Now there is nothing to hinder us from admitting these ideas to possess an objective and hyperbolic existence, except the cosmological ideas, which lead reason into an antinomy: the psychological and theological ideas are not antinomial. They contain no contradiction; and how, then, can any one dispute their objective reality, since he who denies it knows as little about their possibility as we who affirm? And yet, when we wish to admit the existence of a thing, it is not sufficient to convince ourselves that there is no positive obstacle in the way; for it cannot be allowable to regard mere creations of thought, which transcend, though they do not contradict, all our conceptions, as real and determinate objects, solely upon the authority of a speculative reason striving to compass its own aims. They cannot, therefore, be admitted to be real in themselves; they can only possess a comparative reality—that of a schema of the regulative principle of the systematic unity of all cognition. They are to be regarded not as actual things, but as in some measure analogous to them. We abstract from the object of the idea all the conditions which limit the exercise of our understanding, but which, on the other hand, are the sole conditions of our possessing a determinate conception of any given thing. And thus we cogitate a something, of the real nature of which we have not the least conception, but which we represent to ourselves as standing in a relation to the whole system of phenomena, analogous to that in which phenomena stand to each other.

By admitting these ideal beings, we do not really extend our cognitions beyond the objects of possible experience; we extend merely the empirical unity of our experience, by the aid of systematic unity, the schema of which is furnished by the idea, which is therefore valid—not as a constitutive, but as a regulative principle. For although we posit a thing corresponding to the idea—a something, an actual existence—we do not on that account aim at the extension of our cognition by means of transcendent conceptions. This existence is purely ideal, and not objective; it is the mere expression of the systematic unity which is to be the guide of reason in the field of experience. There are no attempts made at deciding what the ground of this unity may be, or what the real nature of this imaginary being.

Thus the transcendental and only determinate conception of God, which is presented to us by speculative reason, is in the strictest sense deistic. In other words, reason does not assure us of the objective validity of the conception; it merely gives us the idea of something, on which the supreme and necessary unity of all experience is based. This something we cannot, following the analogy of a real substance, cogitate otherwise than as the cause of all things operating in accordance with rational laws, if we regard it as an individual object; although we should rest contented with the idea alone as a regulative principle of reason, and make no attempt at completing the sum of the conditions imposed by thought. This attempt is, indeed, inconsistent with the grand aim of complete systematic unity in the sphere of cognition—a unity to which no bounds are set by reason.

Hence it happens that, admitting a divine being, I can have no conception of the internal possibility of its perfection, or of the necessity of its existence. The only advantage of this admission is that it enables me to answer all other questions relating to the contingent, and to give reason the most complete satisfaction as regards the unity which it aims at attaining in the world of experience. But I cannot satisfy reason with regard to this hypothesis itself; and this proves that it is not its intelligence and insight into the subject, but its speculative interest alone which induces it to proceed from a point lying far beyond the sphere of our cognition, for the purpose of being able to consider all objects as parts of a systematic whole.

Here a distinction presents itself, in regard to the way in which we may cogitate a presupposition—a distinction which is somewhat subtle, but of great importance in transcendental philosophy. I may have sufficient grounds to admit something, or the existence of something, in a relative point of view (suppositio relativa), without being justified in admitting it in an absolute sense (suppositio absoluta). This distinction is undoubtedly requisite, in the case of a regulative principle, the necessity of which we recognize, though we are ignorant of the source and cause of that necessity, and which we assume to be based upon some ultimate ground, for the purpose of being able to cogitate the universality of the principle in a more determinate way. For example, I cogitate the existence of a being corresponding to a pure transcendental idea. But I cannot admit that this being exists absolutely and in itself, because all of the conceptions by which I can cogitate an object in a determinate manner fall short of assuring me of its existence; nay, the conditions of the objective validity of my conceptions are excluded by the idea—by the very fact of its being an idea. The conceptions of reality, substance, causality, nay, even that of necessity in existence, have no significance out of the sphere of empirical cognition, and cannot, beyond that sphere, determine any object. They may, accordingly, be employed to explain the possibility of things in the world of sense, but they are utterly inadequate to explain the possibility of the universe itself considered as a whole; because in this case the ground of explanation must lie out of and beyond the world, and cannot, therefore, be an object of possible experience. Now, I may admit the existence of an incomprehensible being of this nature—the object of a mere idea, relatively to the world of sense; although I have no ground to admit its existence absolutely and in itself. For if an idea (that of a systematic and complete unity, of which I shall presently speak more particularly) lies at the foundation of the most extended empirical employment of reason, and if this idea cannot be adequately represented in concreto, although it is indispensably necessary for the approximation of empirical unity to the highest possible degree—I am not only authorized, but compelled, to realize this idea, that is, to posit a real object corresponding thereto. But I cannot profess to know this object; it is to me merely a something, to which, as the ground of systematic unity in cognition, I attribute such properties as are analogous to the conceptions employed by the understanding in the sphere of experience. Following the analogy of the notions of reality, substance, causality, and necessity, I cogitate a being, which possesses all these attributes in the highest degree; and, as this idea is the offspring of my reason alone, I cogitate this being as self-subsistent reason, and as the cause of the universe operating by means of ideas of the greatest possible harmony and unity. Thus I abstract all conditions that would limit my idea, solely for the purpose of rendering systematic unity possible in the world of empirical diversity, and thus securing the widest possible extension for the exercise of reason in that sphere. This I am enabled to do, by regarding all connections and relations in the world of sense, as if they were the dispositions of a supreme reason, of which our reason is but a faint image. I then proceed to cogitate this Supreme Being by conceptions which have, properly, no meaning or application, except in the world of sense. But as I am authorized to employ the transcendental hypothesis of such a being in a relative respect alone, that is, as the substratum of the greatest possible unity in experience—I may attribute to a being which I regard as distinct from the world, such properties as belong solely to the sphere of sense and experience. For I do not desire, and am not justified in desiring, to cognize this object of my idea, as it exists in itself; for I possess no conceptions sufficient for or task, those of reality, substance, causality, nay, even that of necessity in existence, losing all significance, and becoming merely the signs of conceptions, without content and without applicability, when I attempt to carry them beyond the limits of the world of sense. I cogitate merely the relation of a perfectly unknown being to the greatest possible systematic unity of experience, solely for the purpose of employing it as the schema of the regulative principle which directs reason in its empirical exercise.

It is evident, at the first view, that we cannot presuppose the reality of this transcendental object, by means of the conceptions of reality, substance, causality, and so on, because these conceptions cannot be applied to anything that is distinct from the world of sense. Thus the supposition of a Supreme Being or cause is purely relative; it is cogitated only in behalf of the systematic unity of experience; such a being is but a something, of whose existence in itself we have not the least conception. Thus, too, it becomes sufficiently manifest why we required the idea of a necessary being in relation to objects given by sense, although we can never have the least conception of this being, or of its absolute necessity.

And now we can clearly perceive the result of our transcendental dialectic, and the proper aim of the ideas of pure reason—which become dialectical solely from misunderstanding and inconsiderateness. Pure reason is, in fact, occupied with itself, and not with any object. Objects are not presented to it to be embraced in the unity of an empirical conception; it is only the cognitions of the understanding that are presented to it, for the purpose of receiving the unity of a rational conception, that is, of being connected according to a principle. The unity of reason is the unity of system; and this systematic unity is not an objective principle, extending its dominion over objects, but a subjective maxim, extending its authority over the empirical cognition of objects. The systematic connection which reason gives to the empirical employment of the understanding not only advances the extension of that employment, but ensures its correctness, and thus the principle of a systematic unity of this nature is also objective, although only in an indefinite respect (principium vagum). It is not, however, a constitutive principle, determining an object to which it directly relates; it is merely a regulative principle or maxim, advancing and strengthening the empirical exercise of reason, by the opening up of new paths of which the understanding is ignorant, while it never conflicts with the laws of its exercise in the sphere of experience.

But reason cannot cogitate this systematic unity, without at the same time cogitating an object of the idea—an object that cannot be presented in any experience, which contains no concrete example of a complete systematic unity. This being (ens rationis ratiocinatae) is therefore a mere idea and is not assumed to be a thing which is real absolutely and in itself. On the contrary, it forms merely the problematical foundation of the connection which the mind introduces among the phenomena of the sensuous world. We look upon this connection, in the light of the above-mentioned idea, as if it drew its origin from the supposed being which corresponds to the idea. And yet all we aim at is the possession of this idea as a secure foundation for the systematic unity of experience—a unity indispensable to reason, advantageous to the understanding, and promotive of the interests of empirical cognition.

