# Critique of Pure Reason (Meiklejohn)/Volume 2/Chapter 1

TRANSCENDENTAL DOCTRINE OF METHOD.
CHAPTER FIRST.
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.
That natural dispositions and talents (such as imagination and with, 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.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 be 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.
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.
1. 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:
(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.
(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.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.
From this point of view, there is properly no antithetic of pure reason. For the only arena for such a struggle would be upon the field of pure theology and psychology; but on this ground there can appear no combatant whom we need to fear. Ridicule and boasting can be his only weapons; and these may be laughed at, as mere child's play. This consideration restores to Reason her courage; for what source of confidence could be found, if she, whose vocation it is to destroy error, were at variance with herself and without any reasonable hope of ever reaching a state of permanent repose?
Everything in nature is good for some purpose. Even poisons are serviceable; they destroy the evil effects of other poisons generated in our system, and must always find a place in every complete pharmacopoeia. The objections raised against the fallacies and sophistries of speculative reason, are objections given by the nature of this reason itself, and must therefore have a destination and purpose which can only be for the good of humanity. For what purpose has Providence raised many objects, in which we have the deepest interest, so far above us, that we vainly try to cognize them with certainty, ​and our powers of mental vision are rather excited than satisfied by the glimpses we may chance to seize? It is very doubtful whether it is for our benefit to advance bold affirmations regarding subjects involved in such obscurity; perhaps it would even be detrimental to our best interests. But it is undoubtedly always beneficial to leave the investigating, as well as the critical reason, in perfect freedom, and permit it to take charge of its own interests, which are advanced as much by its limitation, as by its extension of its views, and which always suffer by the interference of foreign powers forcing it, against its natural tendencies, to bend to certain preconceived designs.
Allow your opponent to say what he thinks reasonable, and combat him only with the weapons of reason. Have no anxiety for the practical interests of humanity—these are never imperilled in a purely speculative dispute. Such a dispute serves merely to disclose the antinomy of reason, which, as it has its source in the nature of reason, ought to be thoroughly investigated. Reason is benefited by the examination of a subject on both sides, and its judgements are corrected by being limited. It is not the matter that may give occasion to dispute, but the manner. For it is perfectly permissible to employ, in the presence of reason, the language of a firmly rooted faith, even after we have been obliged to renounce all pretensions to knowledge.
If we were to ask the dispassionate David Hume—a philosopher endowed, in a degree that few are, with a well-balanced judgement: What motive induced you to spend so much labour and thought in undermining the consoling and beneficial persuasion that reason is capable of assuring us of the existence, and presenting us with a determinate conception of a Supreme Being?—his answer would be: Nothing but the desire of teaching reason to know its own powers better, and, at the same time, a dislike of the procedure by which that faculty was compelled to support foregone conclusions, and prevented from confessing the internal weaknesses which it cannot but feel when it enters upon a rigid self-examination. If, on the other hand, we were to ask Priestley—a philosopher who had no taste for transcendental speculation, but was entirely devoted to the principles of empiricism—what his motives were for overturning those two main pillars of ​religion—the doctrines of the freedom of the will and the immortality of the soul (in his view the hope of a future life is but the expectation of the miracle of resurrection),—this philosopher, himself a zealous and pious teacher of religion, could give no other answer than this: I acted in the interest of reason, which always suffers, when certain objects are explained and judged by a reference to other supposed laws than those of material nature—the only laws which we know in a determinate manner. It would be unfair to decry the latter philosopher, who endeavoured to harmonize his paradoxical opinions with the interests of religion, and to undervalue an honest and reflecting man, because he finds himself at a loss the moment he has left the field of natural science. The same grace must be accorded to Hume, a man not less well-disposed, and quite as blameless in his moral character, and who pushed his abstract speculations to an extreme length, because, as he rightly believed, the object of them lies entirely beyond the bounds of natural science, and within the sphere of pure ideas.
What is to be done to provide against the danger which seems in the present case to menace the best interests of humanity? The course to be pursued in reference to this subject is a perfectly plain and natural one. Let each thinker pursue his own path; if he shows talent, if be gives evidence of profound thought, in one word, if he shows that he possesses the power of reasoning,—reason is always the gainer. If you have recourse to other means, if you attempt to coerce reason, if you raise the cry of treason to humanity, if you excite the feelings of the crowd, which can neither understand nor sympathize with such subtle speculations,—you will only make yourselves ridiculous. For the question does not concern the advantage or disadvantage which we are expected to reap from such inquiries; the question is merely how far reason can advance in the field of speculation, apart from all kinds of interest, and whether we may depend upon the exertions of speculative reason, or must renounce all reliance on it. Instead of joining the combatants, it is your part to be a tranquil spectator of the struggle—a laborious struggle for the parties engaged, but attended, in its progress as well as in its result, with the most advantageous consequences for the interests of thought and knowledge. It is absurd to expect ​to be enlightened by Reason, and at the same time to prescribe to her what side of the question she must adopt. Moreover, reason is sufficiently held in check by its own power, the limits imposed on it by its own nature are sufficient; it is unnecessary for you to place over it additional guards, as if its power were dangerous to the constitution of the intellectual state. In the dialectic of reason there is no victory gained which need in the least disturb your tranquility.
The strife of dialectic is a necessity of reason, and we cannot but wish that it had been conducted long ere this with that perfect freedom which ought to be its essential condition. In this case, we should have had at an earlier period a matured and profound criticism, which must have put an end to all dialectical disputes, by exposing the illusions and prejudices in which they originated.
There is in human nature an unworthy propensity—a propensity which, like everything that springs from nature, must in its final purpose be conducive to the good of humanity—to conceal our real sentiments, and to give expression only to certain received opinions, which are regarded as at once safe and promotive of the common good. It is true, this tendency, not only to conceal our real sentiments, but to profess those which may gain us favour in the eyes of society, has not only civilized, but, in a certain measure, moralized us; as no one can break through the outward covering of respectability, honour, and morality, and thus the seemingly-good examples which we which we see around us form an excellent school for moral improvement, so long as our belief in their genuineness remains unshaken. But this disposition to represent ourselves as better than we are, and to utter opinions which are not our own, can be nothing more than a kind of provisionary arrangement of nature to lead us from the rudeness of an uncivilized state, and to teach us how to assume at least the appearance and manner of the good we see. But when true principles have been developed, and have obtained a sure foundation in our habit of thought, this conventionalism must be attacked with earnest vigour, otherwise it corrupts the heart, and checks the growth of good dispositions with the mischievous weed of air appearances.
