P 571 II TRANSCENDENTAL DOCTRINE OF METHOD P 573 TRANSCENDENTAL DOCTRINE OF METHOD IF we look upon the sum of all knowledge of pure speculative reason as an edifice for which we have at least the idea within ourselves, it can be said that in the Transcendental Doctrine of Elements we have made an estimate of the materials, and have determined for what sort of edifice and for what height and strength of building they suffice. We have found, indeed, that although we had contemplated building a tower which should reach to the heavens, the supply of materials suffices only for a dwelling-house, just sufficiently commodious for our business on the level of experience, and just sufficiently high to allow of our overlooking it. The bold undertaking that we had designed is thus bound to fail through lack of material -- not to mention the babel of tongues, which inevitably gives rise to disputes among the workers in regard to the plan to be followed, and which must end by scattering them over all the world, leaving each to erect a separate building for himself, according to his own design. At present, however, we are concerned not so much with the materials as with the plan; and inasmuch as we have been warned not to venture at random upon a blind project which may be altogether beyond our capacities, and yet cannot well abstain from building a secure home for ourselves, we must plan our building in conformity with the material which is given to us, and which is also at the same time appropriate to our needs. I understand, therefore, by Transcendental Doctrine of Method the determination of the formal conditions of a complete system of pure reason. In this connection, we shall have to treat of a discipline, a canon, an architectonic, and finally a history of pure reason, and to provide (in its transcendental reference) what, in relation to the use of the understanding in general, the Schools have attempted, though very unsatisfactorily, P 574 under the title of a practical logic. For since universal logic is not confined to any particular kind of knowledge made possible by the understanding (for instance, not to its pure knowledge) and is also not confined to certain objects, it cannot, save by borrowing knowledge from other sciences, do more than present the titles of possible methods and the technical terms which are used for purposes of systematisation in all kinds of sciences; and this serves only to acquaint the novice in advance with names the meaning and use of which he will not learn till later. TRANSCENDENTAL DOCTRINE OF METHOD CHAPTER I THE DISCIPLINE OF PURE REASON Owing to the general desire for knowledge, negative judgments, that is, those which are such not merely as regards their form but also as regards their content, are not held in any very high esteem. They are regarded rather as the jealous enemies of our unceasing endeavour to extend our knowledge, and it almost requires an apology to win for them even tolerance, not to say favour and high repute. As far as logical form is concerned, we can make negative any proposition we like; but in respect to the content of our knowledge in general, which is either extended or limited by a judgment, the task peculiar to negative judgments is that of rejecting error. Accordingly, negative propositions intended to reject false knowledge, where yet no error is possible, are indeed true but empty, that is, are not suited to their purpose, and just for this reason are often quite absurd, like the proposition of the Schoolman, that Alexander could not have conquered any countries without an army. But where the limits of our possible knowledge are very narrow, where the temptation to judge is great, where the illusion that besets us is very deceptive and the harm that results from the error is considerable, there the negative instruction, which serves solely to guard us from errors, has even more importance than many a piece of positive information by P 575 which our knowledge is increased. The compulsion, by which the constant tendency to disobey certain rules is restrained and finally extirpated, we entitle discipline. It is distinguished from culture, which is intended solely to give a certain kind of skill, and not to cancel any habitual mode of action already present. Towards the development of a talent, which has already in itself an impulse to manifest itself, discipline will therefore contribute in a negative, culture and doctrine in a positive, fashion. That temperament and our various talents (such as imagination and wit) which incline to allow themselves a free and unlimited activity are in many respects in need of a discipline, everyone will readily admit. But that reason, whose proper duty it is to prescribe a discipline for all other endeavours, should itself stand in need of such discipline may indeed seem strange; and it has, in fact, hitherto escaped this humiliation, only because, in view of its stately guise and established standing, nobody could lightly come to suspect it of idly substituting fancies for concepts, and words for things. There is no need of a critique of reason in its empirical employment, because in this field its principles are always subject to the test of experience. Nor is it needed in mathematics, where the concepts of reason must be forthwith exhibited in concreto in pure intuition, so that everything unfounded and arbitrary in them is at once exposed. But where neither empirical nor pure intuition keeps reason to a visible track, when, that is to say, reason is being considered in its transcendental employment, in accordance with mere concepts, it stands so greatly in need of a discipline, to restrain its tendency towards extension beyond the narrow limits of possible experience and to guard it against extravagance and error, that the whole P 576 philosophy of pure reason has no other than this strictly negative utility. P 575n ++ I am well aware that in the terminology of the Schools the title discipline is commonly used as synonymous with instruction. However, there are so many other cases where discipline in the sense of training by constraint is carefully distinguished from instruction in the sense of teaching, and the very nature of things itself makes it so imperative that we should preserve the only expressions suitable for this distinction, that it is desirable that the former term should never be used in any but the negative sense. P 576 Particular errors can be got rid of by censure, and their causes by criticism. But where, as in the case of pure reason, we come upon a whole system of illusions and fallacies, intimately bound together and united under common principles, a quite special negative legislation seems to be required, erecting a system of precautions and self-examination under the title of a discipline, founded on the nature of reason and the objects of its pure employment -- a system in face of which no pseudo-rational illusion will be able to stand, but will at once betray itself, no matter what claims it may advance for exceptional treatment. But it is well to note that in this second main division of the transcendental Critique the discipline of pure reason is not directed to the content but only to the method of knowledge through pure reason. The former has already been considered in the Doctrine of Elements. But there is so much similarity in the mode of employing reason, whatever be the object to which it is applied, while yet, at the same time, its transcendental employment is so essentially different from every other, that without the admonitory negative teaching of a discipline, specially devised for the purpose, we cannot hope to avoid the errors which inevitably arise from pursuing in improper fashion methods which are indeed suitable to reason in other fields, only not in this transcendental sphere. CHAPTER I Section I THE DISCIPLINE OF PURE REASON IN ITS DOGMATIC EMPLOYMENT Mathematics presents the most splendid example of the successful extension of pure reason, without the help of experience. Examples are contagious, especially as they quite naturally flatter a faculty which has been successful in one field, [leading it] to expect the same good fortune in other fields. Thus pure reason hopes to be able to extend its domain as successfully and securely in its transcendental as in its mathematical P 577 employment, especially when it resorts to the same method as has been of such obvious utility in mathematics. It is therefore highly important for us to know whether the method of attaining apodeictic certainty which is called mathematical is identical with the method by which we endeavour to obtain the same certainty in philosophy, and which in that field would have to be called dogmatic. Philosophical knowledge is the knowledge gained by reason from concepts; mathematical knowledge is the knowledge gained by reason from the construction of concepts. To construct a concept means to exhibit a priori the intuition which corresponds to the concept. For the construction of a concept we therefore need a non-empirical intuition. The latter must, as intuition, be a single object, and yet none the less, as the construction of a concept (a universal representation), it must in its representation express universal validity for all possible intuitions which fall under the same concept. Thus I construct a triangle by representing the object which corresponds to this concept either by imagination alone, in pure intuition, or in accordance therewith also on paper, in empirical intuition -- in both cases completely a priori, without having borrowed the pattern from any experience. The single figure which we draw is empirical, and yet it serves to express the concept, without impairing its universality. For in this empirical intuition we consider only the act whereby we construct the concept, and abstract from the many determinations (for instance, the magnitude of the sides and of the angles), which are quite indifferent, as not altering the concept 'triangle'. Thus philosophical knowledge considers the particular only in the universal, mathematical knowledge the universal in the particular, or even in the single instance, though still always a priori and by means of reason. Accordingly, just as this single object is determined by certain universal conditions of construction, so the object of the concept, to which the single object corresponds merely as its schema, must likewise be thought as universally determined. The essential difference between these two kinds of knowledge through reason consists therefore in this formal difference, and does not depend on difference of their material or objects. Those who propose to distinguish philosophy from P 578 mathematics by saying that the former has as its object quality only and the latter quantity only, have mistaken the effect for the cause. The form of mathematical knowledge is the cause why it is limited exclusively to quantities. For it is the concept of quantities only that allows of being constructed, that is, exhibited a priori in intuition; whereas qualities cannot be presented in any intuition that is not empirical. Consequently reason can obtain a knowledge of qualities only through concepts. No one can obtain an intuition corresponding to the concept of reality otherwise than from experience; we can never come into possession of it a priori out of our own resources, and prior to the empirical consciousness of reality. The shape of a cone we can form for ourselves in intuition, unassisted by any experience, according to its concept alone, but the colour of this cone must be previously given in some experience or other. I cannot represent in intuition the concept of a cause in general except in an example supplied by experience; and similarly with other concepts. Philosophy, as well as mathematics, does indeed treat of quantities, for instance, of totality, infinity, etc. Mathematics also concerns itself with qualities, for instance, the difference between lines and surfaces, as spaces of different quality, and with the continuity of extension as one of its qualities. But although in such cases they have a common object, the mode in which reason handles that object is wholly different in philosophy and in mathematics. Philosophy confines itself to universal concepts; mathematics can achieve nothing by concepts alone but hastens at once to intuition, in which it considers the concept in concreto, though not empirically, but only in an intuition which it presents a priori, that is, which it has constructed, and in which whatever follows from the universal conditions of the construction must be universally valid of the object of the concept thus constructed. Suppose a philosopher be given the concept of a triangle and he be left to find out, in his own way, what relation the sum of its angles bears to a right angle. He has nothing but the concept of a figure enclosed by three straight lines, and possessing three angles. However long he meditates on this concept, he will never produce anything new. He can analyse and clarify the concept of a straight line or of an angle or of the number three, but he can never arrive at any properties P 579 not already contained in these concepts. Now let the geometrician take up these questions. He at once begins by constructing a triangle. Since he knows that the sum of two right angles is exactly equal to the sum of all the adjacent angles which can be constructed from a single point on a straight line, he prolongs one side of his triangle and obtains two adjacent angles, which together are equal to two right angles. He then divides the external angle by drawing a line parallel to the opposite side of the triangle, and observes that he has thus obtained an external adjacent angle which is equal to an internal angle -- and so on. In this fashion, through a chain of inferences guided throughout by intuition, he arrives at a full evident and universally valid solution of the problem. But mathematics does not only construct magnitudes (quanta) as in geometry; it also constructs magnitude as such (quantitas), as in algebra. In this it abstracts completely from the properties of the object that is to be thought in terms of such a concept of magnitude. It then chooses a certain notation for all constructions of magnitude as such (numbers), that is, for addition, subtraction, extraction of roots, etc. Once it has adopted a notation for the general concept of magnitudes so far as their different relations are concerned, it exhibits in intuition, in accordance with certain universal rules, all the various operations through which the magnitudes are produced and modified. When, for instance, one magnitude is to be divided by another, their symbols are placed together, in accordance with the sign for division, and similarly in the other processes; and thus in algebra by means of a symbolic construction, just as in geometry by means of an ostensive construction (the geometrical construction of the objects themselves), we succeed in arriving at results which discursive knowledge could never have reached by means of mere concepts. Now what can be the reason of this radical difference in the fortunes of the philosopher and the mathematician, both of whom practise the art of reason, the one making his way by means of concepts, the other by means of intuitions which he exhibits a priori in accordance with concepts? The cause is evident from what has been said above, in our exposition of the P 580 fundamental transcendental doctrines. We are not here concerned with analytic propositions, which can be produced by mere analysis of concepts (in this the philosopher would certainly have the advantage over his rival), but with synthetic propositions, and indeed with just those synthetic propositions that can be known a priori. For I must not restrict my attention to what I am actually thinking in my concept of a triangle (this is nothing more than the mere definition); I must pass beyond it to properties which are not contained in this concept, but yet belong to it. Now this is impossible unless I determine my object in accordance with the conditions either of empirical or of pure intuition. The former would only give us an empirical proposition (based on the measurement of the angles), which would not have universality, still less necessity; and so would not at all serve our purpose. The second method of procedure is the mathematical one, and in this case is the method of geometrical