pure perception of the nature and const.i.tution of the parabola, hyperbola, and spiral; but if we are to make trustworthy application of this knowledge to the real, it must first become abstract knowledge, and by this it certainly loses its character of intuition or perception, but on the other hand it gains the certainty and preciseness of abstract knowledge. The differential calculus does not really extend our knowledge of the curve, it contains nothing that was not already in the mere pure perception of the curve; but it alters the kind of knowledge, it changes the intuitive into an abstract knowledge, which is so valuable for application. But here we must refer to another peculiarity of our faculty of knowledge, which could not be observed until the distinction between the knowledge of the senses and understanding and abstract knowledge had been made quite clear. It is this, that relations of s.p.a.ce cannot as such be directly translated into abstract knowledge, but only temporal quant.i.ties,-that is, numbers, are suitable for this. Numbers alone can be expressed in abstract concepts which accurately correspond to them, not s.p.a.cial quant.i.ties. The concept "thousand" is just as different from the concept "ten," as both these temporal quant.i.ties are in perception. We think of a thousand as a distinct multiple of ten, into which we can resolve it at pleasure for perception in time,-that is to say, we can count it. But between the abstract concept of a mile and that of a foot, apart from any concrete perception of either, and without the help of number, there is no accurate distinction corresponding to the quant.i.ties themselves. In both we only think of a s.p.a.cial quant.i.ty in general, and if they must be completely distinguished we are compelled either to call in the a.s.sistance of intuition or perception in s.p.a.ce, which would be a departure from abstract knowledge, or we must think the difference in _numbers_. If then we wish to have abstract knowledge of s.p.a.ce-relations we must first translate them into time-relations,-that is, into numbers; therefore only arithmetic, and not geometry, is the universal science of quant.i.ty, and geometry must be translated into arithmetic if it is to be communicable, accurately precise and applicable in practice. It is true that a s.p.a.ce-relation as such may also be thought in the abstract; for example, "the sine increases as the angle," but if the quant.i.ty of this relation is to be given, it requires number for its expression. This necessity, that if we wish to have abstract knowledge of s.p.a.ce-relations (_i.e._, rational knowledge, not mere intuition or perception), s.p.a.ce with its three dimensions must be translated into time which has only one dimension, this necessity it is, which makes mathematics so difficult. This becomes very clear if we compare the perception of curves with their a.n.a.lytical calculation, or the table of logarithms of the trigonometrical functions with the perception of the changing relations of the parts of a triangle, which are expressed by them. What vast mazes of figures, what laborious calculations it would require to express in the abstract what perception here apprehends at a glance completely and with perfect accuracy, namely, how the co-sine diminishes as the sine increases, how the co-sine of one angle is the sine of another, the inverse relation of the increase and decrease of the two angles, and so forth. How time, we might say, must complain, that with its one dimension it should be compelled to express the three dimensions of s.p.a.ce! Yet this is necessary if we wish to possess, for application, an expression, in abstract concepts, of s.p.a.ce-relations. They could not be translated directly into abstract concepts, but only through the medium of the pure temporal quant.i.ty, number, which alone is directly related to abstract knowledge. Yet it is worthy of remark, that as s.p.a.ce adapts itself so well to perception, and by means of its three dimensions, even its complicated relations are easily apprehended, while it eludes the grasp of abstract knowledge; time, on the contrary, pa.s.ses easily into abstract knowledge, but gives very little to perception. Our perceptions of numbers in their proper element, mere time, without the help of s.p.a.ce, scarcely extends as far as ten, and beyond that we have only abstract concepts of numbers, no knowledge of them which can be presented in perception. On the other hand, we connect with every numeral, and with all algebraical symbols, accurately defined abstract concepts.

We may further remark here that some minds only find full satisfaction in what is known through perception. What they seek is the reason and consequent of being in s.p.a.ce, sensuously expressed; a demonstration after the manner of Euclid, or an arithmetical solution of s.p.a.cial problems, does not please them. Other minds, on the contrary, seek merely the abstract concepts which are needful for applying and communicating knowledge. They have patience and memory for abstract principles, formulas, demonstrations in long trains of reasoning, and calculations, in which the symbols represent the most complicated abstractions. The latter seek preciseness, the former sensible perception. The difference is characteristic.