We mistake the true meaning of this idea when we regard it as an enouncement, or even as a hypothetical declaration of the existence of a real thing, which we are to regard as the origin or ground of a systematic constitution of the universe. On the contrary, it is left completely undetermined what the nature or properties of this so-called ground may be. The idea is merely to be adopted as a point of view, from which this unity, so essential to reason and so beneficial to the understanding, may be regarded as radiating. In one word, this transcendental thing is merely the schema of a regulative principle, by means of which Reason, so far as in her lies, extends the dominion of systematic unity over the whole sphere of experience.

The first object of an idea of this kind is the ego, considered merely as a thinking nature or soul. If I wish to investigate the properties of a thinking being, I must interrogate experience. But I find that I can apply none of the categories to this object, the schema of these categories, which is the condition of their application, being given only in sensuous intuition. But I cannot thus attain to the cognition of a systematic unity of all the phenomena of the internal sense. Instead, therefore, of an empirical conception of what the soul really is, reason takes the conception of the empirical unity of all thought, and, by cogitating this unity as unconditioned and primitive, constructs the rational conception or idea of a simple substance which is in itself unchangeable, possessing personal identity, and in connection with other real things external to it; in one word, it constructs the idea of a simple self-subsistent intelligence. But the real aim of reason in this procedure is the attainment of principles of systematic unity for the explanation of the phenomena of the soul. That is, reason desires to be able to represent all the determinations of the internal sense as existing in one subject, all powers as deduced from one fundamental power, all changes as mere varieties in the condition of a being which is permanent and always the same, and all phenomena in space as entirely different in their nature from the procedure of thought. Essential simplicity (with the other attributes predicated of the ego) is regarded as the mere schema of this regulative principle; it is not assumed that it is the actual ground of the properties of the soul. For these properties may rest upon quite different grounds, of which we are completely ignorant; just as the above predicates could not give us any knowledge of the soul as it is in itself, even if we regarded them as valid in respect of it, inasmuch as they constitute a mere idea, which cannot be represented in concreto. Nothing but good can result from a psychological idea of this kind, if we only take proper care not to consider it as more than an idea; that is, if we regard it as valid merely in relation to the employment of reason, in the sphere of the phenomena of the soul. Under the guidance of this idea, or principle, no empirical laws of corporeal phenomena are called in to explain that which is a phenomenon of the internal sense alone; no windy hypotheses of the generation, annihilation, and palingenesis of souls are admitted. Thus the consideration of this object of the internal sense is kept pure, and unmixed with heterogeneous elements; while the investigation of reason aims at reducing all the grounds of explanation employed in this sphere of knowledge to a single principle. All this is best effected, nay, cannot be effected otherwise than by means of such a schema, which requires us to regard this ideal thing as an actual existence. The psychological idea is, therefore, meaningless and inapplicable, except as the schema of a regulative conception. For, if I ask whether the soul is not really of a spiritual nature—it is a question which has no meaning. From such a conception has been abstracted, not merely all corporeal nature, but all nature, that is, all the predicates of a possible experience; and consequently, all the conditions which enable us to cogitate an object to this conception have disappeared. But, if these conditions are absent, it is evident that the conception is meaningless.

The second regulative idea of speculative reason is the conception of the universe. For nature is properly the only object presented to us, in regard to which reason requires regulative principles. Nature is twofold—thinking and corporeal nature. To cogitate the latter in regard to its internal possibility, that is, to determine the application of the categories to it, no idea is required—no representation which transcends experience. In this sphere, therefore, an idea is impossible, sensuous intuition being our only guide; while, in the sphere of psychology, we require the fundamental idea (I), which contains a priori a certain form of thought namely, the unity of the ego. Pure reason has, therefore, nothing left but nature in general, and the completeness of conditions in nature in accordance with some principle. The absolute totality of the series of these conditions is an idea, which can never be fully realized in the empirical exercise of reason, while it is serviceable as a rule for the procedure of reason in relation to that totality. It requires us, in the explanation of given phenomena (in the regress or ascent in the series), to proceed as if the series were infinite in itself, that is, were prolonged in indefinitum,; while on the other hand, where reason is regarded as itself the determining cause (in the region of freedom), we are required to proceed as if we had not before us an object of sense, but of the pure understanding. In this latter case, the conditions do not exist in the series of phenomena, but may be placed quite out of and beyond it, and the series of conditions may be regarded as if it had an absolute beginning from an intelligible cause. All this proves that the cosmological ideas are nothing but regulative principles, and not constitutive; and that their aim is not to realize an actual totality in such series. The full discussion of this subject will be found in its proper place in the chapter on the antinomy of pure reason.

The third idea of pure reason, containing the hypothesis of a being which is valid merely as a relative hypothesis, is that of the one and all-sufficient cause of all cosmological series, in other words, the idea of God. We have not the slightest ground absolutely to admit the existence of an object corresponding to this idea; for what can empower or authorize us to affirm the existence of a being of the highest perfection—a being whose existence is absolutely necessary—merely because we possess the conception of such a being? The answer is: It is the existence of the world which renders this hypothesis necessary. But this answer makes it perfectly evident that the idea of this being, like all other speculative ideas, is essentially nothing more than a demand upon reason that it shall regulate the connection which it and its subordinate faculties introduce into the phenomena of the world by principles of systematic unity and, consequently, that it shall regard all phenomena as originating from one all-embracing being, as the supreme and all-sufficient cause. From this it is plain that the only aim of reason in this procedure is the establishment of its own formal rule for the extension of its dominion in the world of experience; that it does not aim at an extension of its cognition beyond the limits of experience; and that, consequently, this idea does not contain any constitutive principle.

The highest formal unity, which is based upon ideas alone, is the unity of all things—a unity in accordance with an aim or purpose; and the speculative interest of reason renders it necessary to regard all order in the world as if it originated from the intention and design of a supreme reason. This principle unfolds to the view of reason in the sphere of experience new and enlarged prospects, and invites it to connect the phenomena of the world according to teleological laws, and in this way to attain to the highest possible degree of systematic unity. The hypothesis of a supreme intelligence, as the sole cause of the universe—an intelligence which has for us no more than an ideal existence—is accordingly always of the greatest service to reason. Thus, if we presuppose, in relation to the figure of the earth (which is round, but somewhat flattened at the poles),* or that of mountains or seas, wise designs on the part of an author of the universe, we cannot fail to make, by the light of this supposition, a great number of interesting discoveries. If we keep to this hypothesis, as a principle which is purely regulative, even error cannot be very detrimental. For, in this case, error can have no more serious consequences than that, where we expected to discover a teleological connection (nexus finalis), only a mechanical or physical connection appears. In such a case, we merely fail to find the additional form of unity we expected, but we do not lose the rational unity which the mind requires in its procedure in experience. But even a miscarriage of this sort cannot affect the law in its general and teleological relations. For although we may convict an anatomist of an error, when he connects the limb of some animal with a certain purpose, it is quite impossible to prove in a single case that any arrangement of nature, be it what it may, is entirely without aim or design. And thus medical physiology, by the aid of a principle presented to it by pure reason, extends its very limited empirical knowledge of the purposes of the different parts of an organized body so far that it may be asserted with the utmost confidence, and with the approbation of all reflecting men, that every organ or bodily part of an animal has its use and answers a certain design. Now, this is a supposition which, if regarded as of a constitutive character, goes much farther than any experience or observation of ours can justify. Hence it is evident that it is nothing more than a regulative principle of reason, which aims at the highest degree of systematic unity, by the aid of the idea of a causality according to design in a supreme cause—a cause which it regards as the highest intelligence.

[*Footnote: The advantages which a circular form, in the case of the earth, has over every other, are well known. But few are aware that the slight flattening at the poles, which gives it the figure of a spheroid, is the only cause which prevents the elevations of continents or even of mountains, perhaps thrown up by some internal convulsion, from continually altering the position of the axis of the earth—and that to some considerable degree in a short time. The great protuberance of the earth under the Equator serves to overbalance the impetus of all other masses of earth, and thus to preserve the axis of the earth, so far as we can observe, in its present position. And yet this wise arrangement has been unthinkingly explained from the equilibrium of the formerly fluid mass.]

If, however, we neglect this restriction of the idea to a purely regulative influence, reason is betrayed into numerous errors. For it has then left the ground of experience, in which alone are to be found the criteria of truth, and has ventured into the region of the incomprehensible and unsearchable, on the heights of which it loses its power and collectedness, because it has completely severed its connection with experience.