construction, by means of which I combine in a pure intuition (just as I do in empirical intuition) the manifold which belongs to the schema of a triangle in general, and therefore to its concept. It is by this method that universal synthetic propositions must be constructed. It would therefore be quite futile for me to philosophise upon the triangle, that is, to think about it discursively. I should not be able to advance a single step beyond the mere definition, which was what I had to begin with. There is indeed a transcendental synthesis [framed] from concepts alone, a synthesis with which the philosopher is alone competent to deal; but it relates only to a thing in general, as defining the conditions under which the perception of it can belong to possible experience. But in mathematical problems there is no question of this, nor indeed of existence at all, but only of the properties of the objects in themselves, [that is to say], solely in so far as these properties are connected with the concept of the objects. In the above example we have endeavoured only to make clear the great difference which exists between the discursive employment of reason in accordance with concepts and its intuitive employment by means of the construction of concepts. This naturally leads on to the question, what can be the cause P 581 which necessitates such a twofold employment of reason, and how we are to recognise whether it is the first or the second method that is being employed. All our knowledge relates, finally, to possible intuitions, for it is through them alone that an object is given. Now an a - priori concept, that is, a concept which is not empirical, either already includes in itself a pure intuition (and if so, it can be constructed), or it includes nothing but the synthesis of possible intuitions which are not given a priori. In this latter case we can indeed make use of it in forming synthetic a - priori judgments, but only discursively in accordance with concepts, never intuitively through the construction of the concept. The only intuition that is given a priori is that of the mere form of appearances, space and time. A concept of space and time, as quanta, can be exhibited a priori in intuition, that is, constructed, either in respect of the quality (figure) of the quanta, or through number in their quantity only (the mere synthesis of the homogeneous manifold). But the matter of appearances, by which things are given us in space and time, can only be represented in perception, and therefore a posteriori. The only concept which represents a priori this empirical content of appearances is the concept of a thing in general, and the a priori synthetic knowledge of this thing in general can give us nothing more than the mere rule of the synthesis of that which perception may give a posteriori. It can never yield an a priori intuition of the real object, since this must necessarily be empirical. Synthetic propositions in regard to things in general, the intuition of which does not admit of being given a priori, are transcendental. Transcendental propositions can never be given through construction of concepts, but only in accordance with concepts that are a priori. They contain nothing but the rule according to which we are to seek empirically for a certain synthetic unity of that which is incapable of intuitive representation a priori (that is, of perceptions). But these synthetic principles cannot exhibit a priori any one of their concepts in a specific instance; they can only do this a posteriori, by means of experience, which itself is possible only in conformity with these principles. P 582 If we are to judge synthetically in regard to a concept, we must go beyond this concept and appeal to the intuition in which it is given. For should we confine ourselves to what is contained in the concept, the judgment would be merely analytic, serving only as an explanation of the thought, in terms of what is actually contained in it. But I can pass from the concept to the corresponding pure or empirical intuition, in order to consider it in that intuition in concreto, and so to know, either a priori or a posteriori, what are the properties of the object of the concept. The a priori method gives us our rational and mathematical knowledge through the construction of the concept, the a posteriori method our merely empirical (mechanical) knowledge, which is incapable of yielding necessary and apodeictic propositions. Thus I might analyse my empirical concept of gold without gaining anything more than merely an enumeration of everything that I actually think in using the word, thus improving the logical character of my knowledge but not in any way adding to it. But I take the material body, familiarly known by this name, and obtain perceptions by means of it; and these perceptions yield various propositions which are synthetic but empirical. When the concept is mathematical, as in the concept of a triangle, I am in a position to construct the concept, that is, to give it a priori in intuition, and in this way to obtain knowledge which is at once synthetic and rational. But if what is given me is the transcendental concept of a reality, substance, force, etc. , it indicates neither an empirical nor a pure intuition, but only the synthesis of empirical intuitions, which, as being empirical, cannot be given a priori. And since the synthesis is thus unable to advance a priori, beyond the concept, to the corresponding intuition, the concept cannot yield any determining synthetic proposition, but only a principle of the synthesis of possible empirical intuiti ons. ++ With the concept of cause I do really go beyond the empirical concept of an event (something happening), yet I do not pass to the intuition which exhibits the concept of cause in concreto, but to the time-conditions in general, which in experience may be found to be in accord with this concept. I therefore proceed merely with concepts; I cannot proceed by means of the construction of concepts, since the concept is a rule of the synthesis of perceptions, and the latter are not pure intuitions, and so do not permit of being given a priori. P 583 A transcendental proposition is therefore synthetic knowledge through reason, in accordance with mere concepts; and it is discursive, in that while it is what alone makes possible any synthetic unity of empirical knowledge, it yet gives us no intuition a priori. There is thus a twofold employment of reason; and while the two modes of employment resemble each other in the universality and a priori origin of their knowledge, in outcome they are very different. The reason is that in the [field of] appearance, in terms of which all objects are given us, there are two elements, the form of intuition (space and time), which can be known and determined completely a priori, and the matter (the physical element) or content -- the latter signifying something which is met with in space and time and which therefore contains an existent corresponding to sensation. In respect to this material element, which can never be given in any determinate fashion otherwise than empirically, we can have nothing a priori except indeterminate concepts of the synthesis of possible sensations, in so far as they belong, in a possible experience, to the unity of apperception. As regards the formal element, we can determine our concepts in a priori intuition, inasmuch as we create for ourselves, in space and time, through a homogeneous synthesis, the objects themselves -- these objects being viewed simply as quanta. The former method is called the employment of reason in accordance with concepts; in so employing it we can do nothing more than bring appearances under concepts, according to their actual content. The concepts cannot be made determinate in this manner, save only empirically, that is, a posteriori (although always in accordance with these concepts as rules of an empirical synthesis). The other method is the employment of reason through the construction of concepts; and since the concepts here relate to an a priori intuition, they are for this very reason themselves a priori and can be given in a quite determinate fashion in pure intuition, without the help of any empirical data. The consideration of everything which exists in space or time, in regard to the questions, whether and how far it is a quantum P 584 or not, whether we are to ascribe to it positive being or the absence of such, how far this something occupying space or time is a primary substratum or a mere determination [of substance], whether there be a relation of its existence to some other existence, as cause or effect, and finally in respect of its existence whether it is isolated or is in reciprocal relation to and dependence upon others -- these questions, as also the question of the possibility of this existence, its actuality and necessity, or the opposites of these, one and all belong altogether to knowledge obtained by reason from concepts, such knowledge being termed philosophical. But the determination of an intuition a - priori in space (figure), the division of time (duration), or even just the knowledge of the universal element in the synthesis of one and the same thing in time and space, and the magnitude of an intuition that is thereby generated (number), -- all this is the work of reason through construction of concepts, and is called mathematical. The great success which attends reason in its mathematical employment quite naturally gives rise to the expectation that it, or at any rate its method, will have the same success in other fields as in that of quantity. For this method has the advantage of being able to realise all its concepts in intuitions, which it can provide a priori, and by which it becomes, so to speak, master of nature; whereas pure philosophy is all at sea when it seeks through a priori discursive concepts to obtain insight in regard to the natural world, being unable to intuit a priori (and thereby to confirm) their reality. Nor does there seem to be, on the part of the experts in mathematics, any lack of self-confidence as to this procedure -- or on the part of the vulgar of great expectations from their skill -- should they apply themselves to carry out their project. For, since they have hardly ever attempted to philosophise in regard to their mathematics (a hard task! ), the specific difference between the two employments of reason has never so much as occurred to them. Current, empirical rules, which they borrow from ordinary consciousness, they treat as being axiomatic. In the question as to the source of the concepts of space and time they are not in the least interested, although it is precisely with these concepts (as the only original quanta) that they are themselves occupied. Similarly, they think it unnecessary to investigate P 585 the origin of the pure concepts of understanding and in so doing to determine the extent of their validity; they care only to make use of them. In all this they are entirely in the right, provided only they do not overstep the proper limits, that is, the limits of the natural world. But, unconsciously, they pass from the field of sensibility to the precarious ground of pure and even transcendental concepts, a ground (instabilis tellus, innabilis unda) that permits them neither to stand nor to swim, and where their hasty tracks are soon obliterated. In mathematics, on the other hand, their passage gives rise to a broad highway, which the latest posterity may still tread with confidence. We have made it our duty to determine, with exactitude and certainty, the limits of pure reason in its transcendental employment. But the pursuit of such transcendental knowledge has this peculiarity, that in spite of the plainest and most urgent warnings men still allow themselves to be deluded by false hopes, and therefore to postpone the total abandonment of all proposed attempts to advance beyond the bounds of experience into the enticing regions of the intellectual world. It therefore becomes necessary to cut away the last anchor of these fantastic hopes, that is, to show that the pursuit of the mathematical method cannot be of the least advantage in this kind of knowledge (unless it be in exhibiting more plainly the limitations of the method); and that mathematics and philosophy, although in natural science they do, indeed, go hand in hand, are none the less so completely different, that the procedure of the one can never be imitated by the other. The exactness of mathematics rests upon definitions, axioms and demonstrations. I shall content myself with showing that none of these, in the sense in which they are understood by the mathematician, can be achieved or imitated by the philosopher. I shall show that in philosophy the geometrician can by his method build only so many houses of cards, just as in mathematics the employment of a philosophical method results only in mere talk. Indeed it is precisely in knowing its limits that philosophy consists; and even the mathematician, unless his talent is of such a specialised character that it naturally confines itself to its proper field, cannot afford to ignore the warnings of philosophy, or to behave as if he were superior to them. P 586 1. Definitions. -- To define, as the word itself indicates, really only means to present the complete, original concept of a thing within the limits of its concept. If this be our standard, an empirical concept cannot be defined at all, but only made explicit. For since we find in it only a few characteristics of a certain species of sensible object, it is never certain that we are not using the word, in denoting one and the same object, sometimes so as to stand for more, and sometimes so as to stand for fewer characteristics. Thus in the concept of gold one man may think, in addition to its weight, colour, malleability, also its property of resisting rust, while another will perhaps know nothing of this quality. We make use of certain characteristics only so long as they are adequate for the purpose of making distinctions; new observations remove some properties and add others; and thus the limits of the concept are never assured. And indeed what useful purpose could be served by defining an empirical concept, such, for instance, as that of water? When we speak of water and its properties, we do not stop short at what is thought in the word, water, but proceed to experiments. The word, with the few characteristics which we attach to it, is more properly to be regarded as merely a designation than as a concept of the thing; the so- called definition is nothing more than a determining of the word. In the second place, it is also true that no concept given a priori, such as substance, cause, right, equity, etc. , can, strictly speaking, be defined. For I can never be certain that the clear representation of a given concept, which as given may still be confused, has been completely effected, unless I know that it is adequate to its object. But since the concept of it may, as given, include many obscure representations, which we overlook in our analysis, although we are constantly making use of them in our application of the concept, the completeness of the analysis of my concept is always in doubt, and a multiplicity P 587 of suitable examples suffices only to make the completeness probable, never to make it apodeictically certain. P 586n ++ Completeness means clearness and sufficiency of characteristics; by limits is meant the precision shown in there not being more of these characteristics than belong to the complete concept; by original is meant that this determination of these limits is not derived from anything else, and therefore does not require any proof; for if it did, that would disqualify the supposed explanation from standing at the head of all the judgments regarding its object. P 587 Instead of the term, definition, I prefer to use the term, exposition, as being a more guarded term, which the critic can accept as being up to a certain point valid, though still entertaining doubts as to the completeness of the analysis. Since, then, neither empirical concepts nor concepts given a priori allow of definition, the only remaining kind of concepts, upon which this mental operation can be tried, are arbitrarily invented concepts. A concept which I have invented I can always define; for since it is not given to me either by the nature of understanding or by experience, but is such as I have