The greatest value of rational or abstract knowledge is that it can be communicated and permanently retained. It is princ.i.p.ally on this account that it is so inestimably important for practice. Any one may have a direct perceptive knowledge through the understanding alone, of the causal connection, of the changes and motions of natural bodies, and he may find entire satisfaction in it; but he cannot communicate this knowledge to others until it has been made permanent for thought in concepts. Knowledge of the first kind is even sufficient for practice, if a man puts his knowledge into practice himself, in an action which can be accomplished while the perception is still vivid; but it is not sufficient if the help of others is required, or even if the action is his own but must be carried out at different times, and therefore requires a pre-conceived plan. Thus, for example, a practised billiard-player may have a perfect knowledge of the laws of the impact of elastic bodies upon each other, merely in the understanding, merely for direct perception; and for him it is quite sufficient; but on the other hand it is only the man who has studied the science of mechanics, who has, properly speaking, a rational knowledge of these laws, that is, a knowledge of them in the abstract.

Such knowledge of the understanding in perception is sufficient even for the construction of machines, when the inventor of the machine executes the work himself; as we often see in the case of talented workmen, who have no scientific knowledge. But whenever a number of men, and their united action taking place at different times, is required for the completion of a mechanical work, of a machine, or a building, then he who conducts it must have thought out the plan in the abstract, and such co-operative activity is only possible through the a.s.sistance of reason.

It is, however, remarkable that in the first kind of activity, in which we have supposed that one man alone, in an uninterrupted course of action, accomplishes something, abstract knowledge, the application of reason or reflection, may often be a hindrance to him; for example, in the case of billiard-playing, of fighting, of tuning an instrument, or in the case of singing. Here perceptive knowledge must directly guide action; its pa.s.sage through reflection makes it uncertain, for it divides the attention and confuses the man. Thus savages and untaught men, who are little accustomed to think, perform certain physical exercises, fight with beasts, shoot with bows and arrows and the like, with a certainty and rapidity which the reflecting European never attains to, just because his deliberation makes him hesitate and delay. For he tries, for example, to hit the right position or the right point of time, by finding out the mean between two false extremes; while the savage hits it directly without thinking of the false courses open to him. In the same way it is of no use to me to know in the abstract the exact angle, in degrees and minutes, at which I must apply a razor, if I do not know it intuitively, that is, if I have not got it in my touch. The knowledge of physiognomy also, is interfered with by the application of reason. This knowledge must be gained directly through the understanding. We say that the expression, the meaning of the features, can only be _felt_, that is, it cannot be put into abstract concepts. Every man has his direct intuitive method of physiognomy and pathognomy, yet one man understands more clearly than another these _signatura rerum_. But an abstract science of physiognomy to be taught and learned is not possible; for the distinctions of difference are here so fine that concepts cannot reach them; therefore abstract knowledge is related to them as a mosaic is to a painting by a Van der Werft or a Denner. In mosaics, however fine they may be, the limits of the stones are always there, and therefore no continuous pa.s.sage from one colour to another is possible, and this is also the case with regard to concepts, with their rigidity and sharp delineation; however finely we may divide them by exact definition, they are still incapable of reaching the finer modifications of the perceptible, and this is just what happens in the example we have taken, knowledge of physiognomy.(16)

