I.2.1. Postulates of Empirical Thought; Refutation of Idealism

1. That which agrees, in intuition and in concepts, with the formal conditions of experience, is possible.

2. That which is bound up with the material conditions of experience, that is, with sensation, is actual.

3. That which in its connection with the actual is determined in accordance with universal conditions of experience, is (that is, exists as) necessary.

The categories of modality have the peculiarity that, in determining an object, they do not in the least enlarge the concept to which they are attached as predicates. They only express the relation of the concept to the faculty of knowledge. Even when the concept of a thing is quite complete, I can still enquire whether this object is merely possible or is also actual, or if actual, whether it is not also necessary. No additional determinations are thereby thought in the object itself; the question is only how the object, together with all its determinations, is related to understanding and its empirical employment, to empirical judgment, and to reason in its application to experience.

Just on this account also the principles of modality are nothing but explanations of the concepts of possibility, actuality, and necessity, in their empirical employment; at the same time they restrict all categories to their merely empirical employment, and do not approve or allow their transcendental employment. For if they are not to have a purely logical significance, analytically expressing the form of thought, but are to refer to the possibility, actuality, or necessity of things, they must concern possible experience and its synthetic unity, in which alone objects of knowledge can be given.

The postulate of the possibility of things requires that the concept of the things should agree with the formal conditions of an experience in general. But this, the objective form of experience in general, contains all synthesis that is required for knowledge of objects. A concept which contains a synthesis is to be regarded as empty and as not related to any object, if this synthesis does not belong to experience either as being derived from it, in which case it is an empirical concept, or as being an a priori condition upon which experience in general in its formal aspect rests, in which case it is a pure concept. In the latter case it still belongs to experience, inasmuch as its object is to be met with only in experience. For whence shall we derive the character of the possibility of an object which is thought through a synthetic a priori concept, if not from the synthesis which constitutes the form of the empirical knowledge of objects? It is, indeed, a necessary logical condition that a concept of the possible must not contain any contradiction; but this is not by any means sufficient to determine the objective reality of the concept, that is, the possibility of such an object as is thought through the concept. Thus there is no contradiction in the concept of a figure which is enclosed within two straight lines, since the concepts of two straight lines and of their coming together contain no negation of a figure. The impossibility arises not from the concept in itself, but in connection with its construction in space, that is, from the conditions of space and of its determination. But these have an objective reality of their own, that is, they apply to possible things, since they contain a priori in themselves the form of experience in general.

We shall now proceed to show the far-reaching utility and influence of this postulate of possibility. If I represent to myself a thing which is permanent, so that everything in it which changes belongs only to its state, I can never know from such a concept that a thing of this kind is possible. Or if I represent to myself something which is so constituted that if it is posited something else invariably and inevitably follows from it, this may certainly be so thought without contradiction; but this thought affords no means of judging whether this property (causality) is to be met with in any possible thing. Lastly, I can represent to myself diverse things (substances), which are so constituted that the state of the one carries with it some consequence in the state of the other, and this reciprocally; but I can never determine from these concepts, which contain a merely arbitrary synthesis, whether a relation of this kind can belong to any [possible] things. Only through the fact that these concepts express a priori the relations of perceptions in every experience, do we know their objective reality, that is, their transcendental truth, and this, indeed, independently of experience, though not independently of all relation to the form of an experience in general, and to the synthetic unity in which alone objects can be empirically known.

