The Transcendental Problem: Part 1

§ 6.

§ 6.

HERE is a great and established branch of knowledge, encompassing even now a wonderfully large domain and promising an unlimited extension in the future. Yet it carries with it thoroughly apodeictical certainty, i.e., absolute necessity, which therefore rests upon no empirical grounds. Consequently it is a pure product of reason, and moreover is thoroughly synthetical. [Here the question arises:]

Here is a great, established field of knowledge. It already covers a remarkably large area and promises unlimited growth in the future. Yet its certainty is wholly apodeictic, meaning absolutely necessary, and therefore rests on no empirical evidence. So this field of knowledge is a pure product of reason and is, moreover, entirely synthetic. [Here the question arises:]

"How then is it possible for human reason to produce a cognition of this nature entirely a priori?"

"How, then, can human reason produce this kind of knowledge entirely a priori?"

Does not this faculty [which produces mathematics], as it neither is nor can be based upon experience, presuppose some ground of cognition a priori, which lies deeply hidden, but which might reveal itself by these its effects, if their first beginnings were but diligently ferreted out?

This faculty [which produces mathematics] is not, and cannot be, based on experience. Does it not therefore presuppose some deeply hidden basis for knowledge a priori? This basis might reveal itself through its effects, if their earliest beginnings were carefully investigated.

§ 7. But we find that all mathematical cognition has this peculiarity: it must first exhibit its concept in a visual form (Anschauung) and indeed a priori, therefore in a visual form which is not empirical, but pure. Without this mathematics cannot take a single step; hence its judgments are always visual, viz., "intuitive"; whereas philosophy must be satisfied with discursive judgments from mere concepts, and though it may illustrate its doctrines through a visual figure, can never derive them from it. This observation on the nature of mathematics gives us a clue to the first and highest condition of its possibility, which is, that some non-sensuous visualisation (called pure intuition, or reine Anschauung) must form its basis, in which all its concepts can be exhibited or constructed, in concreto and yet a priori. If we can find out this pure intuition and its possibility, we may thence easily explain how synthetical propositions a priori are possible in pure mathematics, and consequently how this science itself is possible. Empirical intuition [viz., sense-perception] enables us without difficulty to enlarge the concept which we frame of an object of intuition [or sense-perception], by new predicates, which intuition [i.e., sense-perception] itself presents synthetically in experience. Pure intuition [viz., the visualisation of forms in our imagination, from which every thing sensual, i.e., every thought of material qualities, is excluded] does so likewise, only with this difference, that in the latter case the synthetical judgment is a priori certain and apodeictical, in the former, only a posteriori and empirically certain; because this latter contains only that which occurs in contingent empirical intuition, but the former, that which must necessarily be discovered in pure intuition. Here intuition, being an intuition a priori, is before all experience, viz., before any perception of particular objects, inseparably conjoined with its concept.

§ 7. We find that all mathematical knowledge has a distinctive feature. It must first present its concepts in intuition (Anschauung), a kind of direct mental representation. This intuition must be a priori, and therefore pure rather than empirical. Without it, mathematics cannot take a single step. Its judgments are therefore always based on intuition, or "intuitive". Philosophy, by contrast, must be content with discursive judgments drawn from concepts alone. Though philosophy may illustrate its doctrines with a figure, it can never derive them from one. This observation about the nature of mathematics gives us a clue to its first and highest condition of possibility. Mathematics must be based on some non-sensuous representation, called pure intuition (reine Anschauung). In pure intuition, all mathematical concepts can be presented or constructed concretely, yet a priori. If we can discover this pure intuition and how it is possible, we can easily explain how synthetic a priori propositions are possible in pure mathematics. We can consequently explain how pure mathematics itself is possible. Empirical intuition, or sense perception, allows us to expand our concept of an object of perception without difficulty. We do this by adding new predicates that perception itself presents together in experience. Pure intuition does the same. Pure intuition is the representation of forms in our imagination, excluding everything sensuous, that is, every thought of material qualities. The difference is that a synthetic judgment based on pure intuition is certain a priori and apodictic, or necessarily true. A judgment based on empirical intuition is certain only a posteriori and through experience. This is because empirical intuition contains only what occurs in contingent experience. Pure intuition, by contrast, contains what must necessarily be found in it. As an a priori intuition, it is inseparably connected with its concept before all experience, that is, before any perception of particular objects.

§ 8. But with this step our perplexity seems rather to increase than to lessen. For the question now is, "How is it possible to intuite [in a visual form] anything a priori?" An intuition [viz., a visual sense-perception] is such a representation as immediately depends upon the presence of the object. Hence it seems impossible to intuite from the outset a priori, because intuition would in that event take place without either a former or a present object to refer to, and by consequence could not be intuition. Concepts indeed are such, that we can easily form some of them a priori, viz., such as contain nothing but the thought of an object in general; and we need not find ourselves in an immediate relation to the object. Take, for instance, the concepts of Quantity, of Cause, etc. But even these require, in order to make them under stood, a certain concrete use—that is, an application to some sense-experience (Anschauung), by which an object of them is given us. But how can the intuition of the object [its visualisation] precede the object itself?