myself deliberately made it to be, I must know what I have intended to think in using it. I cannot, however, say that I have thereby defined a true object. For if the concept depends on empirical conditions, as e.g. the concept of a ship's clock, this arbitrary concept of mine does not assure me of the existence or of the possibility of its object. I do not even know from it whether it has an object at all, and my explanation may better be described as a declaration of my project than as a definition of an object. There remain, therefore, no concepts which allow of definition, except only those which contain an arbitrary synthesis that admits of a priori construction. Consequently, mathematics is the only science that has definitions. For the object which it thinks it exhibits a priori in intuition, and this object certainly cannot contain either more or less than the concept, since it is through the definition that the concept of the object is given -- and given originally, that is, without its being necessary to derive the definition from any other source. The German language has for the [Latin] terms exposition, explication, declaration, and definition only one word, Erklarung, and we need not, therefore, be so stringent in our requirements as altogether to refuse to philosophical explanations the honourable title, definition. We shall confine ourselves simply to remarking that while philosophical definitions are never more than expositions of given concepts, mathematical definitions are constructions of concepts, P 588 originally framed by the mind itself; and that while the former can be obtained only by analysis (the completeness of which is never apodeictically certain), the latter are produced synthetically. Whereas, therefore, mathematical definitions make their concepts, in philosophical definitions concepts are only explained. From this it follows: (a) That in philosophy we must not imitate mathematics by beginning with definitions, unless it be by way simply of experiment. For since the definitions are analyses of given concepts, they presuppose the prior presence of the concepts, although in a confused state; and the incomplete exposition must precede the complete. Consequently, we can infer a good deal from a few characteristics, derived from an incomplete analysis, without having yet reached the complete exposition, that is, the definition. In short,the definition in all its precision and clarity ought, in philosophy, to come rather at the end than at the beginning of our enquiries. In mathematics, on the other hand, we have no concept whatsoever prior to the definition, through which the concept itself is first given. For this reason mathematical science must always begin, and it can always begin, with the definition. (b) That mathematical definitions can never be in error. For since the concept is first given through the definition, it includes nothing except precisely what the definition intends should be understood by it. But although nothing incorrect can be introduced into its content, there may sometimes, though rarely, be a defect in the form in which it is clothed, namely as regards precision. ++ Philosophy is full of faulty definitions, especially of definitions which, while indeed containing some of the elements required, are yet not complete. If we could make no use of a concept till we had defined it, all philosophy would be in a pitiable plight. But since a good and safe use can still be made of the elements obtained by analysis so far as they go, defective definitions, that is, propositions which are properly not definitions, but are yet true, and are therefore approximations to definitions, can be employed with great advantage. In mathematics definition belongs ad esse, in philosophy ad melius esse. It is desirable to attain an adequate definition, but often very difficult. The jurists are still without a definition of their concept of right. P 588 Thus the common explanation of the circle that it is a curved line every point in which is equidistant P 589 from one and the same point (the centre), has the defect that the determination, curved, is introduced unnecessarily. For there must be a particular theorem, deduced from the definition and easily capable of proof, namely, that if all points in a line are equidistant from one and the same point, the line is curved (no part of it straight). Analytic definitions, on the other hand, may err in many ways, either through introducing characteristics which do not really belong to the concept, or by lacking that completeness which is the essential feature of a definition. The latter defect is due to the fact that we can never be quite certain of the completeness of the analysis. For these reasons the mathematical method of definition does not admit of imitation in philosophy. 2. Axioms. -- These, in so far as they are immediately certain, are synthetic a priori principles. Now one concept cannot be combined with another synthetically and also at the same time immediately, since, to be able to pass beyond either concept, a third something is required to mediate our knowledge. Accordingly, since philosophy is simply what reason knows by means of concepts, no principle deserving the name of an axiom is to be found in it. Mathematics, on the other hand, can have axioms, since by means of the construction of concepts in the intuition of the object it can combine the predicates of the object both a priori and immediately, as, for instance, in the proposition that three points always lie in a plane. But a synthetic principle derived from concepts alone can never be immediately certain, for instance, the proposition that everything which happens has a cause. Here I must look round for a third something, namely, the condition of time- determination in an experience; I cannot obtain knowledge of such a principle directly and immediately from the concepts alone. Discursive principles are therefore quite different from intuitive principles, that is, from axioms; and always require a deduction. Axioms, on the other hand, require no such deduction, and for the same reason are evident -- a claim which the philosophical principles can never advance, however great their certainty. Consequently, the synthetic propositions of pure, transcendental reason are, one and all, infinitely removed from being as evident -- which is yet so often arrogantly claimed on their behalf -- as the proposition that twice two make four. P 590 In the Analytic I have indeed introduced some axioms of intuition into the table of the principles of pure understanding; but the principle there applied is not itself an axiom, but serves only to specify the principle of the possibility of axioms in general, and is itself no more than a principle derived from concepts. For the possibility of mathematics must itself be demonstrated in transcendental philosophy. Philosophy has therefore no axioms, and may never prescribe its a priori principles in any such absolute manner, but must resign itself to establishing its authority in their regard by a thorough deduction. 3. Demonstrations. -- An apodeictic proof can be called a demonstration, only in so far as it is intuitive. Experience teaches us what is, but does not teach us that it could not be other than what it is. Consequently, no empirical grounds of proof can ever amount to apodeictic proof. Even from a - priori concepts, as employed in discursive knowledge, there can never arise intuitive certainty, that is, [demonstrative] evidence, however apodeictically certain the judgment may otherwise be. Mathematics alone, therefore, contains demonstrations, since it derives its knowledge not from concepts but from the construction of them, that is, from intuition, which can be given a priori in accordance with the concepts. Even the method of algebra with its equations, from which the correct answer, together with its proof, is deduced by reduction, is not indeed geometrical in nature, but is still constructive in a way characteristic of the science. The concepts attached to the symbols, especially concerning the relations of magnitudes, are presented in intuition; and this method, in addition to its heuristic advantages, secures all inferences against error by setting each one before our eyes. While philosophical knowledge must do without this advantage, inasmuch as it has always to consider the universal in abstracto (by means of concepts), mathematics can consider the universal in concreto (in the single intuition) and yet at the same time through pure a priori representation, whereby all errors are at once made evident. I should therefore prefer to P 591 call the first kind acroamatic (discursive) proofs, since they may be conducted by the agency of words alone (the object in thought), rather than demonstrations which, as the term itself indicates, proceed in and through the intuition of the object. From all this it follows that it is not in keeping with the nature of philosophy, especially in the field of pure reason, to take pride in a dogmatic procedure, and to deck itself out with the title and insignia of mathematics, to whose ranks it does not belong, though it has every ground to hope for a sisterly union with it. Such pretensions are idle claims which can never be satisfied, and indeed must divert philosophy from its true purpose, namely, to expose the illusions of a reason that forgets its limits, and by sufficiently clarifying our concepts to recall it from its presumptuous speculative pursuits to modest but thorough self-knowledge. Reason must not, therefore, in its transcendental endeavours, hasten forward with sanguine expectations, as though the path which it has traversed led directly to the goal, and as though the accepted premisses could be so securely relied upon that there can be no need of constantly returning to them and of considering whether we may not perhaps, in the course of the inferences, discover defects which have been overlooked in the principles, and which render it necessary either to determine these principles more fully or to change them entirely. I divide all apodeictic propositions, whether demonstrable or immediately certain, into dogmata and mathemata. A synthetic proposition directly derived from concepts is a dogma; a synthetic proposition, when directly obtained through the construction of concepts, is a mathema. Analytic judgments really teach us nothing more about the object than what the concept which we have of it already contains; they do not extend our knowledge beyond the concept of the object, but only clarify the concept. They cannot therefore rightly be called dogmas (a word which might perhaps be translated doctrines). Of the two kinds of synthetic a priori propositions only those belonging to philosophical knowledge can, according to the ordinary usage of words, be entitled dogmas; the propositions of arithmetic or geometry would hardly be so P 592 named. The customary use of words thus confirms our interpretation of the term, namely, that only judgments derived from concepts can be called dogmatic, not those based on the construction of concepts. Now in the whole domain of pure reason, in its merely speculative employment, there is not to be found a single synthetic judgment directly derived from concepts. For, as we have shown, ideas cannot form the basis of any objectively valid synthetic judgment. Through concepts of understanding pure reason does, indeed, establish secure principles, not however directly from concepts alone, but always only indirectly through relation of these concepts to something altogether contingent, namely, possible experience. When such experience (that is, something as object of possible experiences) is presupposed, these principles are indeed apodeictically certain; but in themselves, directly, they can never be known a priori. Thus no one can acquire insight into the proposition that everything which happens has its cause, merely from the concepts involved. It is not, therefore, a dogma, although from another point of view, namely, from that of the sole field of its possible employment, that is, experience, it can be proved with complete apodeictic certainty. But though it needs proof, it should be entitled a principle, not a theorem, because it has the peculiar character that it makes possible the very experience which is its own ground of proof, and that in this experience it must always itself be presupposed. Now if in the speculative employment of pure reason there are no dogmas, to serve as its special subject-matter, all dogmatic methods, whether borrowed from the mathematician or specially invented, are as such inappropriate. For they only serve to conceal defects and errors, and to mislead philosophy, whose true purpose is to present every step of reason in the clearest light. Nevertheless its method can always be systematic. For our reason is itself, subjectively, a system, though in its pure employment, by means of mere concepts, it is no more than a system whereby our investigations can be conducted in accordance with principles of unity, the material being provided by experience alone. We cannot here discuss the method peculiar to transcendental philosophy; we are at present P 593 concerned only with a critical estimate of what may be expected from our faculties -- whether we are in a position to build at all; and to what height, with the material at our disposal (the pure a priori concepts), we may hope to carry the edifice. CHAPTER I Section 2 THE DISCIPLINE OF PURE REASON IN RESPECT OF ITS POLEMICAL EMPLOYMENT Reason must in all its undertakings subject itself to criticism; should it limit freedom of criticism by any prohibitions, it must harm itself, drawing upon itself a damaging suspicion. Nothing is so important through its usefulness, nothing so sacred, that it may be exempted from this searching examination, which knows no respect for persons. Reason depends on this freedom for its very existence. For reason has no dictatorial authority; its verdict is always simply the agreement of free citizens, of whom each one must be permitted to express, without let or hindrance, his objections or even his veto. But while reason can never refuse to submit to criticism, it does not always have cause to fear it. In its dogmatic (non- mathematical) employment it is not, indeed, so thoroughly conscious of such exact observation of its own supreme laws, as not to feel constrained to present itself with diffidence, nay, with entire renunciation of all assumed dogmatic authority, to the critical scrutiny of a higher judicial reason. The situation is, however, quite otherwise, when reason has to deal not with the verdict of a judge, but with the claims of a fellow-citizen, and against these has only to act in self- defence. For since these are intended to be just as dogmatic in denial as its own are in affirmation, it is able to justify itself kat' anthropon, in a manner which ensures it against all interference, and provides it with a title to secure possession that need fear no outside claims, although kat' alytheian the title cannot itself be conclusively proved. By the polemical employment of pure reason I mean the P 594 defence of its propositions as against the dogmatic counter- propositions through which they are denied. Here the contention is not that its own assertions may not, perhaps, be false, but only that no one can assert the opposite with apodeictic certainty, or even, indeed, with a greater degree of likelihood. We do not here hold our possessions upon sufferance; for although our title to them may not be satisfactory, it is yet quite certain that no one can ever be in a position to prove the illegality of the title. It is grievous, indeed, and disheartening, that there should be any such thing as an antithetic of pure reason, and that reason, which is the highest tribunal for all conflicts, should thus be at variance with itself. We had to deal, in a previous chapter, with such an antithetic; but it turned out to be only an apparent conflict, resting upon a misunderstanding. In accordance with the common prejudice, it took appearances as being things in themselves, and then required an absolute completeness of their synthesis in the one mode or in the other (this being equally impossible in either way) -- a demand which is not at all permissible in respect of appearances. There was, therefore, no real self-contradiction of reason in the propounding of the two propositions, that