But if we should seek to frame quite new concepts of substances, forces, reciprocal actions, from the material which perception presents to us, without experience itself yielding the example of their connection, we should be occupying ourselves with mere fancies, of whose possibility there is absolutely no criterion since we have neither borrowed these concepts [directly] from experience, nor have taken experience as our instructress in their formation. Such fictitious concepts, unlike the categories, can acquire the character of possibility not in a priori fashion, as conditions upon which all experience depends, but only a posteriori as being concepts which are given through experience itself. And, consequently, their possibility must either be known a posteriori and empirically, or it cannot be known at all. A substance which would be permanently present in space, but without filling it (like that mode of existence intermediate between matter and thinking being which some would seek to introduce), or a special ultimate mental power of intuitively anticipating the future (and not merely inferring it), or lastly a power of standing in community of thought with other men, however distant they may be—are concepts the possibility of which is altogether groundless, as they cannot be based on experience and its known laws; and without such confirmation they are arbitrary combinations of thoughts, which, although indeed free from contradiction, can make no claim to objective reality, and none, therefore, as to the possibility of an object such as we here profess to think. As regards reality, we obviously cannot think it in concreto, without calling experience to our aid. For reality is bound up with sensation, the matter of experience, not with that form of relation in regard to which we can, if we so choose, resort to a playful inventiveness.

But I leave aside everything the possibility of which can be derived only from its actuality in experience, and have here in view only the possibility of things through a priori concepts; and I maintain the thesis that their possibility can never be established from such concepts taken in and by themselves, but only when the concepts are viewed as formal and objective conditions of experience in general.

It does, indeed, seem as if the possibility of a triangle could be known from its concept in and by itself (the concept is certainly independent of experience), for we can, as a matter of fact, give it an object completely a priori, that is, can construct it. But since this is only the form of an object, it would remain a mere product of imagination, and the possibility of its object would still be doubtful. To determine its possibility, something more is required, namely, that such a figure be thought under no conditions save those upon which all objects of experience rest. That space is a formal a priori condition of outer experiences, that the formative synthesis through which we construct a triangle in imagination is precisely the same as that which we exercise in the apprehension of an appearance, in making for ourselves an empirical concept of it—these are the considerations that alone enable us to connect the representation of the possibility of such a thing with the concept of it. Similarly, since the concepts of continuous magnitudes, indeed of magnitudes in general, are one and all synthetic, the possibility of such magnitudes is never clear from the concepts themselves, but only when they are viewed as formal conditions of the determination of objects in experience in general. And where, indeed, should we seek for objects corresponding to these concepts if not in experience, through which alone objects are given to us? We can, indeed, prior to experience itself, know and characterise the possibility of things, merely by reference to the formal conditions under which in experience anything whatsoever is determined as object, and therefore can do so completely a priori. But, even so, this is possible only in relation to experience and within its limits.

The postulate bearing on the knowledge of things as actual does not, indeed, demand immediate perception (and, therefore, sensation of which we are conscious) of the object whose existence is to be known. What we do, however, require is an apprehension of the connection of the object with some actual perception, in accordance with the analogies of experience, which define all real connection in an experience in general.

In the mere concept of a thing no mark of its existence is to be found. For though it may be so complete that nothing which is required for thinking the thing with all its inner determinations is lacking to it, yet existence has nothing to do with all this, but only with the question whether such a thing be so given us that the perception of it can, if need be, precede the concept. For that the concept precedes the perception signifies the concept’s mere possibility; the perception which supplies the content to the concept is the sole mark of actuality. We can also, however, know the existence of the thing prior to its perception and, consequently, comparatively speaking, in an a priori manner, if only it be bound up with certain perceptions, in accordance with the principles of their empirical connection (the analogies). For the existence of the thing being thus bound up with our perceptions in a possible experience, we are able in the series of possible perceptions and under the guidance of the analogies to make the transition from our actual perception to the thing in question. Thus from the perception of the attracted iron filings we know of the existence of a magnetic matter pervading all bodies, although the constitution of our organs cuts us off from all immediate perception of this medium. For in accordance with the laws of sensibility and the context of our perceptions, we should, were our senses more refined, come also in an experience upon the immediate empirical intuition of it. The grossness of our senses does not in any way decide the form of possible experience in general. Our knowledge of the existence of things reaches, then, only so far as perception and its advance according to empirical laws can extend. If we do not start from experience, or do not proceed in accordance with laws of the empirical connection of appearances, our guessing or enquiring into the existence of anything will only be an idle pretence. Idealism raises, however, what is a serious objection to these rules for proving existence mediately; and this is the proper place for its refutation.