This quality of concepts by which they resemble the stones of a mosaic, and on account of which perception always remains their asymptote, is also the reason why nothing good is produced in art by their means. If the singer or the virtuoso attempts to guide his execution by reflection he remains silent. And this is equally true of the composer, the painter, and the poet. The concept always remains unfruitful in art; it can only direct the technical part of it, its sphere is science. We shall consider more fully in the third book, why all true art proceeds from sensuous knowledge, never from the concept. Indeed, with regard to behaviour also, and personal agreeableness in society, the concept has only a negative value in restraining the grosser manifestations of egotism and brutality; so that a polished manner is its commendable production. But all that is attractive, gracious, charming in behaviour, all affectionateness and friendliness, must not proceed from the concepts, for if it does, "we feel intention, and are put out of tune." All dissimulation is the work of reflection; but it cannot be maintained constantly and without interruption: "_nemo __ potest personam diu ferre fictum_," says Seneca in his book _de clementia_; and so it is generally found out and loses its effect. Reason is needed in the full stress of life, where quick conclusions, bold action, rapid and sure comprehension are required, but it may easily spoil all if it gains the upper hand, and by perplexing hinders the intuitive, direct discovery, and grasp of the right by simple understanding, and thus induces irresolution.

Lastly, virtue and holiness do not proceed from reflection, but from the inner depths of the will, and its relation to knowledge. The exposition of this belongs to another part of our work; this, however, I may remark here, that the dogmas relating to ethics may be the same in the reason of whole nations, but the action of every individual different; and the converse also holds good; action, we say, is guided by _feelings_,-that is, simply not by concepts, but as a matter of fact by the ethical character. Dogmas occupy the idle reason; but action in the end pursues its own course independently of them, generally not according to abstract rules, but according to unspoken maxims, the expression of which is the whole man himself. Therefore, however different the religious dogmas of nations may be, yet in the case of all of them, a good action is accompanied by unspeakable satisfaction, and a bad action by endless remorse. No mockery can shake the former; no priest's absolution can deliver from the latter. Notwithstanding this, we must allow, that for the pursuit of a virtuous life, the application of reason is needful; only it is not its source, but has the subordinate function of preserving resolutions which have been made, of providing maxims to withstand the weakness of the moment, and give consistency to action. It plays the same part ultimately in art also, where it has just as little to do with the essential matter, but a.s.sists in carrying it out, for genius is not always at call, and yet the work must be completed in all its parts and rounded off to a whole.(17)

-- 13. All these discussions of the advantages and disadvantages of the application of reason are intended to show, that although abstract rational knowledge is the reflex of ideas of perception, and is founded on them, it is by no means in such entire congruity with them that it could everywhere take their place: indeed it never corresponds to them quite accurately. And thus, as we have seen, many human actions can only be performed by the help of reason and deliberation, and yet there are some which are better performed without its a.s.sistance. This very incongruity of sensuous and abstract knowledge, on account of which the latter always merely approximates to the former, as mosaic approximates to painting, is the cause of a very remarkable phenomenon which, like reason itself, is peculiar to human nature, and of which the explanations that have ever anew been attempted, are insufficient: I mean _laughter_. On account of the source of this phenomenon, we cannot avoid giving the explanation of it here, though it again interrupts the course of our work to do so. The cause of laughter in every case is simply the sudden perception of the incongruity between a concept and the real objects which have been thought through it in some relation, and laughter itself is just the expression of this incongruity. It often occurs in this way: two or more real objects are thought through _one_ concept, and the ident.i.ty of the concept is transferred to the objects; it then becomes strikingly apparent from the entire difference of the objects in other respects, that the concept was only applicable to them from a one-sided point of view. It occurs just as often, however, that the incongruity between a single real object and the concept under which, from one point of view, it has rightly been subsumed, is suddenly felt. Now the more correct the subsumption of such objects under a concept may be from one point of view, and the greater and more glaring their incongruity with it, from another point of view, the greater is the ludicrous effect which is produced by this contrast. All laughter then is occasioned by a paradox, and therefore by unexpected subsumption, whether this is expressed in words or in actions. This, briefly stated, is the true explanation of the ludicrous.

I shall not pause here to relate anecdotes as examples to ill.u.s.trate my theory; for it is so simple and comprehensible that it does not require them, and everything ludicrous which the reader may remember is equally valuable as a proof of it. But the theory is confirmed and ill.u.s.trated by distinguishing two species into which the ludicrous is divided, and which result from the theory. Either, we have previously known two or more very different real objects, ideas of sense-perception, and have intentionally identified them through the unity of a concept which comprehends them both; this species of the ludicrous is called _wit_. Or, conversely, the concept is first present in knowledge, and we pa.s.s from it to reality, and to operation upon it, to action: objects which in other respects are fundamentally different, but which are all thought in that one concept, are now regarded and treated in the same way, till, to the surprise and astonishment of the person acting, the great difference of their other aspects appears: this species of the ludicrous is called _folly_.