the series of appearances given in themselves has an absolutely first beginning, and that this series is absolutely and in itself without any beginning. For the two propositions are quite consistent with each other, inasmuch as appearances, in respect of their existence (as appearances), are in themselves nothing at all, that is, [so regarded] are something self-contradictory; for the assumption [that they do thus exist in themselves] must naturally lead to self- contradictory inferences. But there are other cases in which we cannot allege any such misunderstanding, and in which we cannot, therefore, dispose of the conflict of reason in the above manner -- when, for instance, it is asserted, on the one hand, theistically, that there is a supreme being, and on the other hand, atheistically, that there is no supreme being; or as in psychology, that everything which thinks is endowed with absolute and abiding unity and is therefore distinct from all transitory material unity, and, in opposition thereto, that the soul is not immaterial unity P 595 and cannot be exempt from transitoriness. For since in these cases the understanding has to deal only with things in themselves and not with appearances, the object of such questions is free from any foreign element that is in contradiction with its nature. There would indeed be a real conflict, if pure reason had anything to say on the negative side which amounted to a positive ground for its negative contentions. For so far as concerns criticism of the grounds of proof offered by those who make dogmatic affirmations, the criticism can be freely admitted, without our having on that account to give up these affirmations, which have at least the interest of reason in their favour -- an interest to which the opposite party cannot appeal. I do not at all share the opinion which certain excellent and thoughtful men (such as Sulzer), in face of the weakness of the arguments hitherto employed, have so often been led to express, that we may hope sometime to discover conclusive demonstrations of the two cardinal propositions of our reason -- that there is a God, and that there is a future life. On the contrary, I am certain that this will never happen. For whence will reason obtain ground for such synthetic assertions, which do not relate to objects of experience and their inner possibility. But it is also apodeictically certain that there will never be anyone who will be able to assert the opposite with the least show [of proof], much less, dogmatically. For since he could prove this only through pure reason, he must undertake to prove that a supreme being, and the thinking subject in us [viewed] as pure intelligence, are impossible. But whence will he obtain the modes of knowledge which could justify him in thus judging synthetically in regard to things that lie beyond all possible experience. We may therefore be so completely assured that no one will ever prove the opposite, that there is no need for us to concern ourselves with formal arguments. We are always in a position to accept these propositions -- propositions which are so very closely bound up with the speculative interest of our reason in its empirical employment, and which, moreover, are the sole means of reconciling the P 596 speculative with the practical interest. As against our opponent who must not be considered here as a critic only, we are equipped with our non liquet, which cannot fail to disconcert him. At the same time we do not mind his turning this argument upon ourselves, since we always have in reserve the subjective maxim of reason, which is necessarily lacking to our opponent, and under its protection can look upon all his vain attacks with a tranquil indifference. There is thus no real antithetic of pure reason. For the arena for such an antithetic would have to be located in the domain of pure theology and psychology; and in that domain no combatant can be adequately equipped, or have weapons that we need fear. Ridicule and boasting form his whole armoury, and these can be laughed at, as mere child's play. This is a comforting consideration, and affords reason fresh courage; for upon what could it rely, if, while it alone is called upon to remove all errors, it should yet be at variance with itself, and without hope of peace and quiet possession. Everything which nature has itself instituted is good for some purpose. Even poisons have their use. They serve to counteract other poisons generated in our bodily humours, and must have a place in every complete pharmacopoeia. The objections against the persuasions and complacency of our purely speculative reason arise from the very nature of reason itself, and must therefore have their own good use and purpose, which ought not to be disdained. Why has Providence placed many things which are closely bound up with our highest interests so far beyond our reach that we are only permitted to apprehend them in a manner lacking in clearness and subject to doubt -- in such fashion that our enquiring gaze is more excited than satisfied? We may, indeed, be in doubt whether it serves any useful purpose, and whether it is not perhaps even harmful, to venture upon bold utterances in regard to such uncertain matters. But there can be no manner of doubt that it is always best to grant reason complete liberty, both of enquiry and of criticism, so that it may not be hindered in attending to its own proper interests. These interests are no less furthered by the limitation than by the extension of its speculations, and will always suffer when outside influences P 597 intervene to divert it from its proper path, and to constrain it by what is irrelevant to its own proper ends. Allow, therefore, your opponent to speak in the name of reason, and combat him only with weapons of reason. For the rest, have no anxiety as to the outcome in its bearing upon our practical interests, since in a merely speculative dispute they are never in any way affected. The conflict serves only to disclose a certain antinomy of reason which, inasmuch as it is due to the very nature of reason, must receive a hearing and be scrutinised. Reason is benefited by the consideration of its object from both sides, and its judgment is corrected in being thus limited. What is here in dispute is not the practical interests of reason but the mode of their presentation. For although we have to surrender the language of knowledge, we still have sufficient ground to employ, in the presence of the most exacting reason, the quite legitimate language of a firm faith. If we should ask the dispassionate David Hume, [by temperament] so peculiarly fitted for balanced judgment, what led him to undermine, through far-fetched subtleties so elaborately thought out, the conviction which is so comforting and beneficial for mankind, that their reason has sufficient insight for the assertion and for the determinate conception of a supreme being, he would answer: 'Solely in order to advance reason in its self-knowledge, and because of a certain indignation at the violence that is done to reason by those who, while boasting of its powers, yet hinder it from candid admission of the weaknesses which have become obvious to it through its own self-examination'. If, on the other hand, we should ask Priestley, who was wholly devoted to the empirical employment of reason and out of sympathy with all transcendent speculation, what motives had induced him -- himself a pious and zealous teacher of religion -- to pull down two such pillars of all religion as the freedom and immortality of the soul (the hope of a future life is for him only the expectation of the miracle of resurrection), he would not be able to give P 598 any other answer than that he was concerned for the interest of reason, which must suffer when we seek to exempt certain objects from the laws of material nature, the only laws which we can know and determine with exactitude. It would be unjust to decry the latter (who knew how to combine his paradoxical teaching with the interests of religion), and so to give pain to a well-intentioned man, simply because he is unable to find his bearings, having strayed outside the field of natural science. And the same favour must be accorded to the no less well disposed and in his moral character quite blameless Hume, when he insists upon the relevance, in this field, of his subtly thought-out speculations. For, as he rightly held, their object lies entirely outside the limits of natural science, in the domain of pure ideas. What, then, is to be done, especially in view of the danger which would thus seem to threaten the best interests of mankind? Nothing is more natural, nothing is more reasonable, than the decision which we are hereby called upon to make. Leave such thinkers free to take their own line. If they exhibit talent, if they initiate new and profound enquiries, in a word, if they show reason, reason always stands to gain. If we resort to other means than those of untrammelled reason, if we raise the cry of high treason, and act as if we were summoning the vulgar to extinguish a conflagration -- the vulgar who have no understanding of such subtle enquiries -- we make ourselves ridiculous. For the question at issue is not as to what, in these enquiries, is beneficial or detrimental to the best interests of mankind, but only how far reason can advance by means of speculation that abstracts from all interests, and whether such speculation can count for anything, or must not rather be given up in exchange for the practical. Instead, therefore, of rushing into the fight, sword in hand, we should rather play the part of the peaceable onlooker, from the safe seat of the critic. The struggle is indeed toilsome to the combatants, but for us can be entertaining; and its outcome -- certain to be quite bloodless -- must be of advantage as contributing to our theoretical insight. For it is indeed absurd to look to reason for enlightenment, and yet to prescribe beforehand which side she must necessarily favour. Besides, reason is already of itself so confined and held P 599 within limits by reason, that we have no need to call out the guard, with a view to bringing the civil power to bear upon that party whose alarming superiority may seem to us to be dangerous. In this dialectic no victory is gained that need give us cause for anxiety. Reason does indeed stand in sore need of such dialectical debate; and it is greatly to be wished that the debate had been instituted sooner and with unqualified public approval. For in that case criticism would sooner have reached a ripe maturity, and all these disputes would of necessity at once have come to an end, the opposing parties having learned to recognise the illusions and prejudices which have set them at variance. There is in human nature a certain disingenuousness, which, like everything that comes from nature, must finally contribute to good ends, namely, a disposition to conceal our real sentiments, and to make show of certain assumed sentiments which are regarded as good and creditable. This tendency to conceal ourselves and to assume the appearance of what contributes to our advantage, has, undoubtedly, not only civilised us, but gradually, in a certain measure, moralised us. For so long as we were not in a position to see through the outward show of respectability, honesty, and modesty, we found in the seemingly genuine examples of goodness with which we were surrounded a school for self- improvement. But this disposition to represent ourselves as better than we are, and to give expression to sentiments which we do not share, serves as a merely provisional arrangement, to lead us from the state of savage rudeness, and to allow of our assuming at least the outward bearing of what we know to be good. But later, when true principles have been developed, and have become part of our way of thought, this duplicity must be more and more earnestly combated; otherwise it corrupts the heart, and checks the growth of good sentiments with the rank weeds of fair appearances. I am sorry to observe the same disingenuousness, misrepresentation, and hypocrisy even in the utterances of speculative thought, where there are far fewer hindrances to our making, as is fitting, frank and unreserved admission of our thoughts, and no advantage whatsoever in acting otherwise. P 600 For what can be more prejudicial to the interests of knowledge than to communicate even our very thoughts in a falsified form, to conceal doubts which we feel in regard to our own assertions, or to give an appearance of conclusiveness to grounds of proofs which we ourselves recognise to be insufficient. So long as mere personal vanity is what breeds these secret devices -- and this is generally the case with those speculative judgments which concern no special interest and do not easily allow of apodeictic certainty -- it is counteracted, in the process of enlisting general acceptance, by the vanity of others; and thus in the end the result is the same as would have been obtained, though much sooner, by entirely sincere and honest procedure. When the common people are of opinion that those who indulge in subtle questionings aim at nothing less than to shake the very foundations of public welfare, it may, indeed, seem not only prudent but permissible, and indeed even commendable, to further the good cause through sophistical arguments rather than allow its supposed antagonists the advantage of having made us lower our tone to that of a merely practical conviction, and of having compelled us to admit our lack of speculative and apodeictic certainty. I cannot, however, but think that nothing is so entirely incompatible with the purpose of maintaining a good cause as deceit, hipocrisy and fraud. Surely the least that can be demanded is that in a matter of pure speculation, when weighing the considerations cited by reason, we should proceed in an entirely sincere manner. If we could confidently count even upon this little, the conflict of speculative reason regarding the important questions of God, the immortality of the soul, and freedom, would long ago have been decided, or would very soon be brought to a conclusion. Thus it often happens that purity of purpose is in inverse ratio to the goodness of the cause, and that candour and honesty are perhaps more likely to be found among its assailants than among its defenders. I shall therefore assume that I have readers who do not wish to see a righteous cause defended in an unrighteous manner; and that they will consequently take it as agreed, that, according to our principles of criticism, and having regard not to what commonly happens, but to what ought to happen, there can, properly speaking, be no polemic of pure reason. P 601 For how can two persons carry on a dispute about a thing the reality of which neither of them can present in actual or even in possible experience -- a dispute in which they brood over the mere idea of the thing, in order to extract from it something more than the idea, namely, the reality of the object itself? What means have they of ending the dispute, since neither of them can make his thesis genuinely comprehensible and certain, but only attack and refute that of his opponent? For this is the fate of all assertions of pure reason: that since they transcend the conditions of all possible experience, outside which the authentication of truth is in no wise possible, while at the same time they have to make use of the laws of the understanding -- laws which are adapted only for empirical employment, but without which no step can be taken in synthetic thought -- neither side can avoid exposing its weakness, and each can therefore take advantage of the weakness of the other. The critique of pure reason can be regarded as the true tribunal for all disputes of pure reason; for it is not involved in these disputes -- disputes which are immediately concerned with objects -- but is directed to the determining and estimating of the rights of reason in general, in accordance with the principles of their first institution. In the absence of this critique reason is, as it were, in the state of nature, and can establish and secure its assertions and claims only through war. The critique, on the other hand, arriving at all its decisions in the light of fundamental principles of its own institution, the authority of which no one can question, secures to us the peace of a legal order, in which our disputes have to be conducted solely