No More Learning

The idea of unity therefore essentially and iudissolubly connected with the nature of our reason. This idea legislative one and hence very natural that we should assume the existence of legislative reason corresponding to
sality
? 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 always possible to answer all the questions which pure reason may raise and that the plea of the limited na ture of our cognition, which unavoidable and proper in many questions regarding natural phsenomena, cannot in this case be admitted, because the questions raised do not relate to the nature of things, but are necessarily originated the nature of reason itself, and relate to its own internal constitu tion. 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 dis cussion of the dialectic of pure reason.
then, the question asked, in relation to transcendental theology first, whether there anything distinct from the world, which contains the ground of cosmical order and con nection according to general laws? The answer Ccr-
After what has been said of the psychological idea of the Ego and its proper employment as regulative principle of the operations of reason, need not enter into details regarding the transcendental illu sion which the systematic unity of all the various phenomena of the internal sense hypostatised. The procedure in this case very simi lar to that which hat heen discussed our remarks on the theological ideal
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? 426
TBAH80ES DENTAL DIALECTIC.
tainly. For the world is a sum of phenomena ; there must therefore be some transcendental basis of these phenomena, that basis cogitable the pare understanding alone. tecondly, the question asked, whether this being sub stance, whether of the greatest reality, whether ne cessary, and so forth answer that this question
utterly without meaning. For all the categories which aid me in
forming conception of an object, cannot be employed except in the world of sense, and are without meaning, when not ap
plied 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 un derstand any subject or thing. If, thirdly, the question whether we may not cogitate this being, which distinct from the world, in analogy with the objects of experience The answer undoubtedly, but only as an ideal, and not as real object. That we must cogitate only as an unkuown substratum of the systematic unity, order, and finality of the world -- unity which reason must employ as the regulative principle of its investigation of nature. Nay, more, we may admit into the idea certain anthromorphic elements, which are promotive of the interests of this regulative principle. For no more than an idea, which does not relate directly to being distinct from the world, but to the regulative prin ciple of the systematic unity of the world, means, however, of schema of this unity -- the schema of Supreme Intel ligence, who the wisely-designing author of the universe. What this basis of cosnucal 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 iperation of reason in the sphere of experience. But, will be asked again, can we on these grounds, admit the existence of wise and omnipotent author of the world?
Without doubt and not only so, but we must assume the ex istence of such 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 something, of which we have no conception, which we do not know as
in itself but, in relation to the systematic disposition of the universe, which we must presupoose in all our observation
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? OT THE HATTTBAL DIALECTIC OF HUMAN REA8OW. 427
nature, we have cogitated this unknown being in analogy witli an intelligent existence (an empirical conception), that is to say, v,e 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 vali dity, 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 ap plying this principle to the empirical employment of reason.
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 re gard 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 arrange
ments disposed to that end ? Yes, you may Jo so ; but at the same time you must regard it as indifferent, whether it is asserted that divine wisdom has disposed all things in confor mity 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 in vestigation of nature, that justified you in accepting the idea of a supreme intelligence as a schema for a regulative princi ple ; 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 dis covery of a necessary and systematic unity in nature, we nave, 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 '. In
? But, it will be asked further, can I make any use of this
? ? ? 428 nUNSCENDBNTAL DIALECTIC! .
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
we may regard as allowable to cogitate this cause R3 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 -- perfection which necessarily transcends that which our knowledge of the order and design in the world would authorize us to predicate of it. For the regulative law of systematic unity requires us to study nature on the suppo sition that systematic and final unity in infinitum every where discoverable, even in the highest diversity. For, although we may discover little of this cosmical perfection, belongs to the legislative prerogative of reason, to require us always to seek for and to expect while must always be beneficial to institute all inquiries into nature in accord ance with this principle. But evident that, this idea of supreme author of all, which place as the founda
tion of all inquiries into nature, do not mean to assert the existence of such being, or that have any knowledge of its existence and, consequently, do not really deduce any thing from the existence of this being, but merely from its idea, that to say, from the nature of things in this world, in accordance with this idea. certain dim consciousness of the true use of this idea seems to have dictated to the philo sophers of all times the moderate language used them regarding the cause of the world. We find them employ ing the expressions, wisdom and care of nature, and divine
? wisdom, as synonymous, -- nay, purely speculative discus*
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? of tat NatUbaA DiAJUfcrtic of humak beasoK. 429
iions, preferring the former, because it does not carry the ap pearance 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, realise 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 misunder stood and employed as constitutive principles of transcendent cognition, they become the parents of illusions and contradic tions, 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
a thorough-going 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 criti cal 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
? experience,
? ? ? 430 tBAHSClNDENfAL DIALECTIC.