Therefore everything ludicrous is either a flash of wit or a foolish action, according as the procedure has been from the discrepancy of the objects to the ident.i.ty of the concept, or the converse; the former always intentional, the latter always unintentional, and from without. To seem to reverse the starting-point, and to conceal wit with the mask of folly, is the art of the jester and the clown. Being quite aware of the diversity of the objects, the jester unites them, with secret wit, under one concept, and then starting from this concept he receives from the subsequently discovered diversity of the objects the surprise which he himself prepared. It follows from this short but sufficient theory of the ludicrous, that, if we set aside the last case, that of the jester, wit must always show itself in words, folly generally in actions, though also in words, when it only expresses an intention and does not actually carry it out, or when it shows itself merely in judgments and opinions.

_Pedantry_ is a form of folly. It arises in this way: a man lacks confidence in his own understanding, and, therefore, does not wish to trust to it, to recognise what is right directly in the particular case.

He, therefore, puts it entirely under the control of the reason, and seeks to be guided by reason in everything; that is to say, he tries always to proceed from general concepts, rules, and maxims, and to confine himself strictly to them in life, in art, and even in moral conduct. Hence that clinging to the form, to the manner, to the expression and word which is characteristic of pedantry, and which with it takes the place of the real nature of the matter. The incongruity then between the concept and reality soon shows itself here, and it becomes evident that the former never condescends to the particular case, and that with its generality and rigid definiteness it can never accurately apply to the fine distinctions of difference and innumerable modifications of the actual. Therefore, the pedant, with his general maxims, almost always misses the mark in life, shows himself to be foolish, awkward, useless. In art, in which the concept is unfruitful, he produces lifeless, stiff, abortive mannerisms.

Even with regard to ethics, the purpose to act rightly or n.o.bly cannot always be carried out in accordance with abstract maxims; for in many cases the excessively nice distinctions in the nature of the circ.u.mstances necessitate a choice of the right proceeding directly from the character; for the application of mere abstract maxims sometimes gives false results, because the maxims only half apply; and sometimes cannot be carried out, because they are foreign to the individual character of the actor, and this never allows itself to be entirely discovered; therefore, inconsistencies arise. Since then Kant makes it a condition of the moral worth of an action, that it shall proceed from pure rational abstract maxims, without any inclination or momentary emotion, we cannot entirely absolve him from the reproach of encouraging moral pedantry. This reproach is the significance of Schiller's epigram, ent.i.tled "Scruples of Conscience." When we speak, especially in connection with politics, of doctrinaires, theorists, savants, and so forth, we mean pedants, that is, persons who know the things well in the abstract, but not in the concrete.

Abstraction consists in thinking away the less general predicates; but it is precisely upon these that so much depends in practice.

To complete our theory it remains for us to mention a spurious kind of wit, the play upon words, the _calembourg_, the pun, to which may be added the equivocation, the _double entendre_, the chief use of which is the expression of what is obscene. Just as the witticism brings two very different real objects under one concept, the pun brings two different concepts, by the a.s.sistance of accident, under one word. The same contrast appears, only familiar and more superficial, because it does not spring from the nature of things, but merely from the accident of nomenclature.

In the case of the witticism the ident.i.ty is in the concept, the difference in the reality, but in the case of the pun the difference is in the concepts and the ident.i.ty in the reality, for the terminology is here the reality. It would only be a somewhat far-fetched comparison if we were to say that the pun is related to the witticism as the parabola (_sic_) of the upper inverted cone to that of the lower. The misunderstanding of the word or the _quid pro quo_ is the unintentional pun, and is related to it exactly as folly is to wit. Thus the deaf man often affords occasion for laughter, just as much as the fool, and inferior writers of comedy often use the former for the latter to raise a laugh.