Idealism—meaning thereby material idealism—is the theory which declares the existence of objects in space outside us either to be merely doubtful and indemonstrable or to be false and impossible. The former is the problematic idealism of Descartes, which holds that there is only one empirical assertion that is indubitably certain, namely, that ‘I am’. The latter is the dogmatic idealism of Berkeley. He maintains that space, with all the things of which it is the inseparable condition, is something which is in itself impossible; and he therefore regards the things in space as merely imaginary entities. Dogmatic idealism is unavoidable, if space be interpreted as a property that must belong to things in themselves. For in that case space, and everything to which it serves as condition, is a non-entity. The ground on which this idealism rests has already been undermined by us in the Transcendental Aesthetic. Problematic idealism, which makes no such assertion, but merely pleads incapacity to prove, through immediate experience, any existence except our own, is, in so far as it allows of no decisive judgment until sufficient proof has been found, reasonable and in accordance with a thorough and philosophical mode of thought. The required proof must, therefore, show that we have experience, and not merely imagination of outer things; and this, it would seem, cannot be achieved save by proof that even our inner experience, which for Descartes is indubitable, is possible only on the assumption of outer experience.

The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.

I am conscious of my own existence as determined in time. All determination of time presupposes something permanent in perception. This permanent cannot, however, be something in me, since it is only through this permanent that my existence in time can itself be determined. Thus perception of this permanent is possible only through a thing outside me and not through the mere representation of a thing outside me; and consequently the determination of my existence in time is possible only through the existence of actual things which I perceive outside me. Now consciousness [of my existence] in time is necessarily bound up with consciousness of the [condition of the] possibility of this time-determination; and it is therefore necessarily bound up with the existence of things outside me, as the condition of the time-determination. In other words, the consciousness of my existence is at the same time an immediate consciousness of the existence of other things outside me.

Note I. It will be observed that in the foregoing proof the game played by idealism has been turned against itself, and with greater justice. Idealism assumed that the only immediate experience is inner experience, and that from it we can only infer outer things—and this, moreover, only in an untrustworthy manner, as in all cases where we are inferring from given effects to determinate causes. In this particular case, the cause of the representations, which we ascribe, perhaps falsely, to outer things, may lie in ourselves. But in the above proof it has been shown that outer experience is really immediate, and that only by means of it is inner experience—not indeed the consciousness of my own existence, but the determination of it in time—possible. Certainly, the representation ‘I am’, which expresses the consciousness that can accompany all thought, immediately includes in itself the existence of a subject; but it does not so include any knowledge of that subject, and therefore also no empirical knowledge, that is, no experience of it. For this we require, in addition to the thought of something existing, also intuition, and in this case inner intuition, in respect of which, that is, of time, the subject must be determined. But in order so to determine it, outer objects are quite indispensable; and it therefore follows that inner experience is itself possible only mediately, and only through outer experience.

Note 2. With this thesis all employment of our cognitive faculty in experience, in the determination of time, entirely agrees. Not only are we unable to perceive any determination of time save through change in outer relations (motion) relatively to the permanent in space (for instance, the motion of the sun relatively to objects on the earth), we have nothing permanent on which, as intuition, we can base the concept of a substance, save only matter; and even this permanence is not obtained from outer experience, but is presupposed a priori as a necessary condition of determination of time, and therefore also as a determination of inner sense in respect of [the determination of] our own existence through the existence of outer things. The consciousness of myself in the representation ‘I’ is not an intuition, but a merely intellectual representation of the spontaneity of a thinking subject. This ‘I’ has not, therefore, the least predicate of intuition, which, as permanent, might serve as correlate for the determination of time in inner sense—in the manner in which, for instance, impenetrability serves in our empirical intuition of matter.

Note 3. From the fact that the existence of outer things is required for the possibility of a determinate consciousness of the self, it does not follow that every intuitive representation of outer things involves the existence of these things, for their representation can very well be the product merely of the imagination (as in dreams and delusions). Such representation is merely the reproduction of previous outer perceptions, which, as has been shown, are possible only through the reality of outer objects. All that we have here sought to prove is that inner experience in general is possible only through outer experience in general. Whether this or that supposed experience be not purely imaginary, must be ascertained from its special determinations, and through its congruence with the criteria of all real experience.