spare ourselves the laborious examination of all the dia lectical 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 dialec tical 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 hu manity, it was advisable at the same time, to give a full ac count 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 theee causes of speculative error.
? ? ? ? n.
TRANSCENDENTAL DOCTRINE OY METHOD.
If we regard the sum of the cognition of pure speculative reason as an edifice, the idea of which, at least, exists iu 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 purposeu 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 necesaarily 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 in tention of erecting a secure abode for the mind, we must pro portion our design to the material which is presented to us, and which at the same time, sufficient for all our wants.
understand, then, the transcendental doctrine of me thod, the determination of the formal conditions of com plete 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. has been badly executed,
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? 432 TBAltSCENbENtAt BOOTBtlTE OF MEtllOD.
piy, because general logic, not being limited to nny particular kind of cognition (not even to the pure cognition of the un derstanding) 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.
TRANSCENDENTAL DOCTRINE OF METHOD.
CHAPTER FIRST.
THE DISCIPLINE OF PUKE REASON.
Negative judgments -- those which are so not merely as re gards 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 ns to tolerate, much less to prixe and to respect them.
All propositions, indeed, may be logically expressed in a negative form ; but, in relation to the content of our cogni
tion, the peculiar province of negative judgments 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 they are reality purposeless, and for this reason often very ridiculous. Such the pro
? 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 subject of the most deceptive character, and the evil consequences of error of no inconsiderable magnitude, --the negative element in knowledge, which useful only to guard us against error, of far mora
position
than much of that, positive instruction which makes additions to the sum of our knowledge. The restraint which employed to repreas, and finally to extirpate the con
importance
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43d
stunt inclination to depart from certain rule*, is termed Disci pline. It is distinguished from culture, which aims at thi formation of a certain degree of skill, without attempting to repress or to destroy any other mental power, already exist ing. 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.
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 thia
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 criti cism requisite in the sphere of mathematics, where the con ceptions 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
when employed in the transcendental sphere of pure conceptions, stands in great need of discipline, to restrain its propensity to overstep the limits of possible experience, nnd to keep from wandering into error. In fact, the utility of the philosophy of pure reason entirely of thia
corrected by particular animadversions, and the causes of these errors may be eradicated criticism. But where we find, as in the case
of pure reason, complete system of illusions and fallacies,
am well aware that, in the language of the schools, the term dim pling usually employed as synonymous with mttruction. But there are so many cases in which necessary to distinguish the notion of the former, as course of corrective training, from that of the Utter, as the communication of knowledge, and the nature of things itself demands the appropriation of the most suitable expressions for this distinction, that
ray desire that the former term should never be emploved in any other than negative signification.
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? 431 TRANSCENDENTAL DOCTRINE. Dl METHOD.
closely connected with each other and depending upon ? rand general principles, there seems to be required a peculiar and negative code of mental legislation, which, nnder the de nomination 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 01 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 cog nition of pure reason. The former task has been com pleted 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 unskilful employment of the methods which are originated by reason bnt which are out of place in this sphere.
CHAPTER FIRST.
Section First.
The Discipline of Pure Reason in the sphere of D<igmatisin.