The first error which arises from our employing the idea of a Supreme Being as a constitutive (in repugnance to the very nature of an idea), and not as a regulative principle, is the error of inactive reason (ignava ratio).* We may so term every principle which requires us to regard our investigations of nature as absolutely complete, and allows reason to cease its inquiries, as if it had fully executed its task. Thus the psychological idea of the ego, when employed as a constitutive principle for the explanation of the phenomena of the soul, and for the extension of our knowledge regarding this subject beyond the limits of experience—even to the condition of the soul after death—is convenient enough for the purposes of pure reason, but detrimental and even ruinous to its interests in the sphere of nature and experience. The dogmatizing spiritualist explains the unchanging unity of our personality through all changes of condition from the unity of a thinking substance, the interest which we take in things and events that can happen only after our death, from a consciousness of the immaterial nature of our thinking subject, and so on. Thus he dispenses with all empirical investigations into the cause of these internal phenomena, and with all possible explanations of them upon purely natural grounds; while, at the dictation of a transcendent reason, he passes by the immanent sources of cognition in experience, greatly to his own ease and convenience, but to the sacrifice of all, genuine insight and intelligence. These prejudicial consequences become still more evident, in the case of the dogmatical treatment of our idea of a Supreme Intelligence, and the theological system of nature (physico-theology) which is falsely based upon it. For, in this case, the aims which we observe in nature, and often those which we merely fancy to exist, make the investigation of causes a very easy task, by directing us to refer such and such phenomena immediately to the unsearchable will and counsel of the Supreme Wisdom, while we ought to investigate their causes in the general laws of the mechanism of matter. We are thus recommended to consider the labour of reason as ended, when we have merely dispensed with its employment, which is guided surely and safely only by the order of nature and the series of changes in the world- which are arranged according to immanent and general laws. This error may be avoided, if we do not merely consider from the view-point of final aims certain parts of nature, such as the division and structure of a continent, the constitution and direction of certain mountain-chains, or even the organization existing in the vegetable and animal kingdoms, but look upon this systematic unity of nature in a perfectly general way, in relation to the idea of a Supreme Intelligence. If we pursue this advice, we lay as a foundation for all investigation the conformity to aims of all phenomena of nature in accordance with universal laws, for which no particular arrangement of nature is exempt, but only cognized by us with more or less difficulty; and we possess a regulative principle of the systematic unity of a teleological connection, which we do not attempt to anticipate or predetermine. All that we do, and ought to do, is to follow out the physico-mechanical connection in nature according to general laws, with the hope of discovering, sooner or later, the teleological connection also. Thus, and thus only, can the principle of final unity aid in the extension of the employment of reason in the sphere of experience, without being in any case detrimental to its interests.

[*Footnote: This was the term applied by the old dialecticians to a sophistical argument, which ran thus: If it is your fate to die of this disease, you will die, whether you employ a physician or not. Cicero says that this mode of reasoning has received this appellation, because, if followed, it puts an end to the employment of reason in the affairs of life. For a similar reason, I have applied this designation to the sophistical argument of pure reason.]

The second error which arises from the misconception of the principle of systematic unity is that of perverted reason (perversa ratio, usteron roteron rationis). The idea of systematic unity is available as a regulative principle in the connection of phenomena according to general natural laws; and, how far soever we have to travel upon the path of experience to discover some fact or event, this idea requires us to believe that we have approached all the more nearly to the completion of its use in the sphere of nature, although that completion can never be attained. But this error reverses the procedure of reason. We begin by hypostatizing the principle of systematic unity, and by giving an anthropomorphic determination to the conception of a Supreme Intelligence, and then proceed forcibly to impose aims upon nature. Thus not only does teleology, which ought to aid in the completion of unity in accordance with general laws, operate to the destruction of its influence, but it hinders reason from attaining its proper aim, that is, the proof, upon natural grounds, of the existence of a supreme intelligent cause. For, if we cannot presuppose supreme finality in nature a priori, that is, as essentially belonging to nature, how can we be directed to endeavour to discover this unity and, rising gradually through its different degrees, to approach the supreme perfection of an author of all—a perfection which is absolutely necessary, and therefore cognizable a priori? The regulative principle directs us to presuppose systematic unity absolutely and, consequently, as following from the essential nature of things—but only as a unity of nature, not merely cognized empirically, but presupposed a priori, although only in an indeterminate manner. But if I insist on basing nature upon the foundation of a supreme ordaining Being, the unity of nature is in effect lost. For, in this case, it is quite foreign and unessential to the nature of things, and cannot be cognized from the general laws of nature. And thus arises a vicious circular argument, what ought to have been proved having been presupposed.

To take the regulative principle of systematic unity in nature for a constitutive principle, and to hypostatize and make a cause out of that which is properly the ideal ground of the consistent and harmonious exercise of reason, involves reason in inextricable embarrassments. The investigation of nature pursues its own path under the guidance of the chain of natural causes, in accordance with the general laws of nature, and ever follows the light of the idea of an author of the universe—not for the purpose of deducing the finality, which it constantly pursues, from this Supreme Being, but to attain to the cognition of his existence from the finality which it seeks in the existence of the phenomena of nature, and, if possible, in that of all things to cognize this being, consequently, as absolutely necessary. Whether this latter purpose succeed or not, the idea is and must always be a true one, and its employment, when merely regulative, must always be accompanied by truthful and beneficial results.

Complete unity, in conformity with aims, constitutes absolute perfection. But if we do not find this unity in the nature of the things which go to constitute the world of experience, that is, of objective cognition, consequently in the universal and necessary laws of nature, how can we infer from this unity the idea of the supreme and absolutely necessary perfection of a primal being, which is the origin of all causality? The greatest systematic unity, and consequently teleological unity, constitutes the very foundation of the possibility of the most extended employment of human reason. The idea of unity is therefore essentially and indissolubly connected with the nature of our reason. This idea is a legislative one; and hence it is very natural that we should assume the existence of a legislative reason corresponding to it, from which the systematic unity of nature- the object of the operations of reason—must be derived.

In the course of our discussion of the antinomies, we stated that it is always possible to answer all the questions which pure reason may raise; and that the plea of the limited nature of our cognition, which is unavoidable and proper in many questions regarding natural phenomena, cannot in this case be admitted, because the questions raised do not relate to the nature of things, but are necessarily originated by the nature of reason itself, and relate to its own internal constitution. We can now establish this assertion, which at first sight appeared so rash, in relation to the two questions in which reason takes the greatest interest, and thus complete our discussion of the dialectic of pure reason.

If, then, the question is asked, in relation to transcendental theology,* first, whether there is anything distinct from the world, which contains the ground of cosmical order and connection according to general laws? The answer is: Certainly. For the world is a sum of phenomena; there must, therefore, be some transcendental basis of these phenomena, that is, a basis cogitable by the pure understanding alone. If, secondly, the question is asked whether this being is substance, whether it is of the greatest reality, whether it is necessary, and so forth? I answer that this question is utterly without meaning. For all the categories which aid me in forming a conception of an object cannot be employed except in the world of sense, and are without meaning when not applied to objects of actual or possible experience. Out of this sphere, they are not properly conceptions, but the mere marks or indices of conceptions, which we may admit, although they cannot, without the help of experience, help us to understand any subject or thing. If, thirdly, the question is whether we may not cogitate this being, which is distinct from the world, in analogy with the objects of experience? The answer is: Undoubtedly, but only as an ideal, and not as a real object. That is, we must cogitate it only as an unknown substratum of the systematic unity, order, and finality of the world—a unity which reason must employ as the regulative principle of its investigation of nature. Nay, more, we may admit into the idea certain anthropomorphic elements, which are promotive of the interests of this regulative principle. For it is no more than an idea, which does not relate directly to a being distinct from the world, but to the regulative principle of the systematic unity of the world, by means, however, of a schema of this unity—the schema of a Supreme Intelligence, who is the wisely-designing author of the universe. What this basis of cosmical unity may be in itself, we know not—we cannot discover from the idea; we merely know how we ought to employ the idea of this unity, in relation to the systematic operation of reason in the sphere of experience.

[*Footnote: After what has been said of the psychological idea of the ego and its proper employment as a regulative principle of the operations of reason, I need not enter into details regarding the transcendental illusion by which the systematic unity of all the various phenomena of the internal sense is hypostatized. The procedure is in this case very similar to that which has been discussed in our remarks on the theological ideal.]