I am sorry to remark the same tendency to misrepresentation and hypocrisy in the sphere of speculative discussion, ​where there is less temptation to restrain the free expression of thought. For what can be more prejudicial to the interests of intelligence than to falsify our real sentiments, to conceal the doubts which we feel in regard to our statements, or to maintain the validity of grounds of proof which we well know to be insufficient? So long as mere personal vanity is the source of these unworthy artifices—and this is generally the case in speculative discussions, which are mostly destitute of practical interest, and are incapable of complete demonstration—the vanity of the opposite party exaggerates as much on the other side; and thus the result is the same, although it is not brought about so soon as if the dispute had been conducted in a sincere and upright spirit. But where the mass entertains the notion that the aim of certain subtle speculators is nothing less than to shake the very foundations of public welfare and morality—it seems not only prudent, but even praise worthy, to maintain the good cause by illusory arguments, rather than to give to our supposed opponents the advantage of lowering our declarations to the moderate tone of a merely practical conviction, and of compelling us to confess our inability to attain to apodeictic certainty in speculative subjects. But we ought to reflect that there is nothing, in the world more fatal to the maintenance of a good cause than deceit, misrepresentation, and falsehood. That the strictest laws of honesty should be observed in the discussion of a purely speculative subject is the least requirement that can be made. If we could reckon with security even upon so little, the conflict of speculative reason regarding the important questions of God, immortality, and freedom, would have been either decided long ago, or would very soon be brought to a conclusion. But, in general, the uprightness of the defence stands in an inverse ratio to the goodness of the cause; and perhaps more honesty and fairness are shown by those who deny than by those who uphold these doctrines.
I shall persuade myself, then, that I have readers who do not wish to see a righteous cause defended by unfair arguments. Such will now recognize the fact that, according to the principles of this Critique, if we consider not what is, but what ought to be the case, there can be really no polemic of pure reason. For how can two persons dispute about a thing, ​the reality of which neither can present in actual or even in possible experience? Each adopts the plan of meditating on his idea for the purpose of drawing from the idea, if he can, what is more than the idea, that is, the reality of the object which it indicates. How shall they settle the dispute, since neither is able to make his assertions directly comprehensible and certain, but must restrict himself to attacking and confuting those of his opponent? All statements enounced by pure reason transcend the conditions of possible experience, beyond the sphere of which we can discover no criterion of truth, while they are at the same time framed in accordance with the laws of the understanding, which are applicable only to experience; and thus it is the fate of all such speculative discussions that while the one party attacks the weaker side of his opponent, he infallibly lays open his own weaknesses.
The critique of pure reason may be regarded as the highest tribunal for all speculative disputes; for it is not involved in these disputes, which have an immediate relation to certain objects and not to the laws of the mind, but is instituted for the purpose of determining the rights and limits of reason.
Without the control of criticism, reason is, as it were, in a state of nature, and can only establish its claims and assertions by war. Criticism, on the contrary, deciding all questions according to the fundamental laws of its own institution, secures to us the peace of law and order, and enables us to discuss all differences in the more tranquil manner of a legal process. In the former case, disputes are ended by victory, which both sides may claim and which is followed by a hollow armistice; in the latter, by a sentence, which, as it strikes at the root of all speculative differences, ensures to all concerned a lasting peace. The endless disputes of a dogmatizing reason compel us to look for some mode of arriving at a settled decision by a critical investigation of reason itself; just as Hobbes maintains that the state of nature is a state of injustice and violence, and that we must leave it and submit ourselves to the constraint of law, which indeed limits individual freedom, but only that it may consist with the freedom of others and with the common good of all.
This freedom will, among other things, permit of our openly stating the difficulties and doubts which we are ourselves unable to solve, without being decried on that account as turbulent ​and dangerous citizens. This privilege forms part of the native rights of human reason, which recognizes no other judge than the universal reason of humanity; and as this reason is the source of all progress and improvement, such a privilege is to be held sacred and inviolable. It is unwise, moreover, to denounce as dangerous any bold assertions against, or rash attacks upon, an opinion which is held by the largest and most moral class of the community; for that would be giving them an importance which they do not deserve. When I hear that the freedom of the will, the hope of a future life, and the existence of God have been overthrown by the arguments of some able writer, I feel a strong desire to read his book; for I expect that he will add to my knowledge and impart greater clearness and distinctness to my views by the argumentative power shown in his writings. But I am perfectly certain, even before I have opened the book, that he has not succeeded in a single point, not because I believe I am in possession of irrefutable demonstrations of these important propositions, but because this transcendental critique, which has disclosed to me the power and the limits of pure reason, has fully convinced me that, as it is insufficient to establish the affirmative, it is as powerless, and even more so, to assure us of the truth of the negative answer to these questions. From what source does this free-thinker derive his knowledge that there is, for example, no Supreme Being? This proposition lies out of the field of possible experience, and, therefore, beyond the limits of human cognition. But I would not read at, all the answer which the dogmatical maintainer of the good cause makes to his opponent, because I know well beforehand, that he will merely attack the fallacious grounds of his adversary, without being able to establish his own assertions. Besides, a new illusory argument, in the construction of which talent and acuteness are shown, is suggestive of new ideas and new trains of reasoning, and in this respect the old and everyday sophistries are quite useless. Again, the dogmatical opponent of religion gives employment to criticism, and enables us to test and correct its principles, while there is no occasion for anxiety in regard to the influence and results of his reasoning.
But, it will be said, must we not warn the youth entrusted to academical care against such writings, must we not preserve ​them from the knowledge of these dangerous assertions, until their judgement is ripened, or rather until the doctrines which we wish to inculcate are so firmly rooted in their minds as to withstand all attempts at instilling the contrary dogmas, from whatever quarter they may come?
If we are to confine ourselves to the dogmatical procedure in the sphere of pure reason, and find ourselves unable to settle such disputes otherwise than by becoming a party in them, and setting counter-assertions against the statements advanced by our opponents, there is certainly no plan more advisable for the moment, but, at the same time, none more absurd and inefficient for the future, than this retaining of the youthful mind under guardianship for a time, and thus preserving it—for so long at least—from seduction into error. But when, at a later period, either curiosity, or the prevalent fashion of thought places such writings in their hands, will the so-called convictions of their youth stand firm? The young thinker, who has in his armoury none but dogmatical weapons with which to resist the attacks of his opponent, and who cannot detect the latent dialectic which lies in his own opinions as well as in those of the opposite party, sees the advance of illusory arguments and grounds of proof which have the advantage of novelty, against as illusory grounds of proof destitute of this advantage, and which, perhaps, excite the suspicion that the natural credulity of his youth has been abused by his instructors. He thinks he can find no better means of showing that he has out grown the discipline of his minority than by despising those well-meant warnings, and, knowing no system of thought but that of dogmatism, he drinks deep draughts of the poison that is to sap the principles in which his early years were trained.