by the recognised methods of legal action. In the former state, the disputes are ended by a victory to which both sides lay claim, and which is generally followed by a merely temporary armistice, arranged by some mediating authority; in the latter, by a judicial sentence which, as it strikes at the very root of the conflicts, effectively secures an eternal peace. The endless disputes of a merely dogmatic reason thus finally constrain us to seek relief in some critique of reason itself, and in a legislation based upon such criticism. As Hobbes maintains, the state of nature is a state of injustice and violence, and we have no option save to abandon it and submit ourselves to the constraint of law, which P 602 limits our freedom solely in order that it may be consistent with the freedom of others and with the common good of all. This freedom will carry with it the right to submit openly for discussion the thoughts and doubts with which we find ourselves unable to deal, and to do so without being decried as troublesome and dangerous citizens. This is one of the original rights of human reason, which recognises no other judge than that universal human reason in which everyone has his say. And since all improvement of which our state is capable must be obtained from this source, such a right is sacred and must not be curtailed. Indeed we are very ill-advised in decrying as dangerous any bold assertions against, or audacious attacks upon, the view which already has on its side the approval of the largest and best portion of the community; in so doing we are ascribing to them an importance which they are not entitled to claim. Whenever I hear that a writer of real ability has demonstrated away the freedom of the human will, the hope of a future life, and the existence of God, I am eager to read the book, for I expect him by his talents to increase my insight into these matters. Already, before having opened it, I am perfectly certain that he has not justified any one of his specific claims; not because I believe that I am in possession of conclusive proofs of these important propositions, but because the transcendental critique, which has disclosed to me all the resources of our pure reason, has completely convinced me that, as reason is incompetent to arrive at affirmative assertions in this field, it is equally unable, indeed even less able, to establish any negative conclusion in regard to these questions. For from what source will the free thinker derive his professed knowledge that there is, for example, no supreme being? This proposition is outside the field of possible experience, and therefore beyond the limits of all human insight. The reply of the dogmatic defender of the good cause I should not read at all. I know beforehand that he will attack the sophistical arguments of his opponent simply in order to gain acceptance for his own; and I also know that a quite familiar line of false argument does not yield so much material for new observations as one that is novel and ingeniously elaborated. P 603 The opponent of religion is indeed, in his own way, no less dogmatic, but he affords me a welcome opportunity of applying and, in this or that respect, amending the principles of my Critique, while at the same time I need be in no fear of these principles being in the least degree endangered. But must not the young, at least, when entrusted to our academical teaching, be warned against such writings, and preserved from a premature knowledge of such dangerous propositions, until their faculty of judgment is mature, or rather until the doctrine which we seek to instil into them has taken such firm root, that they are able effectively to withstand all persuasion to contrary views, from whatever quarter it may come? If we are to insist on holding to dogmatic procedure in matters of pure reason, and on disposing of our opponents in strictly polemical fashion, that is, by ourselves taking sides in the controversy, and therefore equipping ourselves with proofs in support of the opposite assertions, certainly this procedure would for the time being be the most expedient; but in the long run nothing would be more foolish and ineffective than to keep youthful reason thus for a period under tutelage. This will indeed guard the young temporarily against perversion. But when, later, either curiosity or the fashion of the age brings such writings under their notice, will their youthful conviction then stand the test? Whoever, in withstanding the attacks of his opponent, has at his disposal only dogmatic weapons, and is unable to develop the dialectic which lies concealed in his own breast no less than in that of his antagonist, [is in a dangerous position]. He sees sophistical arguments, which have the attraction of novelty, set in opposition to sophistical arguments which no longer have that attraction, but, on the contrary, tend to arouse the suspicion that advantage has been taken of his youthful credulity. And accordingly he comes to believe that there can be no better way of showing that he has outgrown childish discipline than by casting aside these well-meant warnings; and accustomed as he is to dogmatism, he drinks deep draughts of the poison, which destroys his principles by a counter-dogmatism. In academic teaching we ought to pursue the course exactly opposite to that which is here recommended, provided P 604 always that the teaching is based on thorough instruction in the criticism of pure reason. For in order to bring the principles of this criticism into operation as soon as possible, and to show their sufficiency even when dialectical illusion is at its height, it is absolutely necessary that the attacks which seem so terrible to the dogmatist should be made to exercise their full force upon the pupil's reason, which though still weak has been enlightened through criticism, and that the pupil should thus be allowed the opportunity of testing for himself, one by one, by reference to the critical principles, how groundless are the assertions of those who have launched these attacks. As it is by no means difficult for him to resolve these arguments into thin air, he early begins to feel his own capacity to secure himself against such injurious deceptions, which must finally lose for him all their illusory power. Those same blows which destroy the structures of the enemy must indeed be equally destructive to any speculative structure which he may perchance himself wish to erect. This does not, however, in the least disturb him, since he has no need of any such shelter, being still in possession of good expectations in the practical sphere, where he may confidently hope to find firmer ground upon which to erect his own rational and beneficial system. There is, therefore, properly speaking, no polemic in the field of pure reason. Both parties beat the air, and wrestle with their own shadows, since they go beyond the limits of nature, where there is nothing that they can seize and hold with their dogmatic grasp. Fight as they may, the shadows which they cleave asunder grow together again forthwith, like the heroes in Valhalla, to disport themselves anew in the bloodless contests. But neither can we admit that there is any sceptical employment of pure reason, such as might be entitled the principle of neutrality in all its disputes. To set reason at variance with itself, to supply it with weapons on both sides, and then to look on, quietly and scoffingly, at the fierce struggle, is not, from the dogmatic point of view, a seemly spectacle, but appears to suggest a mischievous and malevolent disposition. If, however, we consider the invincible obstinacy and the boastfulness of those who argue dogmatically, and who refuse to allow their claims to be moderated by any criticism, there P 605 is really no other available course of action than to set against the boasting of the one side the no less justified boasting of the other, in the hope that the resistance thus offered to reason may at least serve to disconcert it, to awaken some doubts as to its pretensions, and to make it willing to give a hearing to criticism. But to allow ourselves simply to acquiesce in these doubts, and thereupon to set out to commend the conviction and admission of our ignorance not merely as a remedy against the complacency of the dogmatists, but likewise as the right method of putting an end to the conflict of reason with itself, is a futile procedure, and can never suffice to overcome the restlessness of reason. At best it is merely a means of awakening it from its sweet dogmatic dreams, and of inducing it to enter upon a more careful examination of its own position. Since, however, the sceptical method of escaping from the troublesome affairs of reason appears to be, as it were, a short cut by which we can arrive at a permanent peace in philosophy, or [if it be not that], is at least the road favoured by those who would feign make show of having a philosophical justification for their contemptuous dislike of all enquiries of this kind, I consider it necessary to exhibit this way of thinking in its true light. The Impossibility of a Sceptical Satisfaction of Pure Reason in its Internal Conflicts The consciousness of my ignorance (unless at the same time this ignorance is recognised as being necessary), instead of ending my enquiries, ought rather to be itself the reason for entering upon them. All ignorance is either ignorance of things or ignorance of the function and limits of knowledge. If ignorance is only accidental, it must incite me, in the former regard to a dogmatic enquiry concerning things (objects), in the latter regard to a critical enquiry concerning the limits of my possible knowledge. But that my ignorance is absolutely necessary, and that I am therefore absolved from all further enquiry, cannot be established empirically, from observation, but only through an examination, critically conducted, of the primary sources of our knowledge. The determination of the limits of our reason cannot, therefore, be made save on a priori P 606 grounds; on the other hand, that limitation of it which consists merely in an indeterminate knowledge of an ignorance never to be completely removed, can be recognised a posteriori by reference to that which, notwithstanding all we know, still remains to be known. The former knowledge of our ignorance, which is possible only through criticism of reason itself, is science; the latter is nothing but perception, and we cannot say how far the inferences from perception may extend. If I represent the earth as it appears to my senses, as a flat surface, with a circular horizon, I cannot know how far it extends. But experience teaches me that wherever I may go, I always see a space around me in which I could proceed further; and thus I know the limits of my actual knowledge of the earth at any given time, but not the limits of all possible geography. But if I have got so far as to know that the earth is a sphere and that its surface is spherical, I am able even from a small part of it, for instance, from the magnitude of a degree, to know determinately, in accordance with principles a priori, the diameter, and through it the total superficial area of the earth; and although I am ignorant of the objects which this surface may contain, I yet have knowledge in respect of its circuit, magnitude, and limits. The sum of all the possible objects of our knowledge appears to us to be a plane, with an apparent horizon -- namely, that which in its sweep comprehends it all, and which has been entitled by us the idea of unconditioned totality. To reach this concept empirically is impossible, and all attempts to determine it a priori in accordance with an assured principle have proved vain. None the less all the questions raised by our pure reason are as to what may be outside the horizon, or, it may be, on its boundary line. The celebrated David Hume was one of those geographers of human reason who have imagined that they have sufficiently disposed of all such questions by setting them outside the horizon of human reason -- a horizon which yet he was not able to determine. Hume dwelt in particular upon the principle of causality, and quite rightly observed that its truth, and even the objective validity of the concept of efficient cause in P 607 general, is based on no insight, that is, on no a priori knowledge, and that its authority cannot therefore be ascribed to its necessity, but merely to its general utility in the course of experience, and to a certain subjective necessity which it thereby acquires, and which he entitles custom. From the incapacity of our reason to make use of this principle in any manner that transcends experience, he inferred the nullity of all pretensions of reason to advance beyond the empirical. A procedure of this kind -- subjecting the facts of reason to examination, and if necessary to blame -- may be entitled the censorship of reason. This censorship must certainly lead to doubt regarding all transcendent employment of principles. But this is only the second step, and does not by any means complete the work of enquiry. The first step in matters of pure reason, marking its infancy, is dogmatic. The second step is sceptical; and indicates that experience has rendered our judgment wiser and more circumspect. But a third step, such as can be taken only by fully matured judgment, based on assured principles of proved universality, is now necessary, namely, to subject to examination, not the facts of reason, but reason itself, in the whole extent of its powers, and as regards its aptitude for pure a priori modes of knowledge. This is not the censorship but the criticism of reason, whereby not its present bounds but its determinate [and necessary] limits, not its ignorance on this or that point but its ignorance in regard to all possible questions of a certain kind, are demonstrated from principles, and not merely arrived at by way of conjecture. Scepticism is thus a resting-place for human reason, where it can reflect upon its dogmatic wanderings and make survey of the region in which it finds itself, so that for the future it may be able to choose its path with more certainty. But it is no dwelling-place for permanent settlement. Such can be obtained only through perfect certainty in our knowledge, alike of the objects themselves and of the limits within which all our knowledge of objects is enclosed. Our reason is not like a plane indefinitely far extended, the limits of which we know in a general way only; but must rather be compared to a sphere, the radius of which can be determined from the curvature of the arc of its surface -- that P 608 is to say, from the nature of synthetic a priori propositions -- and whereby we can likewise specify with certainty its volume and its limits. Outside this sphere (the field of experience) there is nothing that can be an object for reason; nay, the very questions in regard to such supposed objects relate only to subjective principles of a complete determination of those relations which can come under the concepts of the understanding and which can be found within the empirical sphere. We are actually in possession of a priori synthetic modes of knowledge, as is shown by the principles of understanding which anticipate experience. If anyone is quite unable to comprehend the possibility of these principles, he may at first be inclined to doubt whether they actually dwell in us a - priori; but he cannot on this account declare that they are beyond the powers of the understanding, and so represent all the steps which reason takes under their guidance as being null and void. All that he can say is that if we could have insight into their origin and authenticity, we should be able to determine the scope and limits of our reason, but that until we can have such insight any assertions as to the limits of reason are made at random. And on this ground a general doubt regarding all dogmatic philosophy, proceeding as such philosophy does without criticism of reason itself, is entirely justified; but we cannot therefore altogether deny to reason the right to take such forward steps, once we have prepared and secured the way for them by a more thorough preparation of the ground. For all the concepts, nay, all the questions, which pure reason presents to us, have their source not in experience, but exclusively in reason itself, and must therefore allow of solution and of being determined in regard to their validity