I have treated laughter here only from the psychical side; with regard to the physical side, I refer to what is said on the subject in the "Parerga," vol. II. ch. vi., -- 98.(18)

-- 14. By means of these various discussions it is hoped that both the difference and the relation between the process of knowledge that belongs to the reason, rational knowledge, the concept on the one hand, and the direct knowledge in purely sensuous, mathematical intuition or perception, and apprehension by the understanding on the other hand, has been clearly brought out. This remarkable relation of our kinds of knowledge led us almost inevitably to give, in pa.s.sing, explanations of feeling and of laughter, but from all this we now turn back to the further consideration of science as the third great benefit which reason confers on man, the other two being speech and deliberate action. The general discussion of science which now devolves upon us, will be concerned partly with its form, partly with the foundation of its judgments, and lastly with its content.

We have seen that, with the exception of the basis of pure logic, rational knowledge in general has not its source in the reason itself; but having been otherwise obtained as knowledge of perception, it is stored up in the reason, for through reason it has entirely changed its character, and has become abstract knowledge. All rational knowledge, that is, knowledge that has been raised to consciousness in the abstract, is related to science strictly so called, as a fragment to the whole. Every one has gained a rational knowledge of many different things through experience, through consideration of the individual objects presented to him, but only he who sets himself the task of acquiring a complete knowledge in the abstract of a particular cla.s.s of objects, strives after science. This cla.s.s can only be marked off by means of a concept; therefore, at the beginning of every science there stands a concept, and by means of it the cla.s.s of objects concerning which this science promises a complete knowledge in the abstract, is separated in thought from the whole world of things. For example, the concept of s.p.a.ce-relations, or of the action of unorganised bodies upon each other, or of the nature of plants, or of animals, or of the successive changes of the surface of the globe, or of the changes of the human race as a whole, or of the construction of a language, and so forth. If science sought to obtain the knowledge of its object, by investigating each individual thing that is thought through the concept, till by degrees it had learned the whole, no human memory would be equal to the task, and no certainty of completeness would be obtainable.

Therefore, it makes use of that property of concept-spheres explained above, that they include each other, and it concerns itself mainly with the wider spheres which lie within the concept of its object in general.

When the relations of these spheres to each other have been determined, all that is thought in them is also generally determined, and can now be more and more accurately determined by the separation of smaller and smaller concept-spheres. In this way it is possible for a science to comprehend its object completely. This path which it follows to knowledge, the path from the general to the particular, distinguishes it from ordinary rational knowledge; therefore, systematic form is an essential and characteristic feature of science. The combination of the most general concept-spheres of every science, that is, the knowledge of its first principles, is the indispensable condition of mastering it; how far we advance from these to the more special propositions is a matter of choice, and does not increase the thoroughness but only the extent of our knowledge of the science. The number of the first principles to which all the rest are subordinated, varies greatly in the different sciences, so that in some there is more subordination, in others more co-ordination; and in this respect, the former make greater claims upon the judgment, the latter upon the memory. It was known to the schoolmen,(19) that, as the syllogism requires two premises, no science can proceed from a single first principle which cannot be the subject of further deduction, but must have several, at least two. The specially cla.s.sifying sciences: Zoology, Botany, and also Physics and Chemistry, inasmuch as they refer all inorganic action to a few fundamental forces, have most subordination; history, on the other hand, has really none at all; for the general in it consists merely in the survey of the princ.i.p.al periods, from which, however, the particular events cannot be deduced, and are only subordinated to them according to time, but according to the concept are co-ordinate with them. Therefore, history, strictly speaking, is certainly rational knowledge, but is not science. In mathematics, according to Euclid's treatment, the axioms alone are indemonstrable first principles, and all demonstrations are in gradation strictly subordinated to them. But this method of treatment is not essential to mathematics, and in fact each proposition introduces quite a new s.p.a.ce construction, which in itself is independent of those which precede it, and indeed can be completely comprehended from itself, quite independently of them, in the pure intuition or perception of s.p.a.ce, in which the most complicated construction is just as directly evident as the axiom; but of this more fully hereafter.