Exactly the opposite of the system here recommended ought to be pursued in academical instruction. This can only be effected, however, by a thorough training in the critical investigation of pure reason. For, in order to bring the principles of this critique into exercise as soon as possible, and to demonstrate their perfect even in the presence of the highest degree of dialectical illusion, the student ought to examine the assertions made on both sides of speculative questions step by step, and to test them by these principles. It cannot be a difficult task for him to show the ​fallacies inherent in these propositions, and thus he begins early to feel his own power of securing himself against the influence of such sophistical arguments, which must finally lose, for him, all their illusory power. And, although the same blows which overturn the edifice of his opponent are as fatal to his own speculative structures, if such he has wished to rear; he need not feel any sorrow in regard to this seeming misfortune, as he has now before him a fair prospect into the practical region in which he may reasonably hope to find a more secure foundation for a rational system.
There is, accordingly, no proper polemic in the sphere of pure reason. Both parties beat the air and fight with their own shadows, as they pass beyond the limits of nature, and can find no tangible point of attack—no firm footing for their dogmatical conflict. Fight as vigorously as they may, the shadows which they hew down, immediately start up again, like the heroes in Walhalla, and renew the bloodless and unceasing contest.
But neither can we admit that there is any proper sceptical employment of pure reason, such as might be based upon the principle of neutrality in all speculative disputes. To excite reason against itself, to place weapons in the hands of the party on the one side as well as in those of the other, and to remain an undisturbed and sarcastic spectator of the fierce struggle that ensues, seems, from the dogmatical point of view, to be a part fitting only a malevolent disposition. But, when the sophist evidences an invincible obstinacy and blindness, and a pride which no criticism can moderate, there is no other practicable course than to oppose to this pride and obstinacy similar feelings and pretensions on the other side, equally well or ill founded, so that reason, staggered by the reflections thus forced upon it, finds it necessary to moderate its confidence in such pretensions and to listen to the advice of criticism. But we cannot stop at these doubts, much less regard the conviction of our ignorance, not only as a cure for the conceit natural to dogmatism, but as the settlement of the disputes in which reason is involved with itself. On the contrary, scepticism is merely a means of awakening reason from its dogmatic dreams and exciting it to a more careful investigation into its own powers and pretensions. But, as scepticism appears ​to be the shortest road to a permanent peace in the domain of philosophy, and as it is the track pursued by the many who aim at giving a philosophical colouring to their contemptuous dislike of all inquiries of this kind, I think it necessary to present to my readers this mode of thought in its true light.
    Scepticism not a Permanent State for Human Reason.
The consciousness of ignorance—unless this ignorance is recognized to be absolutely necessary—ought, instead of forming the conclusion of my inquiries, to be the strongest motive to the pursuit of them. All ignorance is either ignorance of things or of the limits of knowledge. If my ignorance is accidental and not necessary, it must incite me, in the first case, to a dogmatical inquiry regarding the objects of which I am ignorant; in the second, to a critical investigation into the bounds of all possible knowledge. But that my ignorance is absolutely necessary and unavoidable, and that it consequently absolves from the duty of all further investigation, is a fact which cannot be made out upon empirical grounds—from observation—but upon critical grounds alone, that is, by a thoroughgoing investigation into the primary sources of cognition. It follows that the determination of the bounds of reason can be made only on a priori grounds; while the empirical limitation of reason, which is merely an indeterminate cognition of an ignorance that can never be completely removed, can take place only a posteriori. In other words, our empirical knowledge is limited by that which yet remains for us to know. The former cognition of our ignorance, which is possible only on a rational basis, is a science; the latter is merely a perception, and we cannot say how far the inferences drawn from it may extend. If I regard the earth, as it really appears to my senses, as a flat surface, I am ignorant how far this surface extends. But experience teaches me that, how far soever I go, I always see before me a space in which I can proceed farther; and thus I know the limits—merely visual—of my actual knowledge of the earth, although I am ignorant of the limits of the earth itself. But if I have got so far as to know that the earth is a sphere, and that its surface is spherical, I can cognize a priori and determine upon principles, from my knowledge of a small part of ​this surface—say to the extent of a degree—the diameter and circumference of the earth; and although I am ignorant of the objects which this surface contains, I have a perfect knowledge of its limits and extent.
The sum of all the possible objects of our cognition seems to us to be a level surface, with an apparent horizon—that which forms the limit of its extent, and which has been termed by us the idea of unconditioned totality. To reach this limit by empirical means is impossible, and all attempts to determine it a priori according to a principle, are alike in vain. But all the questions raised by pure reason relate to that which lies beyond this horizon, or, at least, in its boundary line.
The celebrated David Hume was one of those geographers of human reason who believe that they have given a sufficient answer to all such questions by declaring them to lie beyond the horizon of our knowledge—a horizon which, however, Hume was unable to determine. His attention especially was directed to the principle of causality; and he remarked with perfect justice that the truth of this principle, and even the objective validity of the conception of a cause, was not commonly based upon clear insight, that is, upon a priori cognition. Hence he concluded that this law does not derive its authority from its universality and necessity, but merely from its general applicability in the course of experience, and a kind of subjective necessity thence arising, which he termed habit. From the inability of reason to establish this principle as a necessary law for the acquisition of all experience, he inferred the nullity of all the attempts of reason to pass the region of the empirical.
This procedure of subjecting the facta of reason to examination, and, if necessary, to disapproval, may be termed the censura of reason. This censura must inevitably lead us to doubts regarding all transcendent employment of principles. But this is only the second step in our inquiry. The first step in regard to the subjects of pure reason, and which marks the infancy of that faculty, is that of dogmatism. The second, which we have just mentioned, is that of scepticism, and it gives evidence that our judgement has been improved by experience. But a third step is necessary—indicative of the maturity and manhood of the judgement, which now lays a firm ​foundation upon universal and necessary principles. This is the period of criticism, in which we do not examine the facta of reason, but reason itself, in the whole extent of its powers, and in regard to its capability of a priori cognition; and thus we determine not merely the empirical and ever-shifting bounds of our knowledge, but its necessary and eternal limits. We demonstrate from indubitable principles, not merely our ignorance in respect to this or that subject, but in regard to all possible questions of a certain class. Thus scepticism is a resting place for reason, in which it may reflect on its dogmatical wanderings and gain some knowledge of the region in which it happens to be, that it may pursue its way with greater certainty; but it cannot be its permanent dwelling-place. It must take up its abode only in the region of complete certitude, whether this relates to the cognition of objects themselves, or to the limits which bound all our cognition.