§ 8. But this step seems to increase our perplexity rather than lessen it. The question now is, "How is it possible to have an intuition [a visual perception] of anything a priori?" An intuition is a representation that depends directly on the presence of its object. So intuition seems impossible a priori, from the outset. It would occur without a past or present object to refer to, and therefore could not be intuition. We can easily form some concepts a priori. These contain nothing but the thought of an object in general, and we need not be directly related to the object. Consider, for example, the concepts of Quantity and Cause. But even these concepts require some concrete use to be understood. They must be applied to some sense experience (Anschauung), through which an object of those concepts is given to us. But how can intuition of an object [its visualization] come before the object itself?

§ 9. If our intuition [i.e., our sense-experience] were perforce of such a nature as to represent things as they are in themselves, there would not be any intuition a priori, but intuition would be always empirical. For I can only know what is contained in the object in itself when it is present and given to me. It is indeed even then incomprehensible how the visualising (Anschauung) of a present thing should make me know this thing as it is in itself, as its properties cannot migrate into my faculty of representation. But even granting this possibility, a visualising of that sort would not take place a priori, that is, before the object were presented to me; for without this latter fact no reason of a relation between my representation and the object can be imagined, unless it depend upon a direct inspiration.

§ 9. If our intuition [that is, our sense-experience] necessarily represented things as they are in themselves, there could be no a priori intuition. All intuition would instead be empirical. For I can know what an object contains in itself only when it is present and given to me. Even then, it is hard to understand how visualizing (Anschauung) a present thing could tell me what it is in itself. Its properties cannot pass into my capacity to form representations. But even if that were possible, such visualization could not occur a priori, that is, before the object was presented to me. Without the object being presented, I can imagine no reason for a relation between my representation and the object, unless that relation depends on direct inspiration.

Therefore in one way only can my intuition (Anschauung) anticipate the actuality of the object, and be a cognition a priori, viz.: if my intuition contains nothing but the form of sensibility, antedating in my subjectivity all the actual impressions through which I am affected by objects.

Therefore, my intuition (Anschauung) can anticipate the actual existence of the object and be knowledge a priori in only one way. My intuition must contain nothing but the form of sensibility. This form must exist in me before all the actual impressions through which objects affect me.

For that objects of sense can only be intuited according to this form of sensibility I can know a priori. Hence it follows: that propositions, which concern this form of sensuous intuition only, are possible and valid for objects of the senses; as also, conversely, that intuitions which are possible a priori can never concern any other things than objects of our senses.¹⁰

I can know a priori that we can perceive objects of the senses only through this form of sensibility. It follows that propositions concerning only this form of sensory intuition can apply to objects of the senses and be valid for them. Conversely, intuitions that are possible a priori can concern only objects of our senses.¹⁰

§ 10. Accordingly, it is only the form of the sensuous intuition by which we can intuite things a priori, but by which we can know objects only as they appear to us (to our senses), not as they are in themselves; and this assumption is absolutely necessary if synthetical propositions a priori be granted as possible, or if, in case they actually occur, their possibility is to be comprehended and determined beforehand.

§ 10. Therefore, only the form of sensible intuition allows us to intuit things a priori. But through this form we can know objects only as they appear to us (to our senses), not as they are in themselves. This assumption is absolutely necessary if synthetic a priori propositions are possible. It is also necessary if such propositions actually occur and we are to understand and determine their possibility beforehand.

Now, the intuitions which pure mathematics lays at the foundation of all its cognitions and judgments which appear at once apodeictic and necessary are Space and Time. For mathematics must first have all its concepts in intuition, and pure mathematics in pure intuition, that is, it must construct them. If it proceeded in any other way, it would be impossible to make any headway, for mathematics proceeds, not analytically by dissection of concepts, but synthetically, and if pure intuition be wanting, there is nothing in which the matter for synthetical judgments a priori can be given. Geometry is based upon the pure intuition of space. Arithmetic accomplishes its concept of number by the successive addition of units in time; and pure mechanics especially cannot attain its concepts of motion without employing the representation of time. Both representations, however, are only intuitions; for if we omit from the empirical intuitions of bodies and their alterations (motion) everything empirical, or belonging to sensation, space and time still remain, which are therefore pure intuitions that lie a priori at the basis of the empirical. Hence they can never be omitted, but at the same time, by their being pure intuitions a priori, they prove that they are mere forms of our sensibility, which must precede all empirical intuition, or perception of actual objects, and conformably to which objects can be known a priori, but only as they appear to us.

The intuitions that pure mathematics uses as the basis for all its knowledge and judgments are space and time. This knowledge and these judgments appear certain and necessary from the outset. Mathematics must first have all its concepts in intuition, and pure mathematics must have them in pure intuition. In other words, mathematics must construct its concepts in intuition. If mathematics proceeded in any other way, it could make no progress. For mathematics does not proceed analytically, by breaking down concepts, but synthetically. Without pure intuition, there would be nothing in which the material for synthetic a priori judgments could be given. Geometry is based on the pure intuition of space. Arithmetic arrives at its concept of number by adding units one after another in time. Pure mechanics, in particular, cannot arrive at its concepts of motion without using the representation of time. Both space and time, however, are only intuitions. Suppose we remove everything empirical, or belonging to sensation, from our empirical intuitions of bodies and their changes (motion). Space and time still remain. They are therefore pure intuitions that underlie empirical intuitions a priori. So space and time can never be removed. At the same time, because they are pure intuitions a priori, they prove that they are merely forms of our sensibility. These forms must come before all empirical intuition, or perception of actual objects. Through them, objects can be known a priori, but only as they appear to us.