The science of Mathematics presents the most brilliant ex
ample 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 na turally flatters itself that it will have the same good fortune in other cases, as fell to its lot in one fortunate instance. Hence pure reason hopes to be able to extend its empire in the trans cendental 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 there fore, of the highest importance for us to know, whether the method of arriving at demonstrative certainty, which termed mathematical, be identical with that which we endeavour to attain the same degree of certainty in philosophy, and which
termed in that science dogmatical*
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by
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? Tilt DISCIPLINE OF PUUJS BEA. SON. 435
Philosophical cognition is the cognition of reason by mean* 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 concep tion (a general representation), it must be seen to be univer sally valid for all the possible intuitions which rank under that conception. Thus I construct a triangle, by the presenta tion 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 univer sality, 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 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 particu lar, nay, in the individual. This done, however, entirely a priori and by means of pure reason, so that, as this indi vidual figure determined under certain universal condi tions 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 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
? to be found its form alone. For the con-
quantity,
ceptiou of quantities only that capable of being constructed, that presented a priori intuition while qualities cannot be given any other than an empirical intuition. Hence the
? ? in is,
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it is
; it
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? 436 TRANSCEND ENTAX DOCTBLNE OT METHOD.
cognition of qualities by reason is possible onlj through con
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 of cone, without the aid of ex
ceptions.
but the colour of the cone we cannot know except from experience. cannot present an intuition of 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
perience
? of different quality, of the continuity of extension --as quality thereof. But, although in such cases they have common object, the mode in which reason considers that object very different in philosophy from what in mathematics. The former confines itself to the general conceptions the latter can do nothing with mere conception, hastens to intuition. In this intuition regards the conception in concrete, not empirically, but in an a priori intuition, which has con structed and in which, all the results which follow from the general conditions of the construction of the conception, are
all cases valid for the object of the constructed conception.
Suppose that the conception of triangle given to phi losopher, and that he required to discover, the philoso phical method, what relation the sum of its angles bears to
right angle. He has nothing before him but the concep tion of figure enclosed within three right lines, and, conse quently, with the same number of angles. He may analyze the conception of right line, of an angle, or of the number three as long as he pleases, but he will not discover any pro perties not contained in these conceptions. But, this ques tion proposed to geometrician, he at once begins con structing triangle. * He knows that two right angles are equal to the sum of all the contiguous angles which proceed from one point in 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, drawing line parallel with the
Either in his own mind -- pure intuition, or upon paper --in em pirical intuition. -- Tr
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? THE DJSClPLIifE Ot PtJEE BEASOtf.
437
opposite side of the triangle, and immediately perceives that he has thus got an exterior adjacent angle which is equal to the in terior. 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 accord ance with general rules. Thus, when ore 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 alge
bra, 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 ad vantage over his rival ; we aim at the discovery of synthetics, 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
? ? ? ? 438 TRANSCENDENTAL DOCTRINE OF METHOD.
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 pro ceed 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 tri angle in general, and consequently to its conception, nnd thus construct synthetical propositions which possess the attribute <<>f universality.
It would be vain to philosophize upon the triangle, that
to reflect on discursively should get no further than the definition with which had been obliged to set out.
There are certainly transcendental synthetical propositions which are framed means of pure conceptions, and which form the peculiar distinction of philosophy but these do not relate to any particular thing, but to thing in general, and enounce the conditions under which the perception of may become 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 concerned merely with the properties of objects in themselves, only so far as these are connected with the conception of the objects.
In the above example, we have merely attempted to show the great difference which exbts between the discursive em ployment of reason in the sphere of conceptions, and its intui tive exercise by means of the construction of conceptions. The question naturally arises --what the cause which neces sitates this twofold exercise of reason, and how are we to discover whether the philosophical or the mathematical method which reason pursuing an argument
All our knowledge relates, finally, to possible intuitions, for these alone that present objects to the mind. An
priori or non-empirical conception contains either pure intuition --and in this case can be constructed or con
tains nothing but the synthesis of possible intuitions, which are not given priori. In this latter case, may help us to form synthetical priori judgments, but only in the discur sive method, by conceptions, not the intuitive, by means of the construc'iou of conceptions.
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? THE DISCIPLINE OF PUBE EEASON. 439
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 constructed, either along 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 repre sents priori this empirical content of phenomena, the conception of 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 posteriori perception utterly inade quate to present an 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 impossible, are transcen dental. 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 incom petent to present any of the conceptions which appear in them in an priori intuition these can be given only a pos teriori, experience, which, however, itself possible only through these synthetical principles.