Reason is not to be considered as an indefinitely extended plane, of the bounds of which we have only a general knowledge; it ought rather to be compared to a sphere, the radius of which may be found from the curvature of its surface—that is, the nature of a priori synthetical propositions—and, consequently, its circumference and extent. Beyond the sphere of experience there are no objects which it can cognize; nay, even questions regarding such supposititious objects relate only to the subjective principles of a complete determination of the relations which exist between the understanding-conceptions which lie within this sphere.
We are actually in possession of a priori synthetical cognitions, as is proved by the existence of the principles of the understanding, which anticipate experience. If any one cannot comprehend the possibility of these principles, he may have some reason to doubt whether they are really a priori; but he cannot on this account declare them to be impossible, and affirm the nullity of the steps which reason may have taken under their guidance. He can only say: If we perceived their origin and their authenticity, we should be able to determine the extent and limits of reason; but, till we can do this, all propositions regarding the latter are mere random assertions. In this view, the doubt respecting all dogmatical philosophy, which proceeds without the guidance of criticism, is well grounded; but we cannot therefore deny to reason the ability to ​construct a sound philosophy, when the way has been prepared by a thorough critical investigation. All the conceptions produced, and all the questions raised, by pure reason, do not lie in the sphere of experience, but in that of reason itself, and hence they must be solved, and shown to be either valid or inadmissible, by that faculty. We have no right to decline the solution of such problems, on the ground that the solution can be discovered only from the nature of things, and under pretence of the limitation of human faculties, for reason is the sole creator of all these ideas, and is therefore bound either to establish their validity or to expose their illusory nature.
The polemic of scepticism is properly directed against the dogmatist, who erects a system of philosophy without having examined the fundamental objective principles on which it is based, for the purpose of evidencing the futility of his designs, and thus bringing him to a knowledge of his own powers. But, in itself, scepticism does not give us any certain information in regard to the bounds of our knowledge. All unsuccessful dogmatical attempts of reason are facia, which it is always useful to submit to the censure of the sceptic. But this cannot help us to any decision regarding the expectations which reason cherishes of better success in future endeavours; the investigations of scepticism cannot, therefore, settle the dispute regarding the rights and powers of human reason.
Hume is perhaps the ablest and most ingenious of all sceptical philosophers, and his writings have, undoubtedly, exerted the most powerful influence in awakening reason to a thorough investigation into its own powers. It will, therefore, well repay our labours to consider for a little the course of reasoning which he followed and the errors into which he strayed, although setting out on the path of truth and certitude.
Hume was probably aware, although he never clearly developed the notion, that we proceed in judgements of a certain class beyond our conception if the object. I have termed this kind of judgement synthetical. As regard the manner in which I pass beyond my conception by the aid of experience, no doubts can be entertained. Experience is itself a synthesis of perceptions; and it employs perceptions to increment the conception, which I obtain by means of another ​perception. But we feel persuaded that we are able to proceed beyond a conception, and to extend our cognition a priori. We attempt this in two ways—either, through the pure understanding, in relation to that which may become an object of experience, or, through pure reason, in relation to such properties of things, or of the existence of things, as can never be presented in any experience. This sceptical philosopher did not distinguish these two kinds of judgements, as he ought to have done, but regarded this augmentation of conceptions, and, if we may so express ourselves, the spontaneous generation of understanding and reason, independently of the impregnation of experience, as altogether impossible. The so-called a priori principles of these faculties he consequently held to be invalid and imaginary, and regarded them as nothing but subjective habits of thought originating in experience, and therefore purely empirical and contingent rules, to which we attribute a spurious necessity and universality. In support of this strange assertion, he referred us to the generally acknowledged principle of the relation between cause and effect. No faculty of the mind can conduct us from the conception of a thing to the existence of something else; and hence he believed he could infer that, without experience, we possess no source from which we can augment a conception, and no ground sufficient to justify us in framing a judgement that is to extend our cognition a priori. That the light of the sun, which shines upon a piece of wax, at the same time melts it, while it hardens clay, no power of the understanding could infer from the conceptions which we previously possessed of these substances; much less is there any a priori law that could conduct us to such a conclusion, which experience alone can certify. On the other hand, we have seen in our discussion of transcendental logic, that, although we can never proceed immediately beyond the content of the conception which is given us, we can always cognize completely a priori—in relation, however, to a third term, namely, possible experience—the law of its connection with other things. For example, if I observe that a piece of wax melts, I can cognize a priori that there must have been something (the sun's heat) preceding, which this law; although, without the aid of experience, I could not cognize a priori and in a determinate manner either the cause from the effect, or the effect ​from the cause. Hume was, therefore, wrong in inferring, from the contingency of the determination according to law, the contingency of the law itself; and the passing beyond the conception of a thing to possible experience (which is an a priori proceeding, constituting the objective reality of the conception), he confounded with our synthesis of objects in actual experience, which is always, of course, empirical. Thus, too, he regarded the principle of affinity, which has its seat in the understanding and indicates a necessary connection, as a mere rule of association, lying in the imitative faculty of imagination, which can present only contingent, and not objective connections.
The sceptical errors of this remarkably acute thinker arose principally from a defect, which was common to him with the dogmatists, namely, that he had never made a systematic review of all the different kinds of a priori synthesis performed by the understanding. Had he done so, he would have found, to take one example among many, that the principle of permanence was of this character, and that it, as well as the principle of causality, anticipates experience. In this way he might have been able to describe the determinate limits of the a priori operations of understanding and reason. But he merely declared the understanding to be limited, instead of showing what its limits were; he created a general mistrust in the power of our faculties, without giving us any determinate knowledge of the bounds of our necessary and unavoidable ignorance; he examined and condemned some of the principles of the understanding, without investigating all its powers with the completeness necessary to criticism. He denies, with truth, certain powers to the understanding, but he goes further, and declares it to be utterly inadequate to the a priori extension of knowledge, although he has not fully examined all the powers which reside in the faculty; and thus the fate which always overtakes scepticism meets him too. That is to say, his own declarations are doubted, for his objections were based upon facta, which are contingent, and not upon principles, which can alone demonstrate the necessary invalidity of all dogmatical assertions.
As Hume makes no distinction between the well-grounded claims of the understanding and the dialectical pretensions of reason, against which, however, his attacks are mainly dir ​ected, reason does not feel itself shut out from all attempts at the extension of a priori cognition, and hence it refuses, in spite of a few checks in this or that quarter, to relinquish such efforts. For one naturally arms oneself to resist an attack, and becomes more obstinate in the resolve to establish the claims he has advanced. But a complete review of the powers of reason, and the conviction thence arising that we are in possession of a limited field of action, while we must admit the vanity of higher claims, puts an end to all doubt and dispute, and induces reason to rest satisfied with the undisturbed possession of its limited domain.