or invalidity. We have no right to ignore these problems, as if their solution really depended on the nature of things, and as if we might therefore, on the plea of our incapacity, decline to occupy ourselves with their further investigation; for since reason is the sole begetter of these ideas, it is under obligation to give an account of their validity or of their illusory, dialectical nature. All sceptical polemic should properly be directed only against the dogmatist, who, without any misgivings as to his fundamental objective principles, that is, without criticism, P 609 proceeds complacently upon his adopted path; it should be designed simply to put him out of countenance and thus to bring him to self-knowledge. In itself, however, this polemic is of no avail whatsoever in enabling us to decide what it is that we can and what it is that we cannot know. All unsuccessful dogmatic attempts of reason are facts, and it is always of advantage to submit them to the censorship of the sceptic. But this can decide nothing regarding those expectations of reason which lead it to hope for better success in its future attempts, and to build claims on this foundation; and consequently no mere censorship can put an end to the dispute regarding the rights of human reason. Hume is perhaps the most ingenious of all the sceptics, and beyond all question is without rival in respect of the influence which the sceptical procedure can exercise in awakening reason to a thorough self-examination. It will therefore well repay us to make clear to ourselves, so far as may be relevant to our purpose, the course of the reasoning, and the errors, of so acute and estimable a man -- a course of reasoning which at the start was certainly on the track of truth. Hume was perhaps aware, although he never followed the matter out, that in judgments of a certain kind we pass beyond our concept of the object. I have entitled this kind of judgments synthetic. There is no difficulty as to how, by means of experience, I can pass beyond the concept which I previously have. Experience is in itself a synthesis of perceptions, whereby the concept which I have obtained by means of a perception is increased through the addition of other perceptions. But we suppose ourselves to be able to pass a priori beyond our concept, and so to extend our knowledge. This we attempt to do either through the pure understanding, in respect of that which is at least capable of being an object of experience, or through pure reason, in respect of such properties of things, or indeed even of the existence of such things, as can never be met with in experience. Our sceptical philosopher did not distinguish these two kinds of judgments, as he yet ought to have done, but straightway proceeded to treat this self- increment of concepts, and, as we may say, this spontaneous generation on the part of our understanding and of our reason, P 610 without impregnation by experience, as being impossible. He therefore regarded all the supposed a priori principles of these faculties as fictitious, and concluded that they are nothing but a custom-bred habit arising from experience and its laws, and are consequently merely empirical, that is, rules that are in themselves contingent, and to which we ascribe a supposititious necessity and universality. In support of his assertion of this startling thesis, he cited the universally recognised principle of the relation between cause and effect. For since no faculty of understanding can carry us from the concept of a thing to the existence of something else that is thereby universally and necessarily given, he believed that he was therefore in a position to conclude that in the absence of experience we have nothing that can increase our concept and justify us in propounding a judgment which thus enlarges itself a priori. That sunlight should melt wax and yet also harden clay, no understanding, he pointed out, can discover from the concepts which we previously possessed of these things, much less infer them according to a law. Only experience is able to teach us such a law. But, as we have discovered in the Transcendental Logic, although we can never pass immediately beyond the content of the concept which is given us, we are nevertheless able, in relation to a third thing, namely, possible experience, to know the law of its connection with other things, and to do so in an a priori manner. If, therefore, wax, which was formerly hard, melts, I can know a priori that something must have preceded, ([that something being] for instance [in this case] the heat of the sun), upon which the melting has followed according to a fixed law, although a priori, independently of experience, I could not determine, in any specific manner, either the cause from the effect, or the effect from the cause. Hume was therefore in error in inferring from the contingency of our determination in accordance with the law the contingency of the law itself. The passing beyond the concept of a thing to possible experience (which takes place a priori and constitutes the objective reality of the concept) he confounded with the synthesis of the objects of actual experience, which is always empirical. He thus confounds a principle of affinity, which has its seat in the understanding and affirms necessary connection, with a rule of P 611 association, which exists only in the imitative faculty of imagination, and which can exhibit only contingent, not objective connections. The sceptical errors of this otherwise singularly acute thinker arose chiefly from a defect which he shares in common with all dogmatists, namely, that he did not make a systematic review of all the various kinds of a priori synthesis ascribable to the understanding. For he would then have found, to mention only one of many possible examples, that the principle of permanence is a principle of this character, and that, like the principle of causality, it anticipates experience. He would thus have been able to prescribe determinate limits to the activities whereby the understanding and pure reason extend themselves a priori. Instead of so doing, he merely restricts the understanding, without defining its limits, and while creating a general mistrust fails to supply any determinate knowledge of the ignorance which for us is unavoidable. For while subjecting to censorship certain principles of the understanding, he makes no attempt to assess the understanding itself, in respect of all its powers, by the assay-balance of criticism; while rightly denying to the understanding what it cannot really supply, he goes on to deny it all power of extending itself a priori, and this in spite of his never having tested it as a whole. Thus the fate that waits upon all scepticism likewise befalls Hume, namely, that his own sceptical teaching comes to be doubted, as being based only on facts which are contingent, not on principles which can constrain to a necessary renunciation of all right to dogmatic assertions. Further, he draws no distinction between the well- grounded claims of the understanding and the dialectical pretensions of reason, though it is indeed chiefly against the latter that his attacks are directed. Accordingly that peculiarly characteristic ardour with which reason insists upon giving free rein to itself, has not in the least been disturbed but only temporarily impeded. It does not feel that it has been shut out from the field in which it is wont to disport itself; and so, in spite of its being thwarted in this and that direction, it cannot be made entirely to desist from these ventures. On the contrary, the attacks lead only to counter-preparations, P 612 and make us the more obstinate in insisting upon our own views. But a complete review of all the powers of reason -- and the conviction thereby obtained of the certainty of its claims to a modest territory, as also of the vanity of higher pretensions -- puts an end to the conflict, and induces it to rest satisfied with a limited but undisputed patrimony. To the uncritical dogmatist, who has not surveyed the sphere of his understanding, and therefore has not determined, in accordance with principles, the limits of his possible knowledge, these sceptical attacks are not only dangerous but even destructive. For he does not know beforehand how far his powers extend, and indeed believes that their limits can be determined by the simple method of trial and failure. In consequence of this, if on being attacked there is a single one of his assertions that he is unable to justify, or which involves illusion for which he also cannot account in terms of any principles, suspicion falls on all his contentions, however plausible they may appear. The sceptic is thus the taskmaster who constrains the dogmatic reasoner to develop a sound critique of the understanding and reason. When we have advanced thus far, we need fear no further challenge, since we have learned to distinguish our real possessions from that which lies entirely outside them; and as we make no claims in regard to this latter domain, we cannot become involved in any dispute in respect to it. While, therefore, the sceptical procedure cannot of itself yield any satisfying answer to the questions of reason, none the less it prepares the way by arousing reason to circumspection, and by indicating the radical measures which are adequate to secure it in its legitimate possessions. CHAPTER I Section 3 THE DISCIPLINE OF PURE REASON IN REGARD TO HYPOTHESES Since criticism of our reason has at last taught us that we cannot by means of its pure and speculative employment arrive at any knowledge whatsoever, may it not seem that a P 613 proportionately wider field is opened for hypotheses? For are we not at liberty, where we cannot make assertions, at least to invent theories and to have opinions? If the imagination is not simply to be visionary, but is to be inventive under the strict surveillance of reason, there must always previously be something that is completely certain, and not invented or merely a matter of opinion, namely, the possibility of the object itself. Once that is established, it is then permissible to have recourse to opinion in regard to its actuality; but this opinion, if it is not to be groundless, must be brought into connection with what is actually given and so far certain, as serving to account for what is thus given. Then, and only then, can the supposition be entitled an hypothesis. As we cannot form the least conception a priori of the possibility of dynamical connection, and as the categories of the pure understanding do not suffice for devising any such conception, but only for apprehending it when met with in experience, we cannot, in accordance with these categories, creatively imagine any object in terms of any new quality that does not allow of being given in experience; and we cannot, therefore, make use of such an object in any legitimate hypothesis; otherwise we should be resting reason on empty figments of the brain, and not on concepts of things. Thus it is not permissible to invent any new original powers, as, for instance, an understanding capable of intuiting its objects without the aid of senses; or a force of attraction without any contact; or a new kind of substance existing in space and yet not impenetrable. Nor is it legitimate to postulate a form of communion of substances which is different from any revealed in experience, a presence that is not spatial, a duration that is not temporal. In a word, our reason can employ as conditions of the possibility of things only the conditions of possible experience; it can never proceed to form concepts of things quite independently of these conditions. Such concepts, though not self-contradictory, would be without an object. P 614 The concepts of reason are, as we have said, mere ideas, and have no object that can be met with in any experience. None the less they do not on this account signify objects that having been invented are thereupon assumed to be possible. They are thought only problematically, in order that upon them (as heuristic fictions), we may base regulative principles of the systematic employment of the understanding in the field of experience. Save in this connection they are merely thought-entities, the possibility of which is not demonstrable, and which therefore do not allow of being employed, in the character of hypotheses, in explanation of the actual appearances. It is quite permissible to think the soul as simple, in order, in conformity with this idea, to employ as the principle of our interpretation of its inner appearances a complete and necessary unity of all its faculties; and this in spite of the fact that this unity is such as can never be apprehended in concreto. But to assume the soul as a simple substance (a transcendent concept), would be [to propound] a proposition which is not only indemonstrable -- as is the case with many physical hypotheses -- but is hazarded in a quite blind and arbitrary fashion. For the simple can never be met with in any experience whatsoever; and if by substance be here meant the permanent object of sensible intuition, the possibility of a simple appearance is quite incomprehensible. Reason does not afford any sufficient ground for assuming, [even] as a matter of opinion, merely intelligible beings, or merely intelligible properties of things belonging to the sensible world, although (as we have no concepts of their possibility or impossibility) we also cannot lay claim to any insight that justifies us in dogmatically denying them. In the explanation of given appearances, no things or grounds of explanation can be adduced other than those which have been found to stand in connection with given appearances in accordance with the already known laws of the appearances. A transcendental hypothesis, in which a mere idea of reason is used in explanation of natural existences would really be no explanation; so to proceed would be to explain something, which in terms of known empirical principles we do not understand sufficiently, by something which P 615 we do not understand at all. Moreover, the principle of such an hypothesis would at most serve only for the satisfaction of reason, not for the furtherance of the employment of the understanding in respect of objects. Order and purposiveness in nature must themselves be explained from natural grounds and according to natural laws; and the wildest hypotheses, if only they are physical, are here more tolerable than a hyperphysical hypothesis, such as the appeal to a divine Author, assumed simply in order that we may have an explanation. That would be a principle of ignava ratio; for we should be passing over all causes the objective reality of which, at least as regards their possibility, can be ascertained in the course of experience, in order to rest in a mere idea -- an idea that is very comforting to reason. As regards the absolute totality of the ground of explanation of the series of these causes, such totality need suggest no difficulty in respect of natural existences; since these existences are nothing but appearances, we need never look to them for any kind of completeness in the synthesis of the series of conditions. It can never be permissible, in the speculative employment of reason, to resort to transcendental hypotheses, and to presume that we can make good the lack of physical grounds of explanation by appealing to the hyperphysical. The objection to such procedure is twofold: partly, that reason, so far from being in the least advanced thereby, is cut off from all progress in its own employment; partly, that this license would in the end deprive reason of all the fruits that spring from the cultivation of its own proper domain, namely, that of experience. For whenever the explanation of natural existences is found to be difficult, there is always at hand a transcendental ground of explanation which relieves us from further investigation, and our enquiry is brought to an end not through insight, but by the aid of a principle which while utterly incomprehensible has from the start been so constructed as necessarily to contain the concept of what is absolutely primordial. The second requirement for the admissibility of an hypothesis is its adequacy in accounting a priori for those consequences which are [de facto] given. If for this purpose we have to call in auxiliary hypotheses, they give rise to the P 616 suspicion that they are mere fictions; for each of them