But, it will be asked again, can we on these grounds, admit the existence of a wise and omnipotent author of the world? Without doubt; and not only so, but we must assume the existence of such a being. But do we thus extend the limits of our knowledge beyond the field of possible experience? By no means. For we have merely presupposed a something, of which we have no conception, which we do not know as it is in itself; but, in relation to the systematic disposition of the universe, which we must presuppose in all our observation of nature, we have cogitated this unknown being in analogy with an intelligent existence (an empirical conception), that is to say, we have endowed it with those attributes, which, judging from the nature of our own reason, may contain the ground of such a systematic unity. This idea is therefore valid only relatively to the employment in experience of our reason. But if we attribute to it absolute and objective validity, we overlook the fact that it is merely an ideal being that we cogitate; and, by setting out from a basis which is not determinable by considerations drawn from experience, we place ourselves in a position which incapacitates us from applying this principle to the empirical employment of reason.

But, it will be asked further, can I make any use of this conception and hypothesis in my investigations into the world and nature? Yes, for this very purpose was the idea established by reason as a fundamental basis. But may I regard certain arrangements, which seemed to have been made in conformity with some fixed aim, as the arrangements of design, and look upon them as proceeding from the divine will, with the intervention, however, of certain other particular arrangements disposed to that end? Yes, you may do so; but at the same time you must regard it as indifferent, whether it is asserted that divine wisdom has disposed all things in conformity with his highest aims, or that the idea of supreme wisdom is a regulative principle in the investigation of nature, and at the same time a principle of the systematic unity of nature according to general laws, even in those cases where we are unable to discover that unity. In other words, it must be perfectly indifferent to you whether you say, when you have discovered this unity: God has wisely willed it so; or: Nature has wisely arranged this. For it was nothing but the systematic unity, which reason requires as a basis for the investigation of nature, that justified you in accepting the idea of a supreme intelligence as a schema for a regulative principle; and, the farther you advance in the discovery of design and finality, the more certain the validity of your idea. But, as the whole aim of this regulative principle was the discovery of a necessary and systematic unity in nature, we have, in so far as we attain this, to attribute our success to the idea of a Supreme Being; while, at the same time, we cannot, without involving ourselves in contradictions, overlook the general laws of nature, as it was in reference to them alone that this idea was employed. We cannot, I say, overlook the general laws of nature, and regard this conformity to aims observable in nature as contingent or hyperphysical in its origin; inasmuch as there is no ground which can justify us in the admission of a being with such properties distinct from and above nature. All that we are authorized to assert is that this idea may be employed as a principle, and that the properties of the being which is assumed to correspond to it may be regarded as systematically connected in analogy with the causal determination of phenomena.

For the same reasons we are justified in introducing into the idea of the supreme cause other anthropomorphic elements (for without these we could not predicate anything of it); we may regard it as allowable to cogitate this cause as a being with understanding, the feelings of pleasure and displeasure, and faculties of desire and will corresponding to these. At the same time, we may attribute to this being infinite perfection—a perfection which necessarily transcends that which our knowledge of the order and design in the world authorize us to predicate of it. For the regulative law of systematic unity requires us to study nature on the supposition that systematic and final unity in infinitum is everywhere discoverable, even in the highest diversity. For, although we may discover little of this cosmical perfection, it belongs to the legislative prerogative of reason to require us always to seek for and to expect it; while it must always be beneficial to institute all inquiries into nature in accordance with this principle. But it is evident that, by this idea of a supreme author of all, which I place as the foundation of all inquiries into nature, I do not mean to assert the existence of such a being, or that I have any knowledge of its existence; and, consequently, I do not really deduce anything from the existence of this being, but merely from its idea, that is to say, from the nature of things in this world, in accordance with this idea. A certain dim consciousness of the true use of this idea seems to have dictated to the philosophers of all times the moderate language used by them regarding the cause of the world. We find them employing the expressions wisdom and care of nature, and divine wisdom, as synonymous—nay, in purely speculative discussions, preferring the former, because it does not carry the appearance of greater pretensions than such as we are entitled to make, and at the same time directs reason to its proper field of action—nature and her phenomena.

Thus, pure reason, which at first seemed to promise us nothing less than the extension of our cognition beyond the limits of experience, is found, when thoroughly examined, to contain nothing but regulative principles, the virtue and function of which is to introduce into our cognition a higher degree of unity than the understanding could of itself. These principles, by placing the goal of all our struggles at so great a distance, realize for us the most thorough connection between the different parts of our cognition, and the highest degree of systematic unity. But, on the other hand, if misunderstood and employed as constitutive principles of transcendent cognition, they become the parents of illusions and contradictions, while pretending to introduce us to new regions of knowledge.

Thus all human cognition begins with intuitions, proceeds from thence to conceptions, and ends with ideas. Although it possesses, in relation to all three elements, a priori sources of cognition, which seemed to transcend the limits of all experience, a thoroughgoing criticism demonstrates that speculative reason can never, by the aid of these elements, pass the bounds of possible experience, and that the proper destination of this highest faculty of cognition is to employ all methods, and all the principles of these methods, for the purpose of penetrating into the innermost secrets of nature, by the aid of the principles of unity (among all kinds of which teleological unity is the highest), while it ought not to attempt to soar above the sphere of experience, beyond which there lies nought for us but the void inane. The critical examination, in our Transcendental Analytic, of all the propositions which professed to extend cognition beyond the sphere of experience, completely demonstrated that they can only conduct us to a possible experience. If we were not distrustful even of the clearest abstract theorems, if we were not allured by specious and inviting prospects to escape from the constraining power of their evidence, we might spare ourselves the laborious examination of all the dialectical arguments which a transcendent reason adduces in support of its pretensions; for we should know with the most complete certainty that, however honest such professions might be, they are null and valueless, because they relate to a kind of knowledge to which no man can by any possibility attain. But, as there is no end to discussion, if we cannot discover the true cause of the illusions by which even the wisest are deceived, and as the analysis of all our transcendent cognition into its elements is of itself of no slight value as a psychological study, while it is a duty incumbent on every philosopher—it was found necessary to investigate the dialectical procedure of reason in its primary sources. And as the inferences of which this dialectic is the parent are not only deceitful, but naturally possess a profound interest for humanity, it was advisable at the same time, to give a full account of the momenta of this dialectical procedure, and to deposit it in the archives of human reason, as a warning to all future metaphysicians to avoid these causes of speculative error.



II.

TRANSCENDENTAL DOCTRINE OF METHOD.

If we regard the sum of the cognition of pure speculative reason as an edifice, the idea of which, at least, exists in the human mind, it may be said that we have in the Transcendental Doctrine of Elements examined the materials and determined to what edifice these belong, and what its height and stability. We have found, indeed, that, although we had purposed to build for ourselves a tower which should reach to Heaven, the supply of materials sufficed merely for a habitation, which was spacious enough for all terrestrial purposes, and high enough to enable us to survey the level plain of experience, but that the bold undertaking designed necessarily failed for want of materials—not to mention the confusion of tongues, which gave rise to endless disputes among the labourers on the plan of the edifice, and at last scattered them over all the world, each to erect a separate building for himself, according to his own plans and his own inclinations. Our present task relates not to the materials, but to the plan of an edifice; and, as we have had sufficient warning not to venture blindly upon a design which may be found to transcend our natural powers, while, at the same time, we cannot give up the intention of erecting a secure abode for the mind, we must proportion our design to the material which is presented to us, and which is, at the same time, sufficient for all our wants.

I understand, then, by the transcendental doctrine of method, the determination of the formal conditions of a complete system of pure reason. We shall accordingly have to treat of the discipline, the canon, the architectonic, and, finally, the history of pure reason. This part of our Critique will accomplish, from the transcendental point of view, what has been usually attempted, but miserably executed, under the name of practical logic. It has been badly executed, I say, because general logic, not being limited to any particular kind of cognition (not even to the pure cognition of the understanding) nor to any particular objects, it cannot, without borrowing from other sciences, do more than present merely the titles or signs of possible methods and the technical expressions, which are employed in the systematic parts of all sciences; and thus the pupil is made acquainted with names, the meaning and application of which he is to learn only at some future time.



CHAPTER I. The Discipline of Pure Reason.

Negative judgements—those which are so not merely as regards their logical form, but in respect of their content—are not commonly held in especial respect. They are, on the contrary, regarded as jealous enemies of our insatiable desire for knowledge; and it almost requires an apology to induce us to tolerate, much less to prize and to respect them.

All propositions, indeed, may be logically expressed in a negative form; but, in relation to the content of our cognition, the peculiar province of negative judgements is solely to prevent error. For this reason, too, negative propositions, which are framed for the purpose of correcting false cognitions where error is absolutely impossible, are undoubtedly true, but inane and senseless; that is, they are in reality purposeless and, for this reason, often very ridiculous. Such is the proposition of the schoolman that Alexander could not have subdued any countries without an army.