§ 11. The problem of the present section is therefore solved. Pure mathematics, as synthetical cognition a priori, is only possible by referring to no other objects than those of the senses. At the basis of their empirical intuition lies a pure intuition (of space and of time) which is a priori. This is possible, because the latter intuition is nothing but the mere form of sensibility, which precedes the actual appearance of the objects, in that it, in fact, makes them possible. Yet this faculty of intuiting a priori affects not the matter of the phenomenon (that is, the sense-element in it, for this constitutes that which is empirical), but its form, viz., space and time. Should any man venture to doubt that these are determinations adhering not to things in themselves, but to their relation to our sensibility, I should be glad to know how it can be possible to know the constitution of things a priori, viz., before we have any acquaintance with them and before they are presented to us. Such, however, is the case with space and time. But this is quite comprehensible as soon as both count for nothing more than formal conditions of our sensibility, while the objects count merely as phenomena; for then the form of the phenomenon, i.e., pure intuition, can by all means be represented as proceeding from ourselves, that is, a priori.

§ 11. The problem of this section is therefore solved. Pure mathematics, as synthetic knowledge a priori, is possible only because it concerns objects of the senses. Our empirical intuition of these objects rests on a pure intuition of space and time. This pure intuition is a priori. It is possible because it is simply the form of our sensibility. This form precedes the actual appearance of objects and makes those appearances possible. Yet our ability to intuit a priori affects only the form of the phenomenon, namely space and time. It does not affect the matter of the phenomenon, that is, the element supplied by the senses. This sensory element is what makes the phenomenon empirical. Suppose someone doubts that space and time belong to things only in relation to our sensibility, not to things in themselves. I would gladly ask how we could know the nature of things a priori, before we encounter them or they are presented to us. Yet this is how we know space and time. This is quite understandable once we regard space and time as nothing more than formal conditions of our sensibility, and objects merely as phenomena. For then we can certainly regard the form of the phenomenon, that is, pure intuition, as coming from ourselves, a priori.

§ 12. In order to add something by way of illustration and confirmation, we need only watch the ordinary and necessary procedure of geometers. All proofs of the complete congruence of two given figures (where the one can in every respect be substituted for the other) come ultimately to this that they may be made to coincide; which is evidently nothing else than a synthetical proposition resting upon immediate intuition, and this intuition must be pure, or given a priori, otherwise the proposition could not rank as apodeictically certain, but would have empirical certainty only. In that case, it could only be said that it is always found to be so, and holds good only as far as our perception reaches. That everywhere space (which [in its entirety] is itself no longer the boundary of another space) has three dimensions, and that space cannot in any way have more, is based on the proposition that not more than three lines can intersect at right angles in one point; but this proposition cannot by any means be shown from concepts, but rests immediately on intuition, and indeed on pure and a priori intuition, because it is apodeictically certain. That we can require a line to be drawn to infinity (in indefinitum), or that a series of changes (for example, spaces traversed by motion) shall be infinitely continued, presupposes a representation of space and time, which can only attach to intuition, namely, so far as it in itself is bounded by nothing, for from concepts it could never be inferred. Consequently, the basis of mathematics actually are pure intuitions, which make its synthetical and apodeictically valid propositions possible. Hence our transcendental deduction of the notions of space and of time explains at the same time the possibility of pure mathematics. Without some such deduction its truth may be granted, but its existence could by no means be understood, and we must assume "that everything which can be given to our senses (to the external senses in space, to the internal one in time) is intuited by us as it appears to us, not as it is in itself."

§ 12. To illustrate and confirm this, we need only observe the ordinary and necessary procedure of geometers. Two figures are completely congruent when either can be substituted for the other in every respect. All proofs of their complete congruence ultimately show that the figures can be made to coincide. This is plainly a synthetic proposition based on immediate intuition. The intuition must be pure, or given a priori. Otherwise, the proposition could not be apodictically certain, but would have only empirical certainty. In that case, we could only say that the figures are always found to coincide. The proposition would hold only as far as our perception reaches. Space everywhere has three dimensions and cannot have more. Space as a whole is not itself the boundary of another space. This claim rests on the proposition that no more than three lines can intersect at right angles at one point. But this proposition cannot be demonstrated from concepts. It rests directly on intuition, specifically on pure, a priori intuition, because it is apodictically certain. We can require that a line be extended indefinitely (in indefinitum). We can also require that a series of changes, such as distances covered by motion, continue infinitely. Both requirements presuppose a representation of space and time as inherently unbounded. Such a representation can belong only to intuition, because it could never be inferred from concepts. Pure intuitions are therefore the actual basis of mathematics. They make its synthetic and apodictically valid propositions possible. Thus our transcendental deduction of the notions of space and time also explains how pure mathematics is possible. Without some such deduction, we may grant that pure mathematics is true, but we could not understand its existence. We must also assume "that everything given to our senses (to the external senses in space, to the internal sense in time) is intuited by us as it appears to us, not as it is in itself."

§ 13. Those who cannot yet rid themselves of the notion that space and time are actual qualities inhering in things in themselves, may exercise their acumen on the following paradox. When they have in vain attempted its solution, and are free from prejudices at least for a few moments, they will suspect that the degradation of space and of time to mere forms of our sensuous intuition may perhaps be well founded.