To the uncritical dogmatist, who has not surveyed the sphere of his understanding, nor determined, in accordance with principles, the limits of possible cognition, who, consequently, is ignorant of his own powers, and believes he will discover them by the attempts he makes in the field of cognition, these attacks of scepticism are not only dangerous, but destructive. For if there is one proposition in his chain of reasoning which be he cannot prove, or the fallacy in which be cannot evolve in accordance with a principle, suspicion falls on all his statements, however plausible they may appear.
And thus scepticism, the bane of dogmatical philosophy, conducts us to a sound investigation into the understanding and the reason. When we are thus far advanced, we need fear no further attacks; for the limits of our domain are clearly marked out, and we can make no claims nor become involved in any disputes regarding the region that lies beyond these limits. Thus the sceptical procedure in philosophy does not present any solution of the problems of reason, but it forms an excellent exercise for its powers, awakening its circumspection, and indicating the means whereby it may most fully establish its claims to its legitimate possessions.

#### SECTION III. The Discipline of Pure Reason in Hypothesis.SECTION III. The Discipline of Pure Reason in Hypothesis.

This critique of reason has now taught us that all its efforts to extend the bounds of knowledge, by means of pure speculation, are utterly fruitless. So much the wider field, it may ​appear, lies open to hypothesis; as, where we cannot know with certainty, we are at liberty to make guesses and to form suppositions.
Imagination may be allowed, under the strict surveillance of reason, to invent suppositions; but, these must be based on something that is perfectly certain—and that is the possibility of the object. If we are well assured upon this point, it is allowable to have recourse to supposition in regard to the reality of the object; but this supposition must, unless it is utterly groundless, be connected, as its ground of explanation, with that which is really given and absolutely certain. Such a supposition is termed a hypothesis.
It is beyond our power to form the least conception a priori of the possibility of dynamical connection in phenomena; and the category of the pure understanding will not enable us to ex. cogitate any such connection, but merely helps us to understand it, when we meet with it in experience. For this reason we cannot, in accordance with the categories, imagine or invent any object or any property of an object not given, or that may not be given in experience, and employ it in a hypothesis; otherwise, we should be basing our chain of reasoning upon mere chimerical fancies, and not upon conceptions of things. Thus, we have no right to assume the existence of new powers, not existing in nature—for example, an understanding with a non-sensuous intuition, a force of attraction without contact, or some new kind of substances occupying space, and yet without the property of impenetrability—and, consequently, we cannot assume that there is any other kind of community among substances than that observable in experience, any kind of presence than that in space, or any kind of duration than that in time. In one word, the conditions of possible experience are for reason the only conditions of the possibility of things; reason cannot venture to form, independently of these conditions, any conceptions of things, because such conceptions, although not self-contradictory, are without object and without application.
The conceptions of reason are, as we have already shown, mere ideas, and do not relate to any object in any kind of experience. At the same time, they do not indicate imaginary or possible objects. They are purely problematical in their nature and, as aids to the heuristic exercise of the fa ​culties, form the basis of the regulative principles for the systematic employment of the understanding in the field of experience. If we leave this ground of experience, they become mere fictions of thought, the possibility of which is quite indemonstrable; and they cannot, consequently, be employed as hypotheses in the explanation of real phenomena. It is quite admissible to cogitate the soul as simple, for the purpose of enabling ourselves to employ the idea of a perfect and necessary unity of all the faculties of the mind as the principle of all our inquiries into its internal phenomena, although we cannot cognize this unity in concreto. But to assume that the soul is a simple substance (a transcendental conception) would be enouncing a proposition which is not only indemonstrable—as many physical hypotheses are—but a proposition which is purely arbitrary, and in the highest degree rash. The simple is never presented in experience; and, if by substance is here meant the permanent object of sensuous intuition, the possibility of a simple phenomenon is perfectly inconceivable. Reason affords no good grounds for admitting the existence of intelligible beings, or of intelligible properties of sensuous things, although—as we have no conception either of their possibility or of their impossibility—it will always be out of our power to affirm dogmatically that they do not exist. In the explanation of given phenomena, no other things and no other grounds of explanation can be employed than those which stand in connection with the given phenomena according to the known laws of experience. A transcendental hypothesis, in which a mere idea of reason is employed to explain the phenomena of nature, would not give us any better insight into a phenomenon, as we should be trying to explain what we do not sufficiently understand from known empirical principles, by what we do not understand at all. The principles of such a hypothesis might conduce to the satisfaction of reason, but it would not assist the understanding in its application to objects. Order and conformity to aims in the sphere of nature must be themselves explained upon natural grounds and according to natural laws; and the wildest hypotheses, if they are only physical, are here more admissible than a hyperphysical hypothesis, such as that of a divine author. For such a hypothesis would introduce the principle of ignava ratio, which requires us to give up the ​search for causes that might be discovered in the course of experience and to rest satisfied with a mere idea. As regards the absolute totality of the grounds of explanation in the series of these causes, this can be no hindrance to the understanding in the case of phenomena; because, as they are to us nothing more than phenomena, we have no right to look for anything like completeness in the synthesis of the series of their conditions.
Transcendental hypotheses are therefore inadmissible; and we cannot use the liberty of employing, in the absence of physical, hyperphysical grounds of explanation. And this for two reasons; first, because such hypothesis do not advance reason, but rather stop it in its progress; secondly, because this licence would render fruitless all its exertions in its own proper sphere, which is that of experience. For, when the explanation of natural phenomena happens to be difficult, we have constantly at hand a transcendental ground of explanation, which lifts us above the necessity of investigating nature; and our inquiries are brought to a close, not because we have obtained all the requisite knowledge, but because we abut upon a principle which is incomprehensible and which, indeed, is so far back in the track of thought as to contain the conception of the absolutely primal being.
The next requisite for the admissibility of a hypothesis is its sufficiency. That is, it must determine a priori the consequences which are given in experience and which are supposed to follow from the hypothesis itself. If we require to employ auxiliary hypotheses, the suspicion naturally arises that they are mere fictions; because the necessity for each of them requires the same justification as in the case of the original hypothesis, and thus their testimony is invalid. If we suppose the existence of an infinitely perfect cause, we possess sufficient grounds for the explanation of the conformity to aims, the order and the greatness which we observe in the universe; but we find ourselves obliged, when we observe the evil in the world and the exceptions to these laws, to employ new hypothesis in support of the original one. We employ the idea of the simple nature of the human soul as the foundation of all the theories we may form of its phenomena; but when we meet with difficulties in our way, when we observe in the soul phenomena similar to the changes which take place in matter, ​we require to call in new auxiliary hypotheses. These may, indeed, not be false, but we do not know them to be true, because the only witness to their certitude is the hypothesis which they themselves have been called in to explain.