requires the same justification as is necessary in the case of the fundamental hypothesis, and they are not, therefore, in a position to bear reliable testimony. If we assume an absolutely perfect cause, we need not be at a loss in explaining the purposiveness, order, and vastness which are displayed in the world; but in view of what, judged at least by our concepts, are the obvious deviations and evils, other new hypotheses are required in order to uphold the original hypothesis in face of the objections which these suggest. If the simple self-sufficiency of the human soul has been employed to account for its appearances, it is controverted by certain difficulties, due to those phenomena which are similar to the changes that take place in matter (growth and decay), and we have therefore to seek the aid of new hypotheses, which are not indeed without plausibility, but which yet have no credentials save what is conferred upon them by that opinion -- the fundamental hypothesis -- which they have themselves been called in to support. If the instances here cited as examples of the assertions made by reason -- the incorporeal unity of the soul and the existence of a supreme being -- are propounded not as hypotheses, but as dogmas proved a priori, I am not at present concerned with them, save to remark that in that case care must be taken that the proof has the apodeictic certainty of a demonstration. For to set out to show no more than that the reality of such ideas is probable is as absurd as to think of proving a proposition of geometry merely as a probability. Reason, when employed apart from all experience, can know propositions entirely a priori, and as necessary, or it can know nothing at all. Its judgments, therefore, are never opinions; either it must abstain from all judgment, or must affirm with apodeictic certainty. Opinions and probable judgments as to what belongs to things can be propounded only in explanation of what is actually given, or as consequences that follow in accordance with empirical laws from what underlies the actually given. They are therefore concerned only with the series of the objects of experience. Outside this field, to form opinions is merely to play with thoughts. For we should then have to presuppose yet another opinion -- the opinion that we may perhaps arrive at the truth by a road that is uncertain. P 617 But although, in dealing with the merely speculative questions of pure reason, hypotheses are not available for the purposes of basing propositions upon them, they are yet entirely permissible for the purposes of defending propositions; that is to say, they may not be employed in any dogmatic, but only in polemical fashion. By the defence of propositions I do not mean the addition of fresh grounds for their assertion, but merely the nullifying of the sophistical arguments by which our opponent professes to invalidate this assertion. Now all synthetic propositions of pure reason have this peculiarity, that while in asserting the reality of this or that idea we can never have knowledge sufficient to give certainty to our proposition, our opponent is just as little able to assert the opposite. This equality of fortune [in the ventures] of human reason does not, in speculative modes of knowledge, favour either of the two parties, and it is consequently the fitting battle-ground for their never-ending feuds. But as will be shown, reason has, in respect of its practical employment, the right to postulate what in the field of mere speculation it can have no kind of right to assume without sufficient proof. For while all such assumptions do violence to [the principle of] completeness of speculation, that is a principle with which the practical interest is not at all concerned. In the practical sphere reason has rights of possession, of which it does not require to offer proof, and of which, in fact, it could not supply proof. The burden of proof accordingly rests upon the opponent. But since the latter knows just as little of the object under question, in trying to prove its non-existence, as does the former in maintaining its reality, it is evident that the former, who is asserting something as a practically necessary supposition, is at an advantage (melior est conditio possidentis). For he is at liberty to employ, as it were in self-defence, on behalf of his own good cause, the very same weapons that his opponent employs against that cause, that is, hypotheses. These are not intended to strengthen the proof of his position, but only to show that the opposing party has much too little understanding of the matter in dispute to allow of his flattering himself that he has the advantage in respect of speculative insight. Hypotheses are therefore, in the domain of pure reason, permissible only as weapons of war, and only for the purpose P 618 of defending a right, not in order to establish it. But the opposing party we must always look for in ourselves. For speculative reason in its transcendental employment is in itself dialectical; the objections which we have to fear lie in ourselves. We must seek them out, just as we would do in the case of claims that, while old, have never become superannuated, in order that by annulling them we may establish a permanent peace. External quiescence is merely specious. The root of these disturbances, which lies deep in the nature of human reason, must be removed. But how can we do so, unless we give it freedom, nay, nourishment, to send out shoots so that it may discover itself to our eyes, and that it may then be entirely destroyed? We must, therefore, bethink ourselves of objections which have never yet occurred to any opponent, and indeed lend him our weapons, and grant him the most favourable position which he could possibly desire. We have nothing to fear in all this, but much to hope for; namely, that we may gain for ourselves a possession which can never again be contested. Thus for our complete equipment we require among other things the hypotheses of pure reason. For although they are but leaden weapons, since they are not steeled by any law of experience, they are yet as effective as those which our opponents can employ against us. If, therefore, having assumed (in some non-speculative connection) the nature of the soul to be immaterial and not subject to any corporeal change, we are met by the difficulty that nevertheless experience seems to prove that the exaltation and the derangement of our mental powers are alike in being merely diverse modifications of our organs, we can weaken the force of this proof by postulating that our body may be nothing more than a fundamental appearance which in this our present state (in this life) serves as a condition of our whole faculty of sensibility, and therewith of all our thought, and that separation from the body may therefore be regarded as the end of this sensible employment of our faculty of knowledge and the beginning of its intellectual employment. Thus regarded, the body would not be the cause of thought, but merely a restrictive condition of it, and therefore, while indeed furthering the sensible and animal life, it would because of this very fact have to be considered a P 619 hindrance to the pure and spiritual life. The dependence of the animal and sensible upon the bodily constitution would then in nowise prove the dependence of our entire life upon the state of our organs. We might go yet further, and discover quite new objections, which either have never been suggested or have never been sufficiently developed. Generation, in man as in non-rational creatures, is dependent upon opportunity, often indeed upon sufficiency of food, upon the moods and caprices of rulers, nay, even upon vice. And this makes it very difficult to suppose that a creature whose life has its first beginning in circumstances so trivial and so entirely dependent upon our own choice, should have an existence that extends to all eternity. As regards the continuance (here on earth) of the species as a whole, this difficulty is negligible, since accident in the individual case is still subject to a general law, but as regards each individual it certainly seems highly questionable to expect so potent an effect from causes so insignificant. But to meet these objections we can propound a transcendental hypothesis, namely, that all life is, strictly speaking, intelligible only, is not subject to changes of time, and neither begins in birth nor ends in death; that this life is an appearance only, that is, a sensible representation of the purely spiritual life, and that the whole sensible world is a mere picture which in our present mode of knowledge hovers before us, and like a dream has in itself no objective reality; that if we could intuit ourselves and things as they are, we should see ourselves in a world of spiritual beings, our sole and true community with which has not begun through birth and will not cease through bodily death -- both birth and death being mere appearances. Now of all this we have not the least knowledge. We plead it only in hypothetical fashion, to meet the attack; we are not actually asserting it. For it is not even an idea of reason, but is a concept devised merely for the purposes of self-defence. None the less we are here proceeding in entire conformity with reason. Our opponent falsely represents the absence of empirical conditions as itself amounting to proof of the total P 620 impossibility of our belief, and is therefore proceeding on the assumption that he has exhausted all the possibilities. What we are doing is merely to show that it is just as little possible for him to comprehend the whole field of possible things through mere laws of experience as it is for us to reach, outside experience, any conclusions justifiable for our reason. Anyone who employs such hypothetical means of defence against the rash and presumptuous negations of his opponent must not be considered to intend the adoption of these opinions as his own; he abandons them, as soon as he has disposed of the dogmatic pretensions of his opponent. For though a merely negative attitude to the assertions of others may seem very modest and moderate, to proceed to represent the objections to an assertion as proofs of the counter-assertion is to make claims no less presumptuous and visionary than if the positive position and its affirmations had been adopted. It is evident, therefore, that in the speculative employment of reason hypotheses, regarded as opinions, have no validity in themselves, but only relatively to the transcendent pretensions of the opposite party. For to make principles of possible experience conditions of the possibility of things in general is just as transcendent a procedure as to assert the objective reality of [transcendent] concepts, the objects of which cannot be found anywhere save outside the limits of all possible experience. What pure reason judges assertorically, must (like everything that reason knows) be necessary; otherwise nothing at all is asserted. Accordingly, pure reason does not, in point of fact, contain any opinions whatsoever. The hypotheses, above referred to, are merely problematic judgments, which at least cannot be refuted, although they do not indeed allow of any proof. They are therefore nothing but private opinions. Nevertheless, we cannot properly dispense with them as weapons against the misgivings which are apt to occur; they are necessary even to secure our inner tranquillity. We must preserve to them this character, carefully guarding against the assumption of their independent authority or absolute validity, since otherwise they would drown reason in fictions and delusions. P 621 CHAPTER I Section 4 THE DISCIPLINE OF PURE REASON IN REGARD TO ITS PROOFS What distinguishes the proofs of transcendental synthetic propositions from all other proofs which yield an a priori synthetic knowledge is that, in the case of the former, reason may not apply itself, by means of its concepts, directly to the object, but must first establish the objective validity of the concepts and the possibility of their a priori synthesis. This rule is not made necessary merely by considerations of prudence, but is essential to the very possibility of the proofs themselves. If I am to pass a priori beyond the concept of an object, I can do so only with the help of some special guidance, supplied from outside this concept. In mathematics it is a - priori intuition which guides my synthesis; and thereby all our conclusions can be drawn immediately from pure intuition. In transcendental knowledge, so long as we are concerned only with concepts of the understanding, our guide is the possibility of experience. Such proof does not show that the given concept (for instance, of that which happens) leads directly to another concept (that of a cause); for such a transition would be a saltus which could not be justified. The proof proceeds by showing that experience itself, and therefore the object of experience, would be impossible without a connection of this kind. Accordingly, the proof must also at the same time show the possibility of arriving synthetically and a priori at some knowledge of things which was not contained in the concepts of them. Unless this requirement be met, the proofs, like streams which break their banks, run wildly at random, whithersoever the current of hidden association may chance to lead them. The semblance of conviction which rests upon subjective causes of association, and which is regarded as insight into a natural affinity, cannot balance the misgivings to which so hazardous a course must rightly give rise. On this account, all attempts to prove the principle of sufficient reason have, by the universal P 622 admission of those concerned, been fruitless; and prior to our own transcendental criticism it was considered better, since that principle could not be surrendered, boldly to appeal to the common sense of mankind -- an expedient which always is a sign that the cause of reason is in desperate straits -- rather than to attempt new dogmatic proofs. But if the proposition to be proved is an assertion of pure reason, and if I am therefore proposing to pass beyond my empirical concepts by means of mere ideas, justification of such a step in synthesis (supposing it to be possible) is all the more necessary as a precondition of any attempt to prove the proposition itself. However plausible the alleged proof of the simple nature of our thinking substance, derived from the unity of apperception, may be, it is faced by the unavoidable difficulty, that since the [notion of] absolute simplicity is not a concept which can be immediately related to a perception, but, as an idea, would have to be inferred, there can be no understanding how the bare consciousness (which is, or at least can be, contained in all thought), though it is indeed so far a simple representation, should conduct us to the consciousness and the knowledge of a thing in which thought alone can be contained. If I represent to myself the power of a body in motion, it is so far for me absolute unity, and my representation of it is simple; and I can therefore express this representation by the motion of a point -- for the volume of the body is not here a relevant consideration, and can be thought, without diminution of the moving power, as small as we please, and therefore even as existing in a point. But I may not therefore conclude that if nothing be given to me but the moving power of a body, the body can be thought as simple substance -- merely because its representation abstracts from the magnitude of its volume and is consequently simple. The simple arrived at by abstraction is entirely different from the simple as an object; though the 'I', taken in abstraction, can contain in itself no manifold, in its other meaning, as signifying the soul itself, it can be a highly complex concept, as containing under itself, and as denoting, what is very composite. I thus detect in these arguments a paralogism. But in order to be armed against this P 623 paralogism (for without some forewarning we should not entertain any suspicion in regard to the proof), it is indispensably necessary to have constantly at hand a criterion of the possibility of those synthetic propositions which are intended to prove more than experience yields. This criterion consists in the requirement that proof should not proceed directly to the desired predicate but only by means of a principle that will