But where the limits of our possible cognition are very much contracted, the attraction to new fields of knowledge great, the illusions to which the mind is subject of the most deceptive character, and the evil consequences of error of no inconsiderable magnitude—the negative element in knowledge, which is useful only to guard us against error, is of far more importance than much of that positive instruction which makes additions to the sum of our knowledge. The restraint which is employed to repress, and finally to extirpate the constant inclination to depart from certain rules, is termed discipline. It is distinguished from culture, which aims at the formation of a certain degree of skill, without attempting to repress or to destroy any other mental power, already existing. In the cultivation of a talent, which has given evidence of an impulse towards self-development, discipline takes a negative,* culture and doctrine a positive, part.

[*Footnote: I am well aware that, in the language of the schools, the term discipline is usually employed as synonymous with instruction. But there are so many cases in which it is necessary to distinguish the notion of the former, as a course of corrective training, from that of the latter, as the communication of knowledge, and the nature of things itself demands the appropriation of the most suitable expressions for this distinction, that it is my desire that the former terms should never be employed in any other than a negative signification.]

That natural dispositions and talents (such as imagination and wit), which ask a free and unlimited development, require in many respects the corrective influence of discipline, every one will readily grant. But it may well appear strange that reason, whose proper duty it is to prescribe rules of discipline to all the other powers of the mind, should itself require this corrective. It has, in fact, hitherto escaped this humiliation, only because, in presence of its magnificent pretensions and high position, no one could readily suspect it to be capable of substituting fancies for conceptions, and words for things.

Reason, when employed in the field of experience, does not stand in need of criticism, because its principles are subjected to the continual test of empirical observations. Nor is criticism requisite in the sphere of mathematics, where the conceptions of reason must always be presented in concreto in pure intuition, and baseless or arbitrary assertions are discovered without difficulty. But where reason is not held in a plain track by the influence of empirical or of pure intuition, that is, when it is employed in the transcendental sphere of pure conceptions, it stands in great need of discipline, to restrain its propensity to overstep the limits of possible experience and to keep it from wandering into error. In fact, the utility of the philosophy of pure reason is entirely of this negative character. Particular errors may be corrected by particular animadversions, and the causes of these errors may be eradicated by criticism. But where we find, as in the case of pure reason, a complete system of illusions and fallacies, closely connected with each other and depending upon grand general principles, there seems to be required a peculiar and negative code of mental legislation, which, under the denomination of a discipline, and founded upon the nature of reason and the objects of its exercise, shall constitute a system of thorough examination and testing, which no fallacy will be able to withstand or escape from, under whatever disguise or concealment it may lurk.

But the reader must remark that, in this the second division of our transcendental Critique the discipline of pure reason is not directed to the content, but to the method of the cognition of pure reason. The former task has been completed in the doctrine of elements. But there is so much similarity in the mode of employing the faculty of reason, whatever be the object to which it is applied, while, at the same time, its employment in the transcendental sphere is so essentially different in kind from every other, that, without the warning negative influence of a discipline specially directed to that end, the errors are unavoidable which spring from the unskillful employment of the methods which are originated by reason but which are out of place in this sphere.



SECTION I. The Discipline of Pure Reason in the Sphere of Dogmatism.

The science of mathematics presents the most brilliant example of the extension of the sphere of pure reason without the aid of experience. Examples are always contagious; and they exert an especial influence on the same faculty, which naturally flatters itself that it will have the same good fortune in other case as fell to its lot in one fortunate instance. Hence pure reason hopes to be able to extend its empire in the transcendental sphere with equal success and security, especially when it applies the same method which was attended with such brilliant results in the science of mathematics. It is, therefore, of the highest importance for us to know whether the method of arriving at demonstrative certainty, which is termed mathematical, be identical with that by which we endeavour to attain the same degree of certainty in philosophy, and which is termed in that science dogmatical.

Philosophical cognition is the cognition of reason by means of conceptions; mathematical cognition is cognition by means of the construction of conceptions. The construction of a conception is the presentation a priori of the intuition which corresponds to the conception. For this purpose a non-empirical intuition is requisite, which, as an intuition, is an individual object; while, as the construction of a conception (a general representation), it must be seen to be universally valid for all the possible intuitions which rank under that conception. Thus I construct a triangle, by the presentation of the object which corresponds to this conception, either by mere imagination, in pure intuition, or upon paper, in empirical intuition, in both cases completely a priori, without borrowing the type of that figure from any experience. The individual figure drawn upon paper is empirical; but it serves, notwithstanding, to indicate the conception, even in its universality, because in this empirical intuition we keep our eye merely on the act of the construction of the conception, and pay no attention to the various modes of determining it, for example, its size, the length of its sides, the size of its angles, these not in the least affecting the essential character of the conception.

Philosophical cognition, accordingly, regards the particular only in the general; mathematical the general in the particular, nay, in the individual. This is done, however, entirely a priori and by means of pure reason, so that, as this individual figure is determined under certain universal conditions of construction, the object of the conception, to which this individual figure corresponds as its schema, must be cogitated as universally determined.

The essential difference of these two modes of cognition consists, therefore, in this formal quality; it does not regard the difference of the matter or objects of both. Those thinkers who aim at distinguishing philosophy from mathematics by asserting that the former has to do with quality merely, and the latter with quantity, have mistaken the effect for the cause. The reason why mathematical cognition can relate only to quantity is to be found in its form alone. For it is the conception of quantities only that is capable of being constructed, that is, presented a priori in intuition; while qualities cannot be given in any other than an empirical intuition. Hence the cognition of qualities by reason is possible only through conceptions. No one can find an intuition which shall correspond to the conception of reality, except in experience; it cannot be presented to the mind a priori and antecedently to the empirical consciousness of a reality. We can form an intuition, by means of the mere conception of it, of a cone, without the aid of experience; but the colour of the cone we cannot know except from experience. I cannot present an intuition of a cause, except in an example which experience offers to me. Besides, philosophy, as well as mathematics, treats of quantities; as, for example, of totality, infinity, and so on. Mathematics, too, treats of the difference of lines and surfaces—as spaces of different quality, of the continuity of extension—as a quality thereof. But, although in such cases they have a common object, the mode in which reason considers that object is very different in philosophy from what it is in mathematics. The former confines itself to the general conceptions; the latter can do nothing with a mere conception, it hastens to intuition. In this intuition it regards the conception in concreto, not empirically, but in an a priori intuition, which it has constructed; and in which, all the results which follow from the general conditions of the construction of the conception are in all cases valid for the object of the constructed conception.

Suppose that the conception of a triangle is given to a philosopher and that he is required to discover, by the philosophical method, what relation the sum of its angles bears to a right angle. He has nothing before him but the conception of a figure enclosed within three right lines, and, consequently, with the same number of angles. He may analyse the conception of a right line, of an angle, or of the number three as long as he pleases, but he will not discover any properties not contained in these conceptions. But, if this question is proposed to a geometrician, he at once begins by constructing a triangle. He knows that two right angles are equal to the sum of all the contiguous angles which proceed from one point in a straight line; and he goes on to produce one side of his triangle, thus forming two adjacent angles which are together equal to two right angles. He then divides the exterior of these angles, by drawing a line parallel with the opposite side of the triangle, and immediately perceives that he has thus got an exterior adjacent angle which is equal to the interior. Proceeding in this way, through a chain of inferences, and always on the ground of intuition, he arrives at a clear and universally valid solution of the question.

But mathematics does not confine itself to the construction of quantities (quanta), as in the case of geometry; it occupies itself with pure quantity also (quantitas), as in the case of algebra, where complete abstraction is made of the properties of the object indicated by the conception of quantity. In algebra, a certain method of notation by signs is adopted, and these indicate the different possible constructions of quantities, the extraction of roots, and so on. After having thus denoted the general conception of quantities, according to their different relations, the different operations by which quantity or number is increased or diminished are presented in intuition in accordance with general rules. Thus, when one quantity is to be divided by another, the signs which denote both are placed in the form peculiar to the operation of division; and thus algebra, by means of a symbolical construction of quantity, just as geometry, with its ostensive or geometrical construction (a construction of the objects themselves), arrives at results which discursive cognition cannot hope to reach by the aid of mere conceptions.