We are not discussing the above-mentioned assertions regarding the immaterial unity of the soul and the existence of a Supreme Being as dogmata, which certain philosophers profess to demonstrate a priori, but purely as hypotheses. In the former case, the dogmatist must take care that his arguments possess the apodeictic certainty of a demonstration. For the assertion that the reality of such ideas is probable is as absurd as a proof of the probability of a proposition in geometry. Pure abstract reason, apart from all experience, can either cognize nothing at all; and hence the judgements it enounces are never mere opinions, they are either apodeictic certainties, or declarations that nothing can be known on the subject. Opinions and probable judgements on the nature of things can only be employed to explain given phenomena, or they may relate to the effect, in accordance with empirical laws, of an actually existing cause. In other words, we must restrict the sphere of opinion to the world of experience and nature. Beyond this region opinion is mere invention; unless we are groping about for the truth on a path not yet fully known, and have some hopes of stumbling upon it by chance.
But, although hypotheses are inadmissible in answers to the questions of pure speculative reason, they may be employed in the defence of these answers. That is to say, hypotheses are admissible in polemic, but not in the sphere of dogmatism. By the defence of statements of this character, I do not mean an attempt at discovering new grounds for their support, but merely the refutation of the arguments of opponents. All a priori synthetical propositions possess the peculiarity that, although the philosopher who maintains the reality of the ideas contained in the proposition is not in possession of sufficient knowledge to establish the certainty of his statements, his opponent is as little able to prove the truth of the opposite. This equality of fortune does not allow the one party to be superior to the other in the sphere of speculative cognition; and it is this sphere, accordingly, that is the proper arena of these endless speculative conflicts. But we shall ​afterwards show that, in relation to its practical exercise, Reason has the right of admitting what, in the field of pure speculation, she would not be justified in supposing, except upon perfectly sufficient grounds; because all such suppositions destroy the necessary completeness of speculation—a condition which the practical reason, however, does not consider to be requisite. In this sphere, therefore, Reason is mistress of a possession, her title to which she does not require to prove—which, in fact, she could not do. The burden of proof accordingly rests upon the opponent. But as he has just as little knowledge regarding the subject discussed, and is as little able to prove the non-existence of the object of an idea, as the philosopher on the other side is to demonstrate its reality, it is evident that there is an advantage on the side of the philosopher who maintains his proposition as a practically necessary supposition (melior est conditio possidentis). For he is at liberty to employ, in self-defence, the same weapons as his opponent makes use of in attacking him; that is, he has a right to use hypotheses not for the purpose of supporting the arguments in favour of his own propositions, but to show that his opponent knows no more than himself regarding the subject under 'discussion and cannot boast of any speculative advantage.
Hypotheses are, therefore, admissible in the sphere of pure reason only as weapons for self-defence, and not as supports to dogmatical assertions. But the opposing party we must always seek for in ourselves. For speculative reason is, in the sphere of transcendentalism, dialectical in its own nature. The difficulties and objections we have to fear lie in ourselves. They are like old but never superannuated claims; and we must seek them out, and settle them once and for ever, if we are to expect a permanent peace. External tranquility is hollow and unreal. The root of these contradictions, which lies in the nature of human reason, must be destroyed; and this can only be done by giving it, in the first instance, freedom to grow, nay, by nourishing it, that it may send out shoots, and thus betray its own existence. It is our duty, therefore, to try to discover new objections, to put weapons in the bands of our opponent, and to grant him the most favourable position in the arena that he can wish. We have nothing to fear from these concessions; on the contrary, we may rather h ​ope that we shall thus make ourselves master of a possession which no one will ever venture to dispute.
The thinker requires, to be fully equipped, the hypotheses of pure reason, which, although but leaden weapons (for they have not been steeled in the armoury of experience), are as useful as any that can be employed by his opponents. If, accordingly, we have assumed, from a non-speculative point of view, the immaterial nature of the soul, and are met by the objection that experience seems to prove that the growth and decay of our mental faculties are mere modifications of the sensuous organism—we can weaken the force of this objection by the assumption that the body is nothing but the fundamental phenomenon, to which, as a necessary condition, all sensibility, and consequently all thought, relates in the present state of our existence; and that the separation of soul and body forms the conclusion of the sensuous exercise of our power of cognition and the beginning of the intellectual. The body would, in this view of the question, be regarded, not as the cause of thought, but merely as its restrictive condition, as promotive of the sensuous and animal, but as a hindrance to the pure and spiritual life; and the dependence of the animal life on the constitution of the body, would not prove that the whole life of man was also dependent on the state of the organism. We might go still farther, and discover new objections, or carry out to their extreme consequences those which have already been adduced.
Generation, in the human race as well as among the irrational animals, depends on so many accidents—of occasion, of proper sustenance, of the laws enacted by the government of a country of vice even, that it is difficult to believe in the eternal existence of a being whose life has begun under circumstances so mean and trivial, and so entirely dependent upon our own control. As regards the continuance of the existence of the whole race, we need have no difficulties, for accident in single cases is subject to general laws; but, in the case of each individual, it would seem as if we could hardly expect so wonderful an effect from causes so insignificant. But, in answer to these objections, we may adduce the transcendental hypothesis that all life is properly intelligible, and not subject to changes of time, and that it neither began in birth, nor will end in death. We may assume that this life is nothing more ​than a sensuous representation of pure spiritual life; that the whole world of sense is but an image, hovering before the faculty of cognition which we exercise in this sphere, and with no more objective reality than a dream; and that if we could intuite ourselves and other things as they really are, we should see ourselves in a world of spiritual natures, our connection with which did not begin at our birth and will not cease with the destruction of the body. And so on.
We cannot be said to know what has been above asserted, nor do we seriously maintain the truth of these assertions; and the notions therein indicated are not even ideas of reason, they are purely fictitious conceptions. But this hypothetical procedure is in perfect conformity with the laws of reason. Our opponent mistakes the absence of empirical conditions for a proof of the complete impossibility of all that we have asserted; and we have to show him that be has not exhausted the whole sphere of possibility and that he can as little compass that sphere by the laws of experience and nature, as we can lay a secure foundation for the operations of reason beyond the region of experience. Such hypothetical defences against the pretensions of an opponent must not be regarded as declarations of opinion. The philosopher abandons them, so soon as the opposite party renounces its dogmatical conceit. To maintain a simply negative position in relation to propositions which rest on an insecure foundation, well befits the moderation of a true philosopher; but to uphold the objections urged against an opponent as proofs of the opposite statement is a proceeding just as unwarrantable and arrogant as it is to attack the position of a philosopher who advances affirmative propositions regarding such a subject.