§ 13. Some people still cannot give up the idea that space and time are actual qualities of things in themselves. They can test their ingenuity on the following paradox. After trying in vain to solve it, they may be free from prejudice for at least a few moments. Then they will suspect that reducing space and time to mere forms of our sensory intuition may perhaps be justified.

If two things are quite equal in all respects as much as can be ascertained by all means possible, quantitatively and qualitatively, it must follow, that the one can in all cases and under all circumstances replace the other, and this substitution would not occasion the least perceptible difference. This in fact is true of plane figures in geometry; but some spherical figures exhibit, notwithstanding a complete internal agreement, such a contrast in their external relation, that the one figure cannot possibly be put in the place of the other. For instance, two spherical triangles on opposite hemispheres, which have an arc of the equator as their common base, may be quite equal, both as regards sides and angles, so that nothing is to be found in either, if it be described for itself alone and completed, that would not equally be applicable to both; and yet the one cannot be put in the place of the other (being situated upon the opposite hemisphere). Here then is an internal difference between the two triangles, which difference our understanding cannot describe as internal, and which only manifests itself by external relations in space.

If two things are completely equal in every respect that can be determined by any possible means, both quantitatively and qualitatively, then one must be able to replace the other in every case and under all circumstances. Such a substitution would make no perceptible difference. This is indeed true of plane figures in geometry. But some spherical figures, despite agreeing completely in their internal features, differ in their external relations. This difference makes it impossible to put one figure in the place of the other. For example, two spherical triangles on opposite hemispheres may share an arc of the equator as their base. They may be completely equal in their sides and angles. If either triangle is described on its own and in full, nothing in that description would fail to apply equally to both. Yet one cannot be put in the place of the other, since they are on opposite hemispheres. So there is an internal difference between the two triangles that our understanding cannot describe as internal. This difference shows itself only through external relations in space.

But I shall adduce examples, taken from common life, that are more obvious still.

But I will give even more obvious examples from everyday life.

What can be more similar in every respect and in every part more alike to my hand and to my ear, than their images in a mirror? And yet I cannot put such a hand as is seen in the glass in the place of its archetype; for if this is a right hand, that in the glass is a left one, and the image or reflexion of the right ear is a left one which never can serve as a substitute for the other. There are in this case no internal differences which our understanding could determine by thinking alone. Yet the differences are internal as the senses teach, for, notwithstanding their complete equality and similarity, the left hand cannot be enclosed in the same bounds as the right one (they are not congruent); the glove of one hand cannot be used for the other. What is the solution? These objects are not representations of things as they are in themselves, and as the pure understanding would cognise them, but sensuous intuitions, that is, appearances, the possibility of which rests upon the relation of certain things unknown in themselves to something else, viz., to our sensibility. Space is the form of the external intuition of this sensibility, and the internal determination of every space is only possible by the determination of its external relation to the whole space, of which it is a part (in other words, by its relation to the external sense). That is to say, the part is only possible through the whole, which is never the case with things in themselves, as objects of the mere understanding, but with appearances only. Hence the difference between similar and equal things, which are yet not congruent (for instance, two symmetric helices), cannot be made intelligible by any concept, but only by the relation to the right and the left hands which immediately refers to intuition.

What could be more alike in every respect and every part than my hand and ear and their images in a mirror? Yet I cannot put the hand I see in the mirror in place of my actual hand. If my hand is a right hand, the hand in the mirror is a left hand. Likewise, the image of a right ear is a left ear, which can never serve as a substitute for the right. In this case, there are no internal differences that our understanding could determine by thought alone. Yet, as the senses show, the differences are internal. Despite their complete equality and similarity, the left hand cannot fit within the same boundaries as the right hand. They are not congruent. A glove for one hand cannot be used for the other. What is the solution? These objects do not represent things as they are in themselves, as the pure understanding would know them. Instead, they are sensible intuitions, that is, appearances. These appearances are possible because certain things, unknown in themselves, stand in relation to something else, namely, our sensibility. Space is the form of external intuition for this sensibility. The internal character of any space can be determined only by its external relation to the whole space it is part of. In other words, it can be determined only by its relation to the external sense. That is to say, the part is possible only through the whole. This is never the case with things in themselves, as objects of the understanding alone, but only with appearances. So the difference between things that are similar and equal, yet not congruent, cannot be understood through any concept. Two symmetric helices are an example. Such a difference can be understood only through its relation to the right and left hands, which refers directly to intuition.

Remark I.

Remark 1.

Pure Mathematics, and especially pure geometry, can only have objective reality on condition that they refer to objects of sense. But in regard to the latter the principle holds good, that our sense representation is not a representation of things in themselves, but of the way in which they appear to us. Hence it follows, that the propositions of geometry are not the results of a mere creation of our poetic imagination, and that therefore they cannot be referred with assurance to actual objects; but rather that they are necessarily valid of space, and consequently of all that may be found in space, because space is nothing else than the form of all external appearances, and it is this form alone in which objects of sense can be given. Sensibility, the form of which is the basis of geometry, is that upon which the possibility of external appearance depends. Therefore these appearances can never contain anything but what geometry prescribes to them.

Pure mathematics, especially pure geometry, can have objective reality only if it refers to objects of sense. But our sensory representations do not represent things as they are in themselves. They represent things as they appear to us. It follows that the propositions of geometry are not merely creations of our poetic imagination. If they were, we could not confidently apply them to actual objects. Rather, they are necessarily valid for space and therefore for everything that may be found in space. This is because space is nothing other than the form of all external appearances. It is only in this form that objects of sense can be given to us. The form of sensibility is the basis of geometry, and sensibility makes external appearances possible. Therefore, external appearances can never contain anything except what geometry prescribes for them.