If we are to form synthetical judgment regarding con ception, we must go beyond to the intuition in which given. If we keep to what contained in the conception, the judgment merely analytical-- merely an explanation of what we have cogitated in the conception. But can pass from the conception to the pure or empirical intuition which corresponds to it. can proceed to examine my conception in toner eto, and to cognize, either a priori or a posteriori, what find in the object of the conception. The former--a priori cognition-- rational-mathematical cognition by means of the construction of the conception the latter -- posteriori cognition-- purely empirical cognition, which does not possess the attributes of necessity and universality. Thus
may analyze the conception have of gold but gain no
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? 440 TKAKSCJSNDENTAL DOCTRINE OF METHOD.
new information from this analysis, I merely enumerate the different properties which I had couuected with the notion in dicated hy the word. My knowledge has gained iu 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--propo sitions. The mathematical conception of a triangle I should construct, that present priori in intuition, and in this way attain to rational-synthetical cognition. But when the transcendental conception of reality, or substance, or power
presented to my mind, find that does not relate to or indicate either an empirical or pure intuition, hut that indicates merely the synthesis of empirical intuitions, which cannot of course be given priori. The synthesis in such conception cannot proceed priori -- without the aid of expe rience --to the intuition which corresponds to the conception and, for this reason, none of these conceptions can produce determinative synthetical proposition, they can never present
more than principle of the syn thesis* of possible empirical
intuitions. transcendental proposition therefore,
thetical cognition of reason means of pure conceptions and the discursive method, and renders possible all synthetical unity in empirical cognition, though cannot present us with any intuition priori.
There thus twofold exercise of reason. Both modes have the properties of universality and an priori origin common, but are, in their procedure, of widely different cha racter. The reason of this that the world of pheno mena, 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 priori, and the matter or content --that which presented in space and time, and which, consequently, contains some-
In the case of the conception of cause, do really go beyond the em pirical conception of an event --but not to the intuition which presents this conception in concrtto, but only to the time-conditions, which may be found in experience to correspond to the conception. My procedure '">>, therefore, strictly according to conceptions cannot in case of this Kind employ the construction of conceptions, because the conception merely rule for the synthesis of perceptions, which are not pure intui tions, and which, therefore, cannot be given priori.
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thing -- an existence corresponding to onr powers of sensation. As regards the latter, which can never be given in a deter minate mode except by experience, there are no a priori no tions which relate to except the undetermined conceptions of the synthesis of possible sensations, in so far as these belong (in possible experience') to the unity of consciousness. As regards the former, we can determine our conceptions
priori in intuition, inasmuch as we are ourselves the creators of the objects of the conceptions in space and time--these ob jects being regarded simply ns quanta. In the one case, reason proceeds according to conceptions, and can do nothing more than subject phenomena to these --which can only be deter- minedempiricftlly, that a posteriori -- in conformity, however, with those conceptions as the rules of all empirical synthesis. In the other case, reason proceeds the construction of con ceptions and, as these conceptions relate to an a priori in tuition, they may be given and determined in pure intuition
priori, and without the aid of empirical data. The exa mination and consideration of everything that exists in space or time --whether quantum or not, in how far the par ticular something (which fills space or time) primary sub
stratum, or mere determination of some other existence, whether relates to anything else -- either as cause or effect, whether its existence isolated or in reciprocal connection with and dependence upon others, the possibility of this ex istence, its reality and necessity or their opposites, --all these form part of the cognition of reason on the ground of concep tions, and this cognition termed philosophical. But to de termine a priori an intuition in space (its figure), to divide time into periods, or merely to cognize the quantity of an in tuition in space and time, and to determine number, -- all this an operation reason means of the construction of conceptions, and 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, applies the mathematical method in other regions of mental endeavour besides that of
Its success thus great, because can sup port all its conceptions by priori intuitions, and in this way, make itself master, as were, over nature while pure
with its a prnri discursive conceptions, bungles
? quantities. philosophy,
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? 442 TRANSCENDENTAX DOCTRINE OT METHOD.
abont iu 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 com mon sense stamps everywhere with ita 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 jnst as unnecessary to examine into the origin of the pure concep tions of the understanding and the extent of their validity. All they have to do with them is to employ them. In nll 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 transcen dental conceptions (instabilii tellut, innabilis undo), where they can neither stand nor swim, and where the tracks of their foot steps 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 ot 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 experi ence 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 mathe matical 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 hand in hand in the field of natural science, and, consequently, that tha
procedure of the one can never be imitated by the other.