Now, what is the cause of this difference in the fortune of the philosopher and the mathematician, the former of whom follows the path of conceptions, while the latter pursues that of intuitions, which he represents, a priori, in correspondence with his conceptions? The cause is evident from what has been already demonstrated in the introduction to this Critique. We do not, in the present case, want to discover analytical propositions, which may be produced merely by analysing our conceptions—for in this the philosopher would have the advantage over his rival; we aim at the discovery of synthetical propositions—such synthetical propositions, moreover, as can be cognized a priori. I must not confine myself to that which I actually cogitate in my conception of a triangle, for this is nothing more than the mere definition; I must try to go beyond that, and to arrive at properties which are not contained in, although they belong to, the conception. Now, this is impossible, unless I determine the object present to my mind according to the conditions, either of empirical, or of pure, intuition. In the former case, I should have an empirical proposition (arrived at by actual measurement of the angles of the triangle), which would possess neither universality nor necessity; but that would be of no value. In the latter, I proceed by geometrical construction, by means of which I collect, in a pure intuition, just as I would in an empirical intuition, all the various properties which belong to the schema of a triangle in general, and consequently to its conception, and thus construct synthetical propositions which possess the attribute of universality.

It would be vain to philosophize upon the triangle, that is, to reflect on it discursively; I should get no further than the definition with which I had been obliged to set out. There are certainly transcendental synthetical propositions which are framed by means of pure conceptions, and which form the peculiar distinction of philosophy; but these do not relate to any particular thing, but to a thing in general, and enounce the conditions under which the perception of it may become a part of possible experience. But the science of mathematics has nothing to do with such questions, nor with the question of existence in any fashion; it is concerned merely with the properties of objects in themselves, only in so far as these are connected with the conception of the objects.

In the above example, we merely attempted to show the great difference which exists between the discursive employment of reason in the sphere of conceptions, and its intuitive exercise by means of the construction of conceptions. The question naturally arises: What is the cause which necessitates this twofold exercise of reason, and how are we to discover whether it is the philosophical or the mathematical method which reason is pursuing in an argument?

All our knowledge relates, finally, to possible intuitions, for it is these alone that present objects to the mind. An a priori or non-empirical conception contains either a pure intuition—and in this case it can be constructed; or it contains nothing but the synthesis of possible intuitions, which are not given a priori. In this latter case, it may help us to form synthetical a priori judgements, but only in the discursive method, by conceptions, not in the intuitive, by means of the construction of conceptions.

The only a priori intuition is that of the pure form of phenomena- space and time. A conception of space and time as quanta may be presented a priori in intuition, that is, constructed, either alone with their quality (figure), or as pure quantity (the mere synthesis of the homogeneous), by means of number. But the matter of phenomena, by which things are given in space and time, can be presented only in perception, a posteriori. The only conception which represents a priori this empirical content of phenomena is the conception of a thing in general; and the a priori synthetical cognition of this conception can give us nothing more than the rule for the synthesis of that which may be contained in the corresponding a posteriori perception; it is utterly inadequate to present an a priori intuition of the real object, which must necessarily be empirical.

Synthetical propositions, which relate to things in general, an a priori intuition of which is impossible, are transcendental. For this reason transcendental propositions cannot be framed by means of the construction of conceptions; they are a priori, and based entirely on conceptions themselves. They contain merely the rule, by which we are to seek in the world of perception or experience the synthetical unity of that which cannot be intuited a priori. But they are incompetent to present any of the conceptions which appear in them in an a priori intuition; these can be given only a posteriori, in experience, which, however, is itself possible only through these synthetical principles.

If we are to form a synthetical judgement regarding a conception, we must go beyond it, to the intuition in which it is given. If we keep to what is contained in the conception, the judgement is merely analytical—it is merely an explanation of what we have cogitated in the conception. But I can pass from the conception to the pure or empirical intuition which corresponds to it. I can proceed to examine my conception in concreto, and to cognize, either a priori or a posterio, what I find in the object of the conception. The former—a priori cognition—is rational-mathematical cognition by means of the construction of the conception; the latter—a posteriori cognition—is purely empirical cognition, which does not possess the attributes of necessity and universality. Thus I may analyse the conception I have of gold; but I gain no new information from this analysis, I merely enumerate the different properties which I had connected with the notion indicated by the word. My knowledge has gained in logical clearness and arrangement, but no addition has been made to it. But if I take the matter which is indicated by this name, and submit it to the examination of my senses, I am enabled to form several synthetical—although still empirical- propositions. The mathematical conception of a triangle I should construct, that is, present a priori in intuition, and in this way attain to rational-synthetical cognition. But when the transcendental conception of reality, or substance, or power is presented to my mind, I find that it does not relate to or indicate either an empirical or pure intuition, but that it indicates merely the synthesis of empirical intuitions, which cannot of course be given a priori. The synthesis in such a conception cannot proceed a priori—without the aid of experience—to the intuition which corresponds to the conception; and, for this reason, none of these conceptions can produce a determinative synthetical proposition, they can never present more than a principle of the synthesis* of possible empirical intuitions. A transcendental proposition is, therefore, a synthetical cognition of reason by means of pure conceptions and the discursive method, and it renders possible all synthetical unity in empirical cognition, though it cannot present us with any intuition a priori.

[*Footnote: In the case of the conception of cause, I do really go beyond the empirical conception of an event—but not to the intuition which presents this conception in concreto, but only to the time-conditions, which may be found in experience to correspond to the conception. My procedure is, therefore, strictly according to conceptions; I cannot in a case of this kind employ the construction of conceptions, because the conception is merely a rule for the synthesis of perceptions, which are not pure intuitions, and which, therefore, cannot be given a priori.]

There is thus a twofold exercise of reason. Both modes have the properties of universality and an a priori origin in common, but are, in their procedure, of widely different character. The reason of this is that in the world of phenomena, in which alone objects are presented to our minds, there are two main elements—the form of intuition (space and time), which can be cognized and determined completely a priori, and the matter or content—that which is presented in space and time, and which, consequently, contains a something—an existence corresponding to our powers of sensation. As regards the latter, which can never be given in a determinate mode except by experience, there are no a priori notions which relate to it, except the undetermined conceptions of the synthesis of possible sensations, in so far as these belong (in a possible experience) to the unity of consciousness. As regards the former, we can determine our conceptions a priori in intuition, inasmuch as we are ourselves the creators of the objects of the conceptions in space and time- these objects being regarded simply as quanta. In the one case, reason proceeds according to conceptions and can do nothing more than subject phenomena to these—which can only be determined empirically, that is, a posteriori—in conformity, however, with those conceptions as the rules of all empirical synthesis. In the other case, reason proceeds by the construction of conceptions; and, as these conceptions relate to an a priori intuition, they may be given and determined in pure intuition a priori, and without the aid of empirical data. The examination and consideration of everything that exists in space or time—whether it is a quantum or not, in how far the particular something (which fills space or time) is a primary substratum, or a mere determination of some other existence, whether it relates to anything else—either as cause or effect, whether its existence is isolated or in reciprocal connection with and dependence upon others, the possibility of this existence, its reality and necessity or opposites—all these form part of the cognition of reason on the ground of conceptions, and this cognition is termed philosophical. But to determine a priori an intuition in space (its figure), to divide time into periods, or merely to cognize the quantity of an intuition in space and time, and to determine it by number—all this is an operation of reason by means of the construction of conceptions, and is called mathematical.

The success which attends the efforts of reason in the sphere of mathematics naturally fosters the expectation that the same good fortune will be its lot, if it applies the mathematical method in other regions of mental endeavour besides that of quantities. Its success is thus great, because it can support all its conceptions by a priori intuitions and, in this way, make itself a master, as it were, over nature; while pure philosophy, with its a priori discursive conceptions, bungles about in the world of nature, and cannot accredit or show any a priori evidence of the reality of these conceptions. Masters in the science of mathematics are confident of the success of this method; indeed, it is a common persuasion that it is capable of being applied to any subject of human thought. They have hardly ever reflected or philosophized on their favourite science—a task of great difficulty; and the specific difference between the two modes of employing the faculty of reason has never entered their thoughts. Rules current in the field of common experience, and which common sense stamps everywhere with its approval, are regarded by them as axiomatic. From what source the conceptions of space and time, with which (as the only primitive quanta) they have to deal, enter their minds, is a question which they do not trouble themselves to answer; and they think it just as unnecessary to examine into the origin of the pure conceptions of the understanding and the extent of their validity. All they have to do with them is to employ them. In all this they are perfectly right, if they do not overstep the limits of the sphere of nature. But they pass, unconsciously, from the world of sense to the insecure ground of pure transcendental conceptions (instabilis tellus, innabilis unda), where they can neither stand nor swim, and where the tracks of their footsteps are obliterated by time; while the march of mathematics is pursued on a broad and magnificent highway, which the latest posterity shall frequent without fear of danger or impediment.

