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. [pg 057] 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-bass is to music, or less exactly, as ethics is to virtue, or æsthetics to art; we must yet remember that no one ever became an artist by the study of æsthetics; that a noble character was never [pg 058] formed by the study of ethics; that long before Rameau, men composed correctly and beautifully, and that we do not need to know thorough-bass 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-bass is of the greatest use in the practice of musical composition, although it may not be necessary for the understanding of it; and indeed æsthetics 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 class 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 [pg 059] 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 [pg 060] 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 analogy 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 multitude, 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 [pg 061] 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 passion, 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 assertions 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 constitute 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 [pg 062] 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 Sextus 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 (Sext. 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 assertion 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 [pg 063] 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 passion, 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 unobserved, 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 [pg 064] 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 illustrate 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 passage 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 passing, than ought to belong to it, from the nature of the subject. I have chosen as an illustration the concept of travelling. Its sphere partially includes four others, to any of which the sophist may pass 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 passing from one sphere to another, it is only necessary always to follow the direction from the centre (the given chief concept) to the circumference, and never to reverse this process. Such a piece of sophistry may be either an unbroken speech, or it may assume 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 [pg 065]are to be established, what constitutes 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 identity, 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 pass for pure rational science. In all other sciences reason has received its content from ideas of perception; in mathematics from the relations of space 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 space 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 [pg 066]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 circumstance 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, æsthetic 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 space relations presented a priori in perception, and also the [pg 067] 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 illustration, 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 [pg 068] 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 noble 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 classes 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 hitherto 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 [pg 069] 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 substitute abstract concepts for ideas of perception, and take them as the guide of action; and if they are right, the anticipated result will happen. In the same way we have perfect knowledge in pure perception of the nature and constitution 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 space cannot as such be directly translated into abstract knowledge, but only temporal quantities,—that is, numbers, are suitable for this. [pg 070] Numbers alone can be expressed in abstract concepts which accurately correspond to them, not spacial quantities. The concept “thousand” is just as different from the concept “ten,” as both these temporal quantities 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 quantities themselves. In both we only think of a spacial quantity in general, and if they must be completely distinguished we are compelled either to call in the assistance of intuition or perception in space, 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 space-relations we must first translate them into time-relations,—that is, into numbers; therefore only arithmetic, and not geometry, is the universal science of quantity, and geometry must be translated into arithmetic if it is to be communicable, accurately precise and applicable in practice. It is true that a space-relation as such may also be thought in the abstract; for example, “the sine increases as the angle,” but if the quantity of this relation is to be given, it requires number for its expression. This necessity, that if we wish to have abstract knowledge of space-relations (i.e., rational knowledge, not mere intuition or perception), space 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 analytical 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 [pg 071] 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 space! Yet this is necessary if we wish to possess, for application, an expression, in abstract concepts, of space-relations. They could not be translated directly into abstract concepts, but only through the medium of the pure temporal quantity, number, which alone is directly related to abstract knowledge. Yet it is worthy of remark, that as space 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, passes easily into abstract knowledge, but gives very little to perception. Our perceptions of numbers in their proper element, mere time, without the help of space, 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.