? ? ? ? THE DISCIPLUTB Of FUBE SEASON. 443
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 mathema tics, 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 depart ment of knowledge, cannot turn a deaf ear to the warnings of philosophy, or set himself above its direction.
1. Of Definitions. -- A definition as the term itself indi cates, the representation, upon primary grounds, of the complete conception of a thing within its own limits. * Accordingly, an empirical conception cannot be defined, can only be explained. For, as there are in such conception only certain number of marks or signs, which denote 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 greater, at another 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 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 observa
tion and experiment; and the word, with the few signs
The definition must describe the conception complete! )/, that omit none of the marks or signs of which composed within ill own limitt, that must be precise, and enumerate no more higus than belong to the conception and on primary ground*, that to say, the limitation of the bounds of the conception must not be deduced from other concep tions, as in this case proof vould be necessary, and the so-called definition would be incapable of taking its place at the head of all the judgments we have to form regarding an object.
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attached to more properly designation than concep tion of the thing. definition in this case, would evidently" be nothing more than determination, of the word. In the second place, no priori conception, such as those of sub stance, cause, right, fitness, and so on, can be defined. For
can never be sure, that the clear representation of given conception (which given in confused state) has been fully developed, until know that the representation adequate with its object. But, inasmuch as the conception, as presented to the mind, may contain number of obscure representations, which we do not observe our analysis, although we employ them in our application of the concep tion, can never be sure that my analysis complete, while examples may make this probable, although they can never demonstrate the fact. Instead of the word definition, should rather employ the term exposition -- more modest expression, which the critic may accept without surrendering his doubt* as to the completeness
tion. As, therefore, neither empirical nor a priori concep tions 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 conception can always be defined for must know thoroughly what wished to cogitate as was who created and was not given to my mind either the nature of my understand ing or experience. At the same time, cannot say that,
such definition, have defined real object. If the
based upon empirical conditions, for example, have conception of clock for ship, this arbitrary con
ception does not rssnre me of the existence or even of the possibility of the object. My definition of uch conception would with more propriety be termed declaration of pro ject than definition of an object. There are no other
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 pre sented a priori in intuition and thus can never contain more or less than the conception, because the conception
the object has been given by the definition -- and primarily, that '"ithout deriving the definition from any other source
conception
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? TELE DISCIPLINE OF PITRE EEA. SON. 44 S
Philosophical definitions are, therefore, merely expositions of given conceptions, while mathematical definitions are con structions 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 syn thesis. In a mathematical definition the conception is formed, in a philosophical definition it is only explained. From this it follows :
a. That we must not imitate, in philosophy, the mathe matical usage of commencing with definitions --except by way of hypothesis or experiment. For, as all so-called philoso phical definitions are merely analyses of given conceptions, these conceptions, although only in a confused form, must precede the analysis ; and the incomplete exposition must pre cede the complete, so that we may be able to draw certain in ferences 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 commence ment of every chain of mathematical reasoning.
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
* Philosophy abounds in faulty definitions, especially such as contain some of the elements requisite to form a complete definition. If a con ception 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 defi nitions, that is, propositions which are properly not definitions, but merely approximations thereto, may be used with great advantage. In ma thematics, definition belongs ad ate, in philosophy ad meliut em. It is a difficult task to construct a proper definition. Jurists are still withoof
a complete definition of the idea of right.
? ? ? ? 446 TllAKSCENDXNTAI, DOCTRINE OF METHOD.
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 that not even the smallest part of can be straight. Analytical definitions, on the other hand, may be erroneous in many respects, either the in troduction of signs which do not actually exist in the concep tion, or by wanting in that completeness which forms the es sential of definition. In the latter case, the definition necessarily defective, because we can never be fully certain the completeness of our analysis. For these reasons, the me thod of definition employed mathematics cannot be imitated in philosophy.