As we have taken upon us the task of determining, clearly and certainly, the limits of pure reason in the sphere of transcendentalism, and as the efforts of reason in this direction are persisted in, even after the plainest and most expressive warnings, hope still beckoning us past the limits of experience into the splendours of the intellectual world—it becomes necessary to cut away the last anchor of this fallacious and fantastic hope. We shall, accordingly, show that the mathematical method is unattended in the sphere of philosophy by the least advantage—except, perhaps, that it more plainly exhibits its own inadequacy—that geometry and philosophy are two quite different things, although they go band in hand in hand in the field of natural science, and, consequently, that the procedure of the one can never be imitated by the other.

The evidence of mathematics rests upon definitions, axioms, and demonstrations. I shall be satisfied with showing that none of these forms can be employed or imitated in philosophy in the sense in which they are understood by mathematicians; and that the geometrician, if he employs his method in philosophy, will succeed only in building card-castles, while the employment of the philosophical method in mathematics can result in nothing but mere verbiage. The essential business of philosophy, indeed, is to mark out the limits of the science; and even the mathematician, unless his talent is naturally circumscribed and limited to this particular department of knowledge, cannot turn a deaf ear to the warnings of philosophy, or set himself above its direction.

I. Of Definitions. A definition is, as the term itself indicates, the representation, upon primary grounds, of the complete conception of a thing within its own limits.* Accordingly, an empirical conception cannot be defined, it can only be explained. For, as there are in such a conception only a certain number of marks or signs, which denote a certain class of sensuous objects, we can never be sure that we do not cogitate under the word which indicates the same object, at one time a greater, at another a smaller number of signs. Thus, one person may cogitate in his conception of gold, in addition to its properties of weight, colour, malleability, that of resisting rust, while another person may be ignorant of this quality. We employ certain signs only so long as we require them for the sake of distinction; new observations abstract some and add new ones, so that an empirical conception never remains within permanent limits. It is, in fact, useless to define a conception of this kind. If, for example, we are speaking of water and its properties, we do not stop at what we actually think by the word water, but proceed to observation and experiment; and the word, with the few signs attached to it, is more properly a designation than a conception of the thing. A definition in this case would evidently be nothing more than a determination of the word. In the second place, no a priori conception, such as those of substance, cause, right, fitness, and so on, can be defined. For I can never be sure, that the clear representation of a given conception (which is given in a confused state) has been fully developed, until I know that the representation is adequate with its object. But, inasmuch as the conception, as it is presented to the mind, may contain a number of obscure representations, which we do not observe in our analysis, although we employ them in our application of the conception, I can never be sure that my analysis is complete, while examples may make this probable, although they can never demonstrate the fact. Instead of the word definition, I should rather employ the term exposition— a more modest expression, which the critic may accept without surrendering his doubts as to the completeness of the analysis of any such conception. As, therefore, neither empirical nor a priori conceptions are capable of definition, we have to see whether the only other kind of conceptions—arbitrary conceptions—can be subjected to this mental operation. Such a conception can always be defined; for I must know thoroughly what I wished to cogitate in it, as it was I who created it, and it was not given to my mind either by the nature of my understanding or by experience. At the same time, I cannot say that, by such a definition, I have defined a real object. If the conception is based upon empirical conditions, if, for example, I have a conception of a clock for a ship, this arbitrary conception does not assure me of the existence or even of the possibility of the object. My definition of such a conception would with more propriety be termed a declaration of a project than a definition of an object. There are no other conceptions which can bear definition, except those which contain an arbitrary synthesis, which can be constructed a priori. Consequently, the science of mathematics alone possesses definitions. For the object here thought is presented a priori in intuition; and thus it can never contain more or less than the conception, because the conception of the object has been given by the definition—and primarily, that is, without deriving the definition from any other source. Philosophical definitions are, therefore, merely expositions of given conceptions, while mathematical definitions are constructions of conceptions originally formed by the mind itself; the former are produced by analysis, the completeness of which is never demonstratively certain, the latter by a synthesis. In a mathematical definition the conception is formed, in a philosophical definition it is only explained. From this it follows:

[*Footnote: The definition must describe the conception completely that is, omit none of the marks or signs of which it composed; within its own limits, that is, it must be precise, and enumerate no more signs than belong to the conception; and on primary grounds, that is to say, the limitations of the bounds of the conception must not be deduced from other conceptions, as in this case a proof would be necessary, and the so-called definition would be incapable of taking its place at the bead of all the judgements we have to form regarding an object.]

(a) That we must not imitate, in philosophy, the mathematical usage of commencing with definitions—except by way of hypothesis or experiment. For, as all so-called philosophical definitions are merely analyses of given conceptions, these conceptions, although only in a confused form, must precede the analysis; and the incomplete exposition must precede the complete, so that we may be able to draw certain inferences from the characteristics which an incomplete analysis has enabled us to discover, before we attain to the complete exposition or definition of the conception. In one word, a full and clear definition ought, in philosophy, rather to form the conclusion than the commencement of our labours.* In mathematics, on the contrary, we cannot have a conception prior to the definition; it is the definition which gives us the conception, and it must for this reason form the commencement of every chain of mathematical reasoning.

[*Footnote: Philosophy abounds in faulty definitions, especially such as contain some of the elements requisite to form a complete definition. If a conception could not be employed in reasoning before it had been defined, it would fare ill with all philosophical thought. But, as incompletely defined conceptions may always be employed without detriment to truth, so far as our analysis of the elements contained in them proceeds, imperfect definitions, that is, propositions which are properly not definitions, but merely approximations thereto, may be used with great advantage. In mathematics, definition belongs ad esse, in philosophy ad melius esse. It is a difficult task to construct a proper definition. Jurists are still without a complete definition of the idea of right.]

(b) Mathematical definitions cannot be erroneous. For the conception is given only in and through the definition, and thus it contains only what has been cogitated in the definition. But although a definition cannot be incorrect, as regards its content, an error may sometimes, although seldom, creep into the form. This error consists in a want of precision. Thus the common definition of a circle—that it is a curved line, every point in which is equally distant from another point called the centre—is faulty, from the fact that the determination indicated by the word curved is superfluous. For there ought to be a particular theorem, which may be easily proved from the definition, to the effect that every line, which has all its points at equal distances from another point, must be a curved line—that is, that not even the smallest part of it can be straight. Analytical definitions, on the other hand, may be erroneous in many respects, either by the introduction of signs which do not actually exist in the conception, or by wanting in that completeness which forms the essential of a definition. In the latter case, the definition is necessarily defective, because we can never be fully certain of the completeness of our analysis. For these reasons, the method of definition employed in mathematics cannot be imitated in philosophy.

2. Of Axioms. These, in so far as they are immediately certain, are a priori synthetical principles. Now, one conception cannot be connected synthetically and yet immediately with another; because, if we wish to proceed out of and beyond a conception, a third mediating cognition is necessary. And, as philosophy is a cognition of reason by the aid of conceptions alone, there is to be found in it no principle which deserves to be called an axiom. Mathematics, on the other hand, may possess axioms, because it can always connect the predicates of an object a priori, and without any mediating term, by means of the construction of conceptions in intuition. Such is the case with the proposition: Three points can always lie in a plane. On the other hand, no synthetical principle which is based upon conceptions, can ever be immediately certain (for example, the proposition: Everything that happens has a cause), because I require a mediating term to connect the two conceptions of event and cause- namely, the condition of time-determination in an experience, and I cannot cognize any such principle immediately and from conceptions alone. Discursive principles are, accordingly, very different from intuitive principles or axioms. The former always require deduction, which in the case of the latter may be altogether dispensed with. Axioms are, for this reason, always self-evident, while philosophical principles, whatever may be the degree of certainty they possess, cannot lay any claim to such a distinction. No synthetical proposition of pure transcendental reason can be so evident, as is often rashly enough declared, as the statement, twice two are four. It is true that in the Analytic I introduced into the list of principles of the pure understanding, certain axioms of intuition; but the principle there discussed was not itself an axiom, but served merely to present the principle of the possibility of axioms in general, while it was really nothing more than a principle based upon conceptions. For it is one part of the duty of transcendental philosophy to establish the possibility of mathematics itself. Philosophy possesses, then, no axioms, and has no right to impose its a priori principles upon thought, until it has established their authority and validity by a thoroughgoing deduction.