It is evident, therefore, that hypotheses, in the speculative sphere, are valid, not as independent propositions, but only relatively to opposite transcendent assumptions. For, to make the principles of possible experience conditions of the possibility of things in general is just as transcendent a procedure as to maintain the objective reality of ideas which can be applied to no objects except such as lie without the limits of possible experience. The judgements enounced by pure reason must be necessary, or they must not be enounced at all. Reason cannot trouble herself with opinions. But the hypotheses we have been discussing are merely problematical ​judgements, which can neither be confuted nor proved; while, therefore, they are not personal opinions, they are indispensable as answers to objections which are liable to be raised. But we must take care to confine them to this function, and guard against any assumption on their part of absolute validity, a proceeding which would involve reason in inextricable difficulties and contradictions.

#### SECTION IV. The Discipline of Pure Reason in Relation to Proofs.SECTION IV. The Discipline of Pure Reason in Relation to Proofs.

It is a peculiarity, which distinguishes the proofs of transcendental synthetical propositions from those of all other a priori synthetical cognitions, that reason, in the case of the former, does not apply its conceptions directly to an object, but is first obliged to prove, a priori, the objective validity of these conceptions and the possibility of their syntheses. This is not merely a prudential rule, it is essential to the very possibility of the proof of a transcendental proposition. If I am required to pass, a priori, beyond the conception of an object, I find that it is utterly impossible without the guidance of something which is not contained in the conception. In mathematics, it is a priori intuition that guides my synthesis; and, in this case, all our conclusions may be drawn immediately from pure intuition. In transcendental cognition, so long as we are dealing only with conceptions of the understanding, we are guided by possible experience. That is to say, a proof in the sphere of transcendental cognition does not show that the given conception (that of an event, for example) leads directly to another conception (that of a cause)- for this would be a saltus which nothing can justify; but it shows that experience itself, and consequently the object of experience, is impossible without the connection indicated by these conceptions. It follows that such a proof must demonstrate the possibility of arriving, synthetically and a priori, at a certain knowledge of things, which was not contained in our conceptions of these things. Unless we pay particular attention to this requirement, our proofs, instead of pursuing ​the straight path indicated by reason, follow the tortuous road of mere subjective association. The illusory conviction, which rests upon subjective causes of association, and which is considered as resulting from the perception of a real and objective natural affinity, is always open to doubt and suspicion. For this reason, all the attempts which have been made to prove the principle of sufficient reason, have, according to the universal admission of philosophers, been quite unsuccessful; and, before the appearance of transcendental criticism, it was considered better, as this principle could not be abandoned, to appeal boldly to the common sense of mankind (a proceeding which always proves that the problem, which reason ought to solve, is one in which philosophers find great difficulties), rather than attempt to discover new dogmatical proofs.
But, if the proposition to be proved is a proposition of pure reason, and if I aim at passing beyond my empirical conceptions by the aid of mere ideas, it is necessary that the proof should first show that such a step in synthesis is possible (which it is not), before it proceeds to prove the truth of the proposition itself. The so-called proof of the simple nature of the soul from the unity of apperception, is a very plausible one. But it contains no answer to the objection, that, as the notion of absolute simplicity is not a conception which is directly applicable to a perception, but is an idea which must be inferred—if at all—from observation, it is by no means evident how the mere fact of consciousness, which is contained in all thought, although in so far a simple representation, can conduct me to the consciousness and cognition of a thing which is purely a thinking substance. When I represent to my mind the power of my body as in motion, my body in this thought is so far absolute unity, and my representation of it is a simple one; and hence I can indicate this representation by the motion of a point, because I have made abstraction of the size or volume of the body. But I cannot hence infer that, given merely the moving power of a body, the body may be cogitated as simple substance, merely because the representation in my mind takes no account of its content in space, and is consequently simple. The simple, in abstraction, is very different from the objectively simple; and hence the Ego, which is simple in the first sense, may, in the second sense, as ​indicating the soul itself, be a very complex conception, with a very various content. Thus it is evident that in all such arguments there lurks a paralogism. We guess (for without some such surmise our suspicion would not be excited in reference to a proof of this character) at the presence of the paralogism, by keeping ever before us a criterion of the possibility of those synthetical propositions which aim at proving more than experience can teach us. This criterion is obtained from the observation that such proofs do not lead us directly from the subject of the proposition to be proved to the required predicate, but find it necessary to presuppose the possibility of extending our cognition a priori by means of ideas. We must, accordingly, always use the greatest caution; we require, before attempting any proof, to consider how it is possible to extend the sphere of cognition by the operations of pure reason, and from what source we are to derive knowledge, which is not obtained from the analysis of conceptions, nor relates, by anticipation, to possible experience. We shall thus spare ourselves much severe and fruitless labour, by not expecting from reason what is beyond its power, or rather by subjecting it to discipline, and teaching it to moderate its vehement desires for the extension of the sphere of cognition.
The first rule for our guidance is, therefore, not to attempt a transcendental proof, before we have considered from what source we are to derive the principles upon which the proof is to be based, and what right we have to expect that our conclusions from these principles will be veracious. If they are principles of the understanding, it is vain to expect that we should attain by their means to ideas of pure reason; for these principles are valid only in regard to objects of possible experience. If they are principles of pure reason, our labour is alike in vain. For the principles of reason, if employed as objective, are without exception dialectical and possess no validity or truth, except as regulative principles of the systematic employment of reason in experience. But when such delusive proof are presented to us, it is our duty to meet them with the non liquet of a matured judgement; and, although we are unable to expose the particular sophism upon which the proof is based, we have a right to demand a deduction of the principles employed in it; and, if these principles have their origin in pure reason alone, such a deduction is ​absolutely impossible. And thus it is unnecessary that we should trouble ourselves with the exposure and confutation of every sophistical illusion; we may, at once, bring all dialectic, which is inexhaustible in the production of fallacies, before the bar of critical reason, which tests the principles upon which all dialectical procedure is based. The second peculiarity of transcendental proof is that a transcendental proposition cannot rest upon more than a single proof. If I am drawing conclusions, not from conceptions, but from intuition corresponding to a conception, be it pure intuition, as in mathematics, or empirical, as in natural science, the intuition which forms the basis of my inferences presents me with materials for many synthetical propositions, which I can connect in various modes, while, as it is allowable to proceed from different points in the intention, I can arrive by different paths at the same proposition.