It would be quite otherwise if the senses were so constituted as to represent objects as they are in themselves. For then it would not by any means follow from the conception of space, which with all its properties serves to the geometer as an a priori foundation, together with what is thence inferred, must be so in nature. The space of the geometer would be considered a mere fiction, and it would not be credited with objective validity, because we cannot see how things must of necessity agree with an image of them, which we make spontaneously and previous to our acquaintance with them. But if this image, or rather this formal intuition, is the essential property of our sensibility, by means of which alone objects are given to us, and if this sensibility represents not things in themselves, but their appearances: we shall easily comprehend, and at the same time indisputably prove, that all external objects of our world of sense must necessarily coincide in the most rigorous way with the propositions of geometry; because sensibility by means of its form of external intuition, viz., by space, the same with which the geometer is occupied, makes those objects at all possible as mere appearances.

Things would be quite different if our senses represented objects as they are in themselves. In that case, the geometer uses the concept of space and all its properties as a foundation known a priori. But it would not follow that what the geometer deduces from this concept must hold true in nature. The geometer's space would be considered a mere fiction and would not be regarded as objectively valid. For we cannot see why things must necessarily agree with an image we form on our own before encountering them. But suppose this image, or rather this formal intuition, is an essential feature of our sensibility. Suppose it is the only means by which objects are given to us. And suppose our sensibility represents not things in themselves, but their appearances. Then we can easily understand and prove beyond dispute that all external objects in our world of sense must conform strictly to the propositions of geometry. This is because our sensibility makes those objects possible at all as mere appearances. It does so through its form of external intuition, namely space, the same space the geometer studies.

It will always remain a remarkable phenomenon in the history of philosophy, that there was a time, when even mathematicians, who at the same time were philosophers, began to doubt, not of the accuracy of their geometrical propositions so far as they concerned space, but of their objective validity and the applicability of this concept itself, and of all its corollaries, to nature. They showed much concern whether a line in nature might not consist of physical points, and consequently that true space in the object might consist of simple [discrete] parts, while the space which the geometer has in his mind [being continuous] cannot be such. They did not recognise that this mental space renders possible the physical space, i.e., the extension of matter; that this pure space is not at all a quality of things in themselves, but a form of our sensuous faculty of representation; and that all objects in space are mere appearances, i.e., not things in themselves but representations of our sensuous intuition. But such is the case, for the space of the geometer is exactly the form of sensuous intuition which we find a priori in us, and contains the ground of the possibility of all external appearances (according to their form), and the latter must necessarily and most rigidly agree with the propositions of the geometer, which he draws not from any fictitious concept, but from the subjective basis of all external phenomena, which is sensibility itself. In this and no other way can geometry be made secure as to the undoubted objective reality of its propositions against all the intrigues of a shallow Metaphysics, which is surprised at them [the geometrical propositions], because it has not traced them to the sources of their concepts.

It will always be a remarkable fact in the history of philosophy that even mathematicians who were also philosophers once began to doubt. They did not doubt the accuracy of their geometrical propositions as far as they concerned space. Rather, they doubted whether those propositions were objectively valid and whether the concept of space itself, and all that follows from it, applied to nature. They were deeply concerned that a line in nature might consist of physical points. If so, real space in the object might consist of simple [discrete] parts, while the space the geometer has in mind [being continuous] cannot consist of such parts. They did not recognize that this mental space makes physical space possible, that is, the extension of matter. They did not recognize that pure space is not a property of things in themselves. Rather, it is a form of our capacity for sensory representation. Nor did they recognize that all objects in space are mere appearances. They are not things in themselves, but representations given through our sensible intuition. Yet this is the case, because the geometer’s space is exactly the form of sensible intuition that we find in ourselves a priori. It contains the basis for the possibility of all external appearances, as far as their form is concerned. These appearances must necessarily and strictly conform to the geometer’s propositions. The geometer does not draw those propositions from any invented concept. Instead, the geometer draws them from the subjective basis of all external phenomena, which is sensibility itself. In this way, and no other, geometry can secure the unquestionable objective reality of its propositions against all the schemes of a shallow Metaphysics. Such Metaphysics is surprised by geometrical propositions because it has not traced them back to the sources of their concepts.

Remark II.

Note II.

Whatever is given us as object, must be given us in intuition. All our intuition however takes place by means of the senses only; the understanding intuites nothing, but only reflects. And as we have just shown that the senses never and in no manner enable us to know things in themselves, but only their appearances, which are mere representations of the sensibility, we conclude that 'all bodies, together with the space in which they are, must be considered nothing but mere representations in us, and exist nowhere but in our thoughts.' You will say: Is not this manifest idealism?

Whatever is given to us as an object must be given to us in intuition. But all our intuition occurs through the senses alone. The understanding does not intuit anything. It only reflects. We have just shown that the senses never enable us to know things in themselves in any way. They enable us to know only appearances, which are mere representations produced by our senses. So we conclude that 'all bodies, together with the space in which they exist, must be considered nothing but mere representations in us, existing nowhere but in our thoughts.' You will ask: Is this not clearly idealism?