3. Of Demonstrations. Only an apodeictic proof, based upon intuition, can be termed a demonstration. Experience teaches us what is, but it cannot convince us that it might not have been otherwise. Hence a proof upon empirical grounds cannot be apodeictic. A priori conceptions, in discursive cognition, can never produce intuitive certainty or evidence, however certain the judgement they present may be. Mathematics alone, therefore, contains demonstrations, because it does not deduce its cognition from conceptions, but from the construction of conceptions, that is, from intuition, which can be given a priori in accordance with conceptions. The method of algebra, in equations, from which the correct answer is deduced by reduction, is a kind of construction—not geometrical, but by symbols- in which all conceptions, especially those of the relations of quantities, are represented in intuition by signs; and thus the conclusions in that science are secured from errors by the fact that every proof is submitted to ocular evidence. Philosophical cognition does not possess this advantage, it being required to consider the general always in abstracto (by means of conceptions), while mathematics can always consider it in concreto (in an individual intuition), and at the same time by means of a priori representation, whereby all errors are rendered manifest to the senses. The former—discursive proofs—ought to be termed acroamatic proofs, rather than demonstrations, as only words are employed in them, while demonstrations proper, as the term itself indicates, always require a reference to the intuition of the object.

It follows from all these considerations that it is not consonant with the nature of philosophy, especially in the sphere of pure reason, to employ the dogmatical method, and to adorn itself with the titles and insignia of mathematical science. It does not belong to that order, and can only hope for a fraternal union with that science. Its attempts at mathematical evidence are vain pretensions, which can only keep it back from its true aim, which is to detect the illusory procedure of reason when transgressing its proper limits, and by fully explaining and analysing our conceptions, to conduct us from the dim regions of speculation to the clear region of modest self-knowledge. Reason must not, therefore, in its transcendental endeavours, look forward with such confidence, as if the path it is pursuing led straight to its aim, nor reckon with such security upon its premisses, as to consider it unnecessary to take a step back, or to keep a strict watch for errors, which, overlooked in the principles, may be detected in the arguments themselves—in which case it may be requisite either to determine these principles with greater strictness, or to change them entirely.

I divide all apodeictic propositions, whether demonstrable or immediately certain, into dogmata and mathemata. A direct synthetical proposition, based on conceptions, is a dogma; a proposition of the same kind, based on the construction of conceptions, is a mathema. Analytical judgements do not teach us any more about an object than what was contained in the conception we had of it; because they do not extend our cognition beyond our conception of an object, they merely elucidate the conception. They cannot therefore be with propriety termed dogmas. Of the two kinds of a priori synthetical propositions above mentioned, only those which are employed in philosophy can, according to the general mode of speech, bear this name; those of arithmetic or geometry would not be rightly so denominated. Thus the customary mode of speaking confirms the explanation given above, and the conclusion arrived at, that only those judgements which are based upon conceptions, not on the construction of conceptions, can be termed dogmatical.

Thus, pure reason, in the sphere of speculation, does not contain a single direct synthetical judgement based upon conceptions. By means of ideas, it is, as we have shown, incapable of producing synthetical judgements, which are objectively valid; by means of the conceptions of the understanding, it establishes certain indubitable principles, not, however, directly on the basis of conceptions, but only indirectly by means of the relation of these conceptions to something of a purely contingent nature, namely, possible experience. When experience is presupposed, these principles are apodeictically certain, but in themselves, and directly, they cannot even be cognized a priori. Thus the given conceptions of cause and event will not be sufficient for the demonstration of the proposition: Every event has a cause. For this reason, it is not a dogma; although from another point of view, that of experience, it is capable of being proved to demonstration. The proper term for such a proposition is principle, and not theorem (although it does require to be proved), because it possesses the remarkable peculiarity of being the condition of the possibility of its own ground of proof, that is, experience, and of forming a necessary presupposition in all empirical observation.

If then, in the speculative sphere of pure reason, no dogmata are to be found; all dogmatical methods, whether borrowed from mathematics, or invented by philosophical thinkers, are alike inappropriate and inefficient. They only serve to conceal errors and fallacies, and to deceive philosophy, whose duty it is to see that reason pursues a safe and straight path. A philosophical method may, however, be systematical. For our reason is, subjectively considered, itself a system, and, in the sphere of mere conceptions, a system of investigation according to principles of unity, the material being supplied by experience alone. But this is not the proper place for discussing the peculiar method of transcendental philosophy, as our present task is simply to examine whether our faculties are capable of erecting an edifice on the basis of pure reason, and how far they may proceed with the materials at their command.



SECTION II. The Discipline of Pure Reason in Polemics.

Reason must be subject, in all its operations, to criticism, which must always be permitted to exercise its functions without restraint; otherwise its interests are imperilled and its influence obnoxious to suspicion. There is nothing, however useful, however sacred it may be, that can claim exemption from the searching examination of this supreme tribunal, which has no respect of persons. The very existence of reason depends upon this freedom; for the voice of reason is not that of a dictatorial and despotic power, it is rather like the vote of the citizens of a free state, every member of which must have the privilege of giving free expression to his doubts, and possess even the right of veto.

But while reason can never decline to submit itself to the tribunal of criticism, it has not always cause to dread the judgement of this court. Pure reason, however, when engaged in the sphere of dogmatism, is not so thoroughly conscious of a strict observance of its highest laws, as to appear before a higher judicial reason with perfect confidence. On the contrary, it must renounce its magnificent dogmatical pretensions in philosophy.

Very different is the case when it has to defend itself, not before a judge, but against an equal. If dogmatical assertions are advanced on the negative side, in opposition to those made by reason on the positive side, its justification kat authrhopon is complete, although the proof of its propositions is kat aletheian unsatisfactory.

By the polemic of pure reason I mean the defence of its propositions made by reason, in opposition to the dogmatical counter-propositions advanced by other parties. The question here is not whether its own statements may not also be false; it merely regards the fact that reason proves that the opposite cannot be established with demonstrative certainty, nor even asserted with a higher degree of probability. Reason does not hold her possessions upon sufferance; for, although she cannot show a perfectly satisfactory title to them, no one can prove that she is not the rightful possessor.

It is a melancholy reflection that reason, in its highest exercise, falls into an antithetic; and that the supreme tribunal for the settlement of differences should not be at union with itself. It is true that we had to discuss the question of an apparent antithetic, but we found that it was based upon a misconception. In conformity with the common prejudice, phenomena were regarded as things in themselves, and thus an absolute completeness in their synthesis was required in the one mode or in the other (it was shown to be impossible in both); a demand entirely out of place in regard to phenomena. There was, then, no real self-contradiction of reason in the propositions: The series of phenomena given in themselves has an absolutely first beginning; and: This series is absolutely and in itself without beginning. The two propositions are perfectly consistent with each other, because phenomena as phenomena are in themselves nothing, and consequently the hypothesis that they are things in themselves must lead to self-contradictory inferences.

But there are cases in which a similar misunderstanding cannot be provided against, and the dispute must remain unsettled. Take, for example, the theistic proposition: There is a Supreme Being; and on the other hand, the atheistic counter-statement: There exists no Supreme Being; or, in psychology: Everything that thinks possesses the attribute of absolute and permanent unity, which is utterly different from the transitory unity of material phenomena; and the counter-proposition: The soul is not an immaterial unity, and its nature is transitory, like that of phenomena. The objects of these questions contain no heterogeneous or contradictory elements, for they relate to things in themselves, and not to phenomena. There would arise, indeed, a real contradiction, if reason came forward with a statement on the negative side of these questions alone. As regards the criticism to which the grounds of proof on the affirmative side must be subjected, it may be freely admitted, without necessitating the surrender of the affirmative propositions, which have, at least, the interest of reason in their favour—an advantage which the opposite party cannot lay claim to.

I cannot agree with the opinion of several admirable thinkers—Sulzer among the rest—that, in spite of the weakness of the arguments hitherto in use, we may hope, one day, to see sufficient demonstrations of the two cardinal propositions of pure reason—the existence of a Supreme Being, and the immortality of the soul. I am certain, on the contrary, that this will never be the case. For on what ground can reason base such synthetical propositions, which do not relate to the objects of experience and their internal possibility? But it is also demonstratively certain that no one will ever be able to maintain the contrary with the least show of probability. For, as he can attempt such a proof solely upon the basis of pure reason, he is bound to prove that a Supreme Being, and a thinking subject in the character of a pure intelligence, are impossible. But where will he find the knowledge which can enable him to enounce synthetical judgements in regard to things which transcend the region of experience? We may, therefore, rest assured that the opposite never will be demonstrated. We need not, then, have recourse to scholastic arguments; we may always admit the truth of those propositions which are consistent with the speculative interests of reason in the sphere of experience, and form, moreover, the only means of uniting the speculative with the practical interest. Our opponent, who must not be considered here as a critic solely, we can be ready to meet with a non liquet which cannot fail to disconcert him; while we cannot deny his right to a similar retort, as we have on our side the advantage of the support of the subjective maxim of reason, and can therefore look upon all his sophistical arguments with calm indifference.