But every transcendental proposition sets out from a conception, and posits the synthetical condition of the possibility of an object according to this conception. There must, therefore, be but one ground of proof, because it is the conception alone which determines the object; and thus the proof cannot contain anything more than the determination of the object according to the conception. In our Transcendental Analytic, for example, we inferred the principle: Every event has a cause, from the only condition of the objective possibility of our conception of an event. This is that an event cannot be determined in time, and consequently cannot form a part of experience, unless it stands under this dynamical law. This is the only possible ground of proof; for our conception of an event possesses objective validity, that is, is a true conception, only because the law of causality determines an object to which it can refer. Other arguments in support of this principle have been attempted—such as that from the contingent nature of a phenomenon; but when this argument is considered, we can discover no criterion of contingency, except the fact of an event—of something happening, that is to say, the existence which is preceded by the non-existence of an object, and thus we fall back on the very thing to be proved. If the proposition: "Every thinking being is simple," is to be proved, we keep to the conception of the ego, which is simple, and to which all thought has a relation. The same is the case with ​the transcendental proof of the existence of a Deity, which is based solely upon the harmony and reciprocal fitness of the conceptions of an ens realissimum and a necessary being, and cannot be attempted in any other manner.
This caution serves to simplify very much the criticism of all propositions of reason. When reason employs conceptions alone, only one proof of its thesis is possible, if any. When, therefore, the dogmatist advances with ten arguments in favour of a proposition, we may be sure that not one of them is conclusive. For if he possessed one which proved the proposition he brings forward to demonstration—as must always be the case with the propositions of pure reason—what need is there for any more? His intention can only be similar to that of the advocate who had different arguments for different judges; this availing himself of the weakness of those who examine his arguments, who, without going into any profound investigation, adopt the view of the case which seems most probable at first sight and decide according to it.
The third rule for the guidance of pure reason in the conduct of a proof is that all transcendental proofs must never be apagogic or indirect, but always ostensive or direct. The direct or ostensive proof not only establishes the truth of the proposition to be proved, but exposes the grounds of its truth; the apagogic, on the other hand, may assure us of the truth of the proposition, but it cannot enable us to comprehend the grounds of its possibility. The latter is, accordingly, rather an auxiliary to an argument, than a strictly philosophical and rational mode of procedure. In one respect, however, they have an advantage over direct proofs, from the fact that the mode of arguing by contradiction, which they employ, renders our understanding of the question more clear, and approximates the proof to the certainty of an intuitional demonstration.
The true reason why indirect proofs are employed in different sciences is this. When the grounds upon which we seek to base a cognition are too various or too profound, we try whether or not we may not discover the truth of our cognition from its consequences. The modus ponens of reasoning from the truth of its inferences to the truth of a proposition would be admissible if all the inferences that can be drawn from it are known to be true; for in this case there can be ​only one possible ground for these inferences, and that is the true one. But this is a quite impracticable procedure, as it surpasses all our powers to discover all the possible inferences that can be drawn from a proposition. But this mode of reasoning is employed, under favour, when we wish to prove the truth of an hypothesis; in which case we admit the truth of the conclusion- which is supported by analogy—that, if all the inferences we have drawn and examined agree with the proposition assumed, all other possible inferences will also agree with it. But, in this way, an hypothesis can never be established as a demonstrated truth. The modus tollens of reasoning from known inferences to the unknown proposition, is not only a rigorous, but a very easy mode of proof. For, if it can be shown that but one inference from a proposition is false, then the proposition must itself be false. Instead, then, of examining, in an ostensive argument, the whole series of the grounds on which the truth of a proposition rests, we need only take the opposite of this proposition, and if one inference from it be false, then must the opposite be itself false; and, consequently, the proposition which we wished to prove must be true.
The apagogic method of proof is admissible only in those sciences where it is impossible to mistake a subjective representation for an objective cognition. Where this is possible, it is plain that the opposite of a given proposition may contradict merely the subjective conditions of thought, and not the objective cognition; or it may happen that both propositions contradict each other only under a subjective condition, which is incorrectly considered to be objective, and, as the condition is itself false, both propositions may be false, and it will, consequently, be impossible to conclude the truth of the one from the falseness of the other.
In mathematics such subreptions are impossible; and it is in this science, accordingly, that the indirect mode of proof has its true place. In the science of nature, where all assertion is based upon empirical intuition, such subreptions may be guarded against by the repeated comparison of observations; but this mode of proof is of little value in this sphere of knowledge. But the transcendental efforts of pure reason are all made in the sphere of the subjective, which is the real medium of all dialectical illusion; and thus reason endeavours, ​in its premisses, to impose upon us subjective representations for objective cognitions. In the transcendental sphere of pure reason, then, and in the case of synthetical propositions, it is inadmissible to support a statement by disproving the counter-statement. For only two cases are possible; either, the counter-statement is nothing but the enouncement of the inconsistency of the opposite opinion with the subjective conditions of reason, which does not affect the real case (for example, we cannot comprehend the unconditioned necessity of the existence of a being, and hence every speculative proof of the existence of such a being must be opposed on subjective grounds, while the possibility of this being in itself cannot with justice be denied); or, both propositions, being dialectical in their nature, are based upon an impossible conception. In this latter case the rule applies: non entis nulla sunt predicata; that is to say, what we affirm and what we deny, respecting such an object, are equally untrue, and the apagogic mode of arriving at the truth is in this case impossible. If, for example, we presuppose that the world of sense is given in itself in its totality, it is false, either that it is infinite, or that it is finite and limited in space. Both are false, because the hypothesis is false. For the notion of phenomena (as mere representations) which are given in themselves (as objects) is self-contradictory; and the infinitude of this imaginary whole would, indeed, be unconditioned, but would be inconsistent (as everything in the phenomenal world is conditioned) with the unconditioned determination and finitude of quantities which is presupposed in our conception.
The apagogic mode of proof is the true source of those illusions which have always had so strong an attraction for the admirers of dogmatical philosophy. It may be compared to a champion who maintains the honour and claims of the party he has adopted by offering battle to all who doubt the validity of these claims and the purity of that honour; while nothing can be proved in this way, except the respective strength of the combatants, and the advantage, in this respect, is always on the side of the attacking party. Spectators, observing that each party is alternately conqueror and conquered, are led to regard the subject of dispute as beyond the power of man to ​decide upon. But such an opinion cannot be justified; and it is sufficient to apply to these reasoners the remark:—
Non defensoribus istis Tempus eget.
Each must try to establish his assertions by a transcendental deduction of the grounds of proof employed in his argument, and thus enable us to see in what way the claims of reason may be supported. If an opponent bases his assertions upon subjective grounds, he may be refuted with ease; not, however to the advantage of the dogmatist, who likewise depends upon subjective sources of cognition and is in like manner driven into a corner by his opponent. But, if parties employ the direct method of procedure, they will soon discover the difficulty, nay, the impossibility of proving their assertions, and will be forced to appeal to prescription and precedence; or they will, by the help of criticism, discover with ease the dogmatical illusions by which they had been mocked, and compel reason to renounce its exaggerated pretensions to speculative insight and to confine itself within the limits of its proper sphere—that of practical principles.
* ↑ 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.
* ↑ 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.
* ↑ 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.
* ↑ 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.