Idealism consists in the assertion, that there are none but thinking beings, all other things, which we think are perceived in intuition, being nothing but representations in the thinking beings, to which no object external to them corresponds in fact. Whereas I say, that things as objects of our senses existing outside us are given, but we know nothing of what they may be in themselves, knowing only their appearances, i.e., the representations which they cause in us by affecting our senses. Consequently I grant by all means that there are bodies without us, that is, things which, though quite unknown to us as to what they are in themselves, we yet know by the representations which their influence on our sensibility procures us, and which we call bodies, a term signifying merely the appearance of the thing which is unknown to us, but not therefore less actual. Can this be termed idealism? It is the very contrary.

Idealism claims that only thinking beings exist. All other things that we think we perceive directly are merely representations in those thinking beings. In fact, nothing outside those beings corresponds to these representations. I say, on the contrary, that things outside us are given to us as objects of our senses. But we know nothing of what these things may be in themselves. We know only their appearances, that is, the representations they cause in us by affecting our senses. I therefore fully acknowledge that bodies exist outside us. These are things whose nature in itself is quite unknown to us. Yet we know them through the representations their influence on our senses produces in us. We call these things bodies. The term means only the appearance of a thing that is unknown to us, but is no less real for that. Can this be called idealism? It is the exact opposite.

Long before Locke's time, but assuredly since him, it has been generally assumed and granted without detriment to the actual existence of external things, that many of their predicates may be said to belong not to the things in themselves, but to their appearances, and to have no proper existence outside our representation. Heat, color, and taste, for instance, are of this kind. Now, if I go farther, and for weighty reasons rank as mere appearances the remaining qualities of bodies also, which are called primary, such as extension, place, and in general space, with all that which belongs to it (impenetrability or materiality, space, etc.)—no one in the least can adduce the reason of its being inadmissible. As little as the man who admits colors not to be properties of the object in itself, but only as modifications of the sense of sight, should on that account be called an idealist, so little can my system be named idealistic, merely because I find that more, nay,

Long before Locke’s time, and certainly since then, people have generally accepted the following view without denying that external things exist. Many qualities belong not to things in themselves, but to their appearances. These qualities have no independent existence outside our representations. Heat, color, and taste, for instance, are qualities of this kind. Now suppose I go further, for important reasons, and also class the remaining qualities of bodies as mere appearances. These are called primary qualities and include extension, location, and space in general, along with everything belonging to space (impenetrability or materiality, space, etc.). No one can give the slightest reason why this view is inadmissible. A person should not be called an idealist simply for accepting that colors are not properties of objects in themselves. Such a person regards colors only as modifications of the sense of sight. Likewise, my system cannot be called idealistic merely because I find that more, indeed,

All the properties which constitute the intuition of a body belong merely to its appearance.

All the properties that make up our intuition of a body belong only to its appearance.

The existence of the thing that appears is thereby not destroyed, as in genuine idealism, but it is only shown, that we cannot possibly know it by the senses as it is in itself.

This does not deny the existence of the thing that appears, as genuine idealism does. It only shows that we cannot possibly know the thing as it is in itself through our senses.

I should be glad to know what my assertions must be in order to avoid all idealism. Undoubtedly, I should say, that the representation of space is not only perfectly conformable to the relation which our sensibility has to objects—that I have said—but that it is quite similar to the object,—an assertion in which I can find as little meaning as if I said that the sensation of red has a similarity to the property of vermilion, which in me excites this sensation.

I would like to know what I must assert to avoid all idealism. No doubt I must say that our representation of space does more than perfectly match the way our senses relate to objects. I have already said that much. I must also say that our representation of space is quite similar to the object. But I can find as little meaning in that claim as in saying that the sensation of red resembles the property of vermilion that produces this sensation in me.

Remark III.

Remark 3.

Hence we may at once dismiss an easily foreseen but futile objection, "that by admitting the ideality of space and of time the whole sensible world would be turned into mere sham." At first all philosophical insight into the nature of sensuous cognition was spoiled, by making the sensibility merely a confused mode of representation, according to which we still know things as they are, but without being able to reduce everything in this our representation to a clear consciousness; whereas proof is offered by us that sensibility consists, not in this logical distinction of clearness and obscurity, but in the genetical one of the origin of cognition itself. For sensuous perception represents things not at all as they are, but only the mode in which they affect our senses, and consequently by sensuous perception appearances only and not things themselves are given to the understanding for reflexion. After this necessary corrective, an objection rises from an unpardonable and almost intentional misconception, as if my doctrine turned all the things of the world of sense into mere illusion.

We can immediately dismiss a predictable but futile objection: "By admitting that space and time are ideal, we turn the whole world of the senses into a mere sham." At first, all philosophical understanding of sensory knowledge was undermined by treating sensibility as merely a confused way of representing things. On that view, we still know things as they are, but cannot become clearly conscious of everything in our representation of them. We, however, offer proof that sensibility is not a matter of this logical difference between clarity and obscurity. Rather, it concerns a difference in the origin of knowledge itself. Sensory perception does not represent things as they are, but only as they affect our senses. It therefore gives the understanding only appearances, not things themselves, to reflect on. Even after this necessary correction, an objection arises from an inexcusable and almost deliberate misunderstanding. It treats my doctrine as if it turned all the things in the world of the senses into mere illusions.