demonstrate the possibility of extending our given concept in an a priori manner to ideas, and of realising the latter. If this precaution be always observed, if before attempting any proof, we discreetly take thought as to how, and with what ground for hope, we may expect such an extension through pure reason, and whence, in such a case, this insight, which is not developed from concepts, and also cannot be anticipated in reference to any possible experience, is yet to be derived, we can by so doing spare ourselves much difficult and yet fruitless labour, not expecting from reason what obviously exceeds its power -- or rather, since reason, when obsessed by passionate desire for the speculative enlargement of its domain, is not easily to be restrained, by subjecting it to the discipline of self-control. The first rule is, therefore, not to attempt any transcendental proofs until we have considered, with a view to obtaining justification for them, from what source we propose to derive the principles on which the proofs are to be based, and with what right we may expect success in our inferences. If they are principles of the understanding (for instance, that of causality), it is useless to attempt, by means of them, to attain to ideas of pure reason; such principles are valid only for objects of possible experience. If they are principles of pure reason, it is again labour lost. Reason has indeed principles of its own; but regarded as objective principles, they are one and all dialectical, and can have no validity save as regulative principles for its employment in experience, with a view to making experience systematically coherent. But if such professed proofs are propounded, we must meet their deceptive power of persuasion with the non liquet of our matured judgment; and although we may not be able to detect the illusion involved, we are yet entirely within our rights in demanding a deduction of the principles employed in them; P 624 and if these principles have their source in reason alone, the demand is one which can never be met. And there is thus no need for us to concern ourselves with the particular nature and with the refutation of each and every groundless illusion; at the tribunal of a critical reason, which insists upon laws, this entire dialectic, so inexhaustible in its artifices, can be disposed of in bulk. The second peculiarity of transcendental proofs is that only one proof can be found for each transcendental proposition. If I am inferring not from concepts but from the intuition which corresponds to a concept, be it a pure intuition as in mathematics, or an empirical intuition as in natural science, the intuition which serves as the basis of the inference supplies me with manifold material for synthetic propositions, material which I can connect in more than one way, so that, as it is permissible for me to start from more than one point, I can arrive at the same proposition by different paths. In the case of transcendental propositions, however, we start always from one concept only, and assert the synthetic condition of the possibility of the object in accordance with this concept. Since outside this concept there is nothing further through which the object could be determined, there can therefore be only one ground of proof. The proof can contain nothing more than the determination of an object in general in accordance with this one single concept. In the Transcendental Analytic, for instance, we derived the principle that everything which happens has a cause, from the condition under which alone a concept of happening in general is objectively possible -- namely, by showing that the determination of an event in time, and therefore the event as belonging to experience, would be impossible save as standing under such a dynamical rule. This is the sole possible ground of proof; for the event, in being represented, has objective validity, that is, truth, only in so far as an object is determined for the concept by means of the law of causality. Other proofs of this principle have, indeed, been attempted, for instance, from the contingency [of that which happens]. But on examining this argument, we can discover no mark of contingency save only the happening, that is, the existence of the object preceded by its non-existence, and thus are brought back to the same P 625 ground of proof as before. Similarly, if the proposition, that everything which thinks is simple, is to be proved, we leave out of account the manifold of thought, and hold only to the concept of the 'I', which is simple and to which all thought is related. The same is true of the transcendental proof of the existence of God; it is based solely on the coincidence of the concepts of the most real being and of necessary being, and is not to be looked for anywhere else. This caution reduces the criticism of the assertions of reason to very small compass. When reason is conducting its business through concepts only, there is but one possible proof, if, that is to say, there be any possible proof at all. If, therefore, we observe the dogmatist coming forward with ten proofs, we can be quite sure that he really has none. For had he one that yielded -- as must always be required in matters of pure reason -- apodeictic proof, what need would he have of the others? His purpose can only be that of the parliamentary advocate, who intends his various arguments for different groups, in order to take advantage of the weakness of those before whom he is pleading -- hearers who, without entering deeply into the matter, desire to be soon quit of it, and therefore seize upon whatever may first happen to attract their attention, and decide accordingly. The third rule peculiar to pure reason, in so far as it is to be subjected to a discipline in respect of transcendental proofs, is that its proofs must never be apagogical, but always ostensive. The direct or ostensive proof, in every kind of knowledge, is that which combines with the conviction of its truth insight into the sources of its truth; the apagogical proof, on the other hand, while it can indeed yield certainty, cannot enable us to comprehend truth in its connection with the grounds of its possibility. The latter is therefore to be regarded rather as a last resort than as a mode of procedure which satisfies all the requirements of reason. In respect of convincing power, it has, however, this advantage over the direct proofs, that contradiction always carries with it more clearness of representation than the best connection, and so approximates to the intuitional certainty of a demonstration. The real reason why apagogical proofs are employed in P 626 various sciences would seem to be this. When the grounds from which this or that knowledge has to be derived are too numerous or too deeply concealed, we try whether we may not arrive at the knowledge in question through its consequences. Now this modus ponens, that is, the inference to the truth of an assertion from the truth of its consequences, is only permissible when all its possible consequences are [known to be] true; for in that case there is only one possible ground for this being so, and that ground must also be true. But this procedure is impracticable; to discover all possible consequences of any given proposition exceeds our powers. None the less this mode of reasoning is resorted to, although indeed with a certain special modification, when we endeavour to prove something merely as an hypothesis. The modification made is that we admit the conclusion as holding according to analogy, namely, on the ground that if all the many consequences examined by us agree with an assumed ground, all other possible consequences will also agree with it. But from the nature of the argument, it is obvious that an hypothesis can never, on such evidence, be transformed into demonstrated truth. The modus tollens of reasoning, which proceeds from consequences to their grounds, is not only a quite rigorous but also an extremely easy mode of proof. For if even a single false consequence can be drawn from a proposition, the proposition is itself false. Instead, then, as in an ostensive proof, of reviewing the whole series of grounds that can lead us to the truth of a proposition, by means of a complete insight into its possibility, we require only to show that a single one of the consequences resulting from its opposite is false, in order to prove that this opposite is itself false, and that the proposition which we had to prove is therefore true. The apagogic method of proof is, however, permissible only in those sciences where it is impossible mistakenly to substitute what is subjective in our representations for what is objective, that is, for the knowledge of that which is in the object. Where such substitution tends to occur, it must often happen that the opposite of a given proposition contradicts only the subjective conditions of thought, and not the object, or that the two propositions contradict each other only under a subjective condition which is falsely treated as being objective; P 627 the condition being false, both can be false, without it being possible to infer from the falsity of the one to the truth of the other. In mathematics this subreption is impossible; and it is there, therefore, that apagogical proofs have their true place. In natural science, where all our knowledge is based upon empirical intuitions, the subreption can generally be guarded against through repeated comparison of observations; but in this field this mode of proof is for the most part of little importance. The transcendental enterprises of pure reason, however, are one and all carried on within the domain proper to dialectical illusion, that is, within the domain of the subjective, which in its premisses presents itself to reason, nay, forces itself upon reason, as being objective. In this field, therefore, it can never be permissible, so far as synthetic propositions are concerned, to justify assertions by disproving their opposite. For either this refutation is nothing but the mere representation of the conflict of the opposite opinion with the subjective conditions under which alone anything can be conceived by our reason, which does not in the least contribute to the disproof of the thing itself-- just as, for instance, we must recognise that while the unconditioned necessity of the existence of a being is altogether inconceivable to us, and that every speculative proof of a necessary supreme being is therefore rightly to be opposed on subjective grounds, we have yet no right to deny the possibility of such a primordial being in itself -- or else both parties, those who adopt the affirmative no less than those who adopt the negative position, have been deceived by transcendental illusion, and base their assertions upon an impossible concept of the object. In that case we can apply the rule: non entis nulla sunt predicata; that is, all that is asserted of the object, whether affirmatively or negatively, is erroneous, and consequently we cannot arrive apagogically at knowledge of the truth through refutation of the opposite. If, for instance, it be assumed that the sensible world is given in itself in its totality, it is false that it must be either infinite in space or finite and limited. Both contentions are false. For appearances (as mere representations) which yet are to be given in themselves (as objects) are something impossible; and though the infinitude of this imaginary whole would P 628 indeed be unconditioned, it would contradict (since everything in appearances is conditioned) the unconditioned determination of magnitude, [that is, of totality], which is presupposed in the concept. The apagogic method of proof is the real deluding influence by which those who reason dogmatically have always held their admirers. It may be compared to a champion who seeks to uphold the honour and incontestable rights of his adopted party by offering battle to all who would question them. Such boasting proves nothing, however, in regard to the merits of the issue but only in regard to the respective strength of the combatants, and this indeed only in respect of those who take the offensive. The spectators, observing that each party is alternately conqueror and conquered, are often led to have sceptical doubts in regard to the very object of the dispute. They are not, however, justified in adopting such an attitude; it is sufficient to declare to the combatants: non defensoribus istis tempus eget. Everyone must defend his position directly, by a legitimate proof that carries with it a transcendental deduction of the grounds upon which it is itself made to rest. Only when this has been done, are we in a position to decide how far its claims allow of rational justification. If an opponent relies on subjective grounds, it is an easy matter to refute him. The dogmatist cannot, however, profit by this advantage. His own judgments are, as a rule, no less dependent upon subjective influences; and he can himself in turn be similarly cornered by his opponent. But if both parties proceed by the direct method, either they will soon discover the difficulty, nay, the impossibility, of showing ground for their assertions, and will be left with no resort save to appeal to some form of prescriptive authority; or our criticism will easily discover the illusion to which their dogmatic procedure is due, compelling pure reason to relinquish its exaggerated pretensions in the realm of speculation, and to withdraw within the limits of its proper territory -- that of practical principles. P 629 THE TRANSCENDENTAL DOCTRINE OF METHOD CHAPTER II THE CANON OF PURE REASON IT is humiliating to human reason that it achieves nothing in its pure employment, and indeed stands in need of a discipline to check its extravagances, and to guard it against the deceptions which arise therefrom. But, on the other hand, reason is reassured and gains self-confidence, on finding that it itself can and must apply this discipline, and that it is not called upon to submit to any outside censorship; and, moreover, that the limits which it is compelled to set to its speculative employment likewise limit the pseudo-rational pretensions of all its opponents, and that it can secure against all attacks whatever may remain over from its former exaggerated claims. The greatest and perhaps the sole use of all philosophy of pure reason is therefore only negative; since it serves not as an organon for the extension but as a discipline for the limitation of pure reason, and, instead of discovering truth, has only the modest merit of guarding against error. There must, however, be some source of positive modes of knowledge which belong to the domain of pure reason, and which, it may be, give occasion to error solely owing to misunderstanding, while yet in actual fact they form the goal towards which reason is directing its efforts. How else can we account for our inextinguishable desire to find firm footing somewhere beyond the limits of experience? Reason has a presentiment of objects which possess a great interest for it. But when it follows the path of pure speculation, in order to approach them, they fly before it. Presumably it may look for better fortune in the only other path which still remains open to it, that of its practical employment. P 630 I understand by a canon the sum-total of the a priori principles of the correct employment of certain faculties of knowledge. Thus general logic, in its analytic portion, is a canon for understanding and reason in general; but only in regard to their form; it abstracts from all content. The transcendental analytic has similarly been shown to be the canon of the pure understanding; for understanding alone is capable of true synthetic modes of knowledge a priori. But when no correct employment of a faculty of knowledge is possible there is no canon. Now all synthetic knowledge through pure reason in its speculative employment is, as has been shown by the proofs given, completely impossible. There is therefore no canon of its speculative employment; such employment is entirely dialectical. All transcendental logic is, in this respect, simply a discipline. Consequently, if there be any correct employment of pure reason, in which case there must be a canon of its employment, the canon will deal not with the speculative but with the practical employment of reason. This practical employment of reason we shall now proceed to investigate.