'1. Of Axioms. These, in so far as they are immediately
certain, are priori synthetical principles. Now, one con
ception cannot be connected synthetically and yet immediately with another because, we wish to proceed out of and beyond
? third mediating cognition necessary. And, as philosophy cognition of reason the aid of concep tions alone, there to be found in no principle which de
conception,
serves to be called an axiom. Mathematics, on the other hand, may possess axioms, because can always connect the pre dicates of an object priori, and without any mediating term, by means of the construction of conceptions in intuition. Such
the case with the proposition, three points can always plane. On the other hand, no synthetical principle
lie
which
certain, (for example, the proposition, Everything that hap pens has cause), because require mediating term to con nect the two conceptions of event and cause --namely, the con dition of time-determination in an experience, and cannot cognize any such principle immediately and from conceptions alone. Discursive principles are, accordingly, very different from intuitive principles or axioms. The former always re quire deduction, which in the case of the latter may be alto gether dispensed with. Axioms are, for this reason, nlways self-evident, while philosophical principles, whatever may b<< the degree of certainty they possess, cannot lay any claim to
such distinction. No synthetical proposition of pur>> trans
based upon conceptions, can ever be immediately
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147
eendenta] 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 prin ciple 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 tc impose its a priori principles upon thought, until it has established their authority and validity by a thorough-going deduction.
3. Of Demonstrations. Only an apodeictic proof, based upon intuition, can be termed a demonstration. Experience
teaches us what but cannot convince us that
have been otherwise. Hence proof upon empirical grounds cannot be apodeictic. priori conceptions, in discursive cogni tion, can never produce intuitive certainty or evidence, however certain the judgment they present may be. Mathematics alone, therefore, contains demonstrations, because does not deduce its cognition from conceptions, but from the construction of conceptions, that from intuition, which can be given a priori in accordance with conceptions. The method of algebra, in
equations, from which the correct answer deduced duction, kind of construction --not geometrical, but symbols -- in which all conceptions, especially those of the re
lations of quantities, are represented in intuition signs and thus the conclusions that science are secured from errors the fact that every proof submitted to ocular evidence.
Philosophical cognition does not possess this advantage, being required to consider the general always in abstracto (by means of conceptions), while mathematics can always consider
? in eonereto (in an individual intuition), and at the same time means of priori representation, whereby all errors are ren
dered manifest to the senses. The former -- discursive proofs --ought to be termed aeroamatic* proofs, rather than demon strations, as only words are employed in them, while demon strations proper, as the term itself indicates, always require reference to the intuition of the object.
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It follows from nil these considerations, that it is not coo- sonant 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 ma thematical evidence are vain pretensions, which can only keep it back from its true aim, which is to detect the illusory pro cedure 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,
ns if the path it is pursuing led straight to its aim, nor reckon with such security upon its premises, as to consider it un necessary 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 maihemata. A direct synthetical proposition, based on conceptions, is a dogma ; a proposition of the same kind, based on the con struction of conceptions, isamathema. Analytical judgments do not teach us any more about an object, than what was con tained 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 there fore be with propriety termed dogmas. Of the two kinds of a priori synthetical propositions above-mentioned, only those which are employed iu philosophy can, according to the ge neral mode of speech, bear this name; those of arithmetic or
? would not be rightly bo denominated. Thus the
geometry
customary mode of speaking confirms the explanation given above, and the conclusion arrived at, that only those judg
ments which are based upon couceptions, not on the construe* tion of conceptions, can be termed dogmatical.
Thus, pure reason, in the sphere of speculation, does not contain a eingle direct synthetical judgment based npon con ceptions. By means of ideas, it as we have showa, in
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? THE DISCIPLINE OT PUBE BEA8OK. 449
capable of producing synthetical judgments, which are ob jectively valid ; by means of the conceptions of the under standing, it establishes certain indubitable principles, not, however, directly on the basis of conceptions, but only indi rectly by means of the relation of these conceptions to some thing of a purely contingent nature, namely, possible experi ence. When experience is presupposed, these principles are apodeictically certain, but in themselves, and directly, they cannot even be cognized a priori. Thus the given concep tions of cause and event will not be sufficient for the demon stration 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 suclT~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 pooof, that is, experience, and of forming a necessary presup position in all empirical observation.
? If then, in the speculative sphere of pure reason, no dog mata are to be found ; all dogmatical methods, whether bor rowed from mathematics, or invented by philosophical thinkers, are alike inappropriate and inefficient.