When an appearance is given us, we are still quite free as to how we should judge the matter. The appearance depends upon the senses, but the judgment upon the understanding, and the only question is, whether in the determination of the object there is truth or not. But the difference between truth and dreaming is not ascertained by the nature of the representations, which are referred to objects (for they are the same in both cases), but by their connexion according to those rules, which determine the coherence of the representations in the concept of an object, and by ascertaining whether they can subsist together in experience or not. And it is not the fault of the appearances if our cognition takes illusion for truth, i.e., if the intuition, by which an object is given us, is considered a concept of the thing or of its existence also, which the understanding can only think. The senses represent to us the paths of the planets as now progressive, now retrogressive, and herein is neither falsehood nor truth, because as long as we hold this path to be nothing but appearance, we do not judge of the objective nature of their motion. But as a false judgment may easily arise when the understanding is not on its guard against this subjective mode of representation being considered objective, we say they appear to move backward; it is not the senses however which must be charged with the illusion, but the understanding, whose province alone it is to give an objective judgment on appearances.

When an appearance is given to us, we are still free to judge it as we choose. The appearance depends on the senses, but the judgment depends on the understanding. The only question is whether our judgment about the object is true. But truth and dreams cannot be distinguished by the nature of the representations we refer to objects. These representations are the same in both cases. The difference lies in how the representations are connected according to rules. These rules determine how representations fit together in the concept of an object. The difference also lies in whether the representations can coexist in experience. And appearances are not at fault if our knowledge mistakes illusion for truth. This happens when we take the intuition through which an object is given to us as a concept of the thing or of its existence. Only the understanding can think such a concept. The senses show us the planets moving now forward, now backward. There is neither falsehood nor truth in this. As long as we regard these paths as mere appearances, we make no judgment about the objective nature of the planets’ motion. But a false judgment can easily arise if the understanding fails to guard against treating this subjective representation as objective. So we say that the planets appear to move backward. The senses are not responsible for the illusion. The understanding is responsible, for it alone can make objective judgments about appearances.

Thus, even if we did not at all reflect on the origin of our representations, whenever we connect our intuitions of sense (whatever they may contain), in space and in time, according to the rules of the coherence of all cognition in experience, illusion or truth will arise according as we are negligent or careful. It is merely a question of the use of sensuous representations in the understanding, and not of their origin. In the same way, if I consider all the representations of the senses, together with their form, space and time, to be nothing but appearances, and space and time to be a mere form of the sensibility, which is not to be met with in objects out of it, and if I make use of these representations in reference to possible experience only, there is nothing in my regarding them as appearances that can lead astray or cause illusion. For all that they can correctly cohere according to rules of truth in experience. Thus all the propositions of geometry hold good of space as well as of all the objects of the senses, consequently of all possible experience, whether I consider space as a mere form of the sensibility, or as something cleaving to the things themselves. In the former case however I comprehend how I can know a priori these propositions concerning all the objects of external intuition. Otherwise, everything else as regards all possible experience remains just as if I had not departed from the vulgar view.

Even if we never consider the origin of our representations, we connect our sensory intuitions in space and time. Whatever these intuitions contain, we connect them according to the rules that make all cognition coherent in experience. Whether illusion or truth results depends on whether we are careless or careful. The question concerns only how the understanding uses sensory representations, not where they come from. Likewise, I may consider all sensory representations, together with their form, space and time, to be nothing but appearances. I may also consider space and time to be merely forms of sensibility, not found in objects apart from sensibility. If I use these representations only in relation to possible experience, regarding them as appearances cannot mislead me or cause illusion. For all these representations can still fit together according to the rules of truth in experience. Thus, all the propositions of geometry hold true for space and for all objects of the senses. They therefore hold true for all possible experience. This is so whether I consider space merely a form of sensibility or something belonging to things themselves. In the first case, however, I understand how I can know these propositions a priori for all objects of outer intuition. Otherwise, everything concerning all possible experience remains just as if I had not departed from the common view.

But if I venture to go beyond all possible experience with my notions of space and time, which I cannot refrain from doing if I proclaim them qualities inherent in things in themselves (for what should prevent me from letting them hold good of the same things, even though my senses might be different, and unsuited to them?), then a grave error may arise due to illusion, for thus I would proclaim to be universally valid what is merely a subjective condition of the intuition of things and sure only for all objects of sense, viz., for all possible experience; I would refer this condition to things in themselves, and do not limit it to the conditions of experience.

But suppose I extend my ideas of space and time beyond all possible experience. I cannot avoid doing this if I claim that space and time are qualities inherent in things in themselves. For what would prevent me from claiming that these qualities still apply to the same things, even if my senses were different and unsuited to them? If I do this, an illusion may lead me into a serious error. I would claim universal validity for what is merely a subjective condition of intuiting things. This condition holds only for all objects of sense, that is, for all possible experience. I would apply it to things in themselves, instead of limiting it to the conditions of experience.

My doctrine of the ideality of space and of time, therefore, far from reducing the whole sensible world to mere illusion, is the only means of securing the application of one of the most important cognitions (that which mathematics propounds a priori) to actual objects, and of preventing its being regarded as mere illusion. For without this observation it would be quite impossible to make out whether the intuitions of space and time, which we borrow from no experience, and which yet lie in our representation a priori, are not mere phantasms of our brain, to which objects do not correspond, at least not adequately, and consequently, whether we have been able to show its unquestionable validity with regard to all the objects of the sensible world just because they are mere appearances.

My doctrine that space and time are ideal does not reduce the whole sensible world to mere illusion. On the contrary, it is the only way to ensure that one of our most important kinds of knowledge applies to actual objects. This is the knowledge that mathematics offers a priori, or independently of experience. My doctrine is also the only way to prevent this knowledge from being regarded as mere illusion. Without this insight, we could not determine whether our intuitions of space and time are merely fantasies of the mind. We do not derive these intuitions from experience, yet they are present in our representations a priori. Objects might not correspond to them, or at least not adequately. Consequently, we could not determine whether we have shown the unquestionable validity of mathematics for all objects of the sensible world precisely because they are mere appearances.

Secondly, though these my principles make appearances of the representations of the senses, they are so far from turning the truth of experience into mere illusion, that they are rather the only means of preventing the transcendental illusion, by which metaphysics has hitherto been deceived, leading to the childish endeavor of catching at bubbles, because appearances, which are mere representations, were taken for things in themselves. Here originated the remarkable event of the antimony of Reason which I shall mention by and by, and which is destroyed by the single observation, that appearance, as long as it is employed in experience, produces truth, but the moment it transgresses the bounds of experience, and consequently becomes transcendent, produces nothing but illusion.

Secondly, although my principles treat the representations of the senses as appearances, they do not turn the truth of experience into mere illusion. Rather, they are the only way to prevent the transcendental illusion that has deceived metaphysics until now. This illusion led to the childish attempt to catch bubbles, because appearances, which are mere representations, were mistaken for things in themselves. This mistake gave rise to the remarkable antinomy of Reason, which I shall discuss shortly. The antinomy is resolved by a single observation. As long as appearances are used within experience, they produce truth. But the moment appearances go beyond the bounds of experience and so become transcendent, they produce nothing but illusion.

Inasmuch, therefore, as I leave to things as we obtain them by the senses their actuality, and only limit our sensuous intuition of these things to this, that they represent in no respect, not even in the pure intuitions of space and of time, anything more than mere appearance of those things, but never their constitution in themselves, this is not a sweeping illusion invented for nature by me. My protestation too against all charges of idealism is so valid and clear as even to seem superfluous, were there not incompetent judges, who, while they would have an old name for every deviation from their perverse though common opinion, and never judge of the spirit of philosophic nomenclature, but cling to the letter only, are ready to put their own conceits in the place of well-defined notions, and thereby deform and distort them. I have myself given this my theory the name of transcendental idealism, but that cannot authorise any one to confound it either with the empirical idealism of Descartes, (indeed, his was only an insoluble problem, owing to which he thought every one at liberty to deny the existence of the corporeal world, because it could never be proved satisfactorily), or with the mystical and visionary idealism of Berkeley, against which and other similar phantasms our Critique contains the proper antidote. My idealism concerns not the existence of things (the doubting of which, however, constitutes idealism in the ordinary sense), since it never came into my head to doubt it, but it concerns the sensuous representation of things, to which space and time especially belong. Of these [viz., space and time], consequently of all appearances in general, I have only shown, that they are neither things (but mere modes of representation), nor determinations belonging to things in themselves. But the word "transcendental," which with me means a reference of our cognition, i.e., not to things, but only to the cognitive faculty, was meant to obviate this misconception. Yet rather than give further occasion to it by this word, I now retract it, and desire this idealism of mine to be called critical. But if it be really an objectionable idealism to convert actual things (not appearances) into mere representations, by what name shall we call him who conversely changes mere representations to things? It may, I think, be called "dreaming idealism," in contradistinction to the former, which may be called "visionary," both of which are to be refuted by my transcendental, or, better, critical idealism.

I therefore accept that things as we encounter them through the senses are real. I only limit our sensory intuition of them in this way: it represents nothing more than their mere appearance, never what they are in themselves. This is true even of the pure intuitions of space and time. So I have not invented some sweeping illusion and imposed it on nature. My denial of all charges of idealism is valid and clear enough to seem unnecessary. Yet there are incompetent judges who demand an old name for every departure from their misguided but common opinion. They never consider the spirit of philosophical terminology, but cling only to the letter. They are ready to replace well-defined concepts with their own ideas, thereby deforming and distorting them. I have called my theory transcendental idealism. But this does not entitle anyone to confuse it with the empirical idealism of Descartes. Indeed, his idealism was only an insoluble problem. Because he thought the existence of the material world could never be satisfactorily proved, he thought everyone was free to deny it. Nor may anyone confuse my theory with the mystical and visionary idealism of Berkeley. Our Critique contains the proper antidote to Berkeley's idealism and other similar fantasies. My idealism does not concern the existence of things, although doubting their existence constitutes idealism in the ordinary sense. It never occurred to me to doubt that things exist. Rather, my idealism concerns the sensory representation of things, which includes space and time in particular. I have shown only that space and time, and consequently all appearances in general, are not things but mere modes of representation. Nor are they features belonging to things in themselves. By the word "transcendental," I mean that our knowledge refers not to things, but only to the faculty of knowledge. I intended the word to prevent this misunderstanding. But rather than give further occasion for misunderstanding by using it, I now withdraw it. I want my idealism to be called critical. But if it really is an objectionable idealism to turn actual things, not appearances, into mere representations, what shall we call someone who does the reverse and turns mere representations into things? I think it may be called "dreaming idealism," as distinct from the former kind, which may be called "visionary." Both are to be refuted by my transcendental, or, better, critical idealism.