Lastly, as regards the third postulate, it concerns material necessity in existence, and not merely formal and logical necessity in the connection of concepts. Since the existence of any object of the senses cannot be known completely a priori, but only comparatively a priori, relatively to some other previously given existence; and since, even so, we can then arrive only at such an existence as must somewhere be contained in the context of the experience, of which the given perception is a part, the necessity of existence can never be known from concepts, but always only from connection with that which is perceived, in accordance with universal laws of experience. Now there is no existence that can be known as necessary under the condition of other given appearances, save the existence of effects from given causes, in accordance with laws of causality. It is not, therefore, the existence of things (substances) that we can know to be necessary, but only the existence of their state; and this necessity of the existence of their state we can know only from other states, which are given in perception, in accordance with empirical laws of causality. It therefore follows that the criterion of necessity lies solely in the law of possible experience, the law that everything which happens is determined a priori through its cause in the [field of] appearance. We thus know the necessity only of those effects in nature the causes of which are given to us, and the character of necessity in existence extends no further than the field of possible experience, and even in this field is not applicable to the existence of things as substances, since substances can never be viewed as empirical effects—that is, as happening and coming to be. Necessity concerns only the relations of appearances in conformity with the dynamical law of causality and the possibility grounded upon it of inferring a priori from a given existence (a cause) to another existence (the effect). That everything which happens is hypothetically necessary is a principle which subordinates alteration in the world to a law, that is, to a rule of necessary existence, without which there would be nothing that could be entitled nature. The proposition that nothing happens through blind chance (in mundo non datur casus) is therefore an a priori law of nature. So also is the proposition that no necessity in nature is blind, but always a conditioned and therefore intelligible necessity (non datur fatum). Both are laws through which the play of alterations is rendered subject to a nature of things (that is, of things as appearances), or what amounts to the same thing, to the unity of understanding, in which alone they can belong to one experience, that is, to the synthetic unity of appearances. Both belong to the class of dynamical principles. The first is really a consequence of the principle of causality, and so belongs to the analogies of experience. The second is a principle of modality; but this modality, while adding the concept of necessity to causal determination, itself stands under a rule of understanding. The principle of continuity forbids any leap in the series of appearances, that is, of alterations (in mundo non datur saltus); it also forbids, in respect of the sum of all empirical intuitions in space, any gaps or cleft between two appearances (non datur hiatus); for so we may express the proposition, that nothing which proves a vacuum, or which even admits it as a part of empirical synthesis, can enter into experience. As regards a void which may be conceived to lie beyond the field of possible experience, that is, outside the world, such a question does not come within the jurisdiction of the mere understanding—which decides only upon questions that concern the use to be made of given appearances for the obtaining of empirical knowledge. It is a problem for that ideal reason which goes out beyond the sphere of a possible experience and seeks to judge of that which surrounds and limits it; and is a problem which will therefore have to be considered in the Transcendental Dialectic. These four propositions (in mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum), like all principles of transcendental origin, we can easily exhibit in their order, that is, in accordance with the order of the categories, and so assign to each its proper place. But the reader has now had sufficient practice to allow of his doing this for himself, or of easily discovering the guiding principle for so doing. They are all entirely at one in this, that they allow of nothing in the empirical synthesis which may do violence or detriment to the understanding and to the continuous connection of all appearances—that is, to the unity of the concepts of the understanding. For in the understanding alone is possible the unity of experience, in which all perceptions must have their place.

To enquire whether the field of possibility is larger than the field which contains all actuality, and this latter, again, larger than the sum of that which is necessary, is to raise somewhat subtle questions which demand a synthetic solution and yet come under the jurisdiction of reason alone. For they are tantamount to the enquiry whether things as appearances one and all belong to the sum and context of a single experience, of which every given perception is a part, a part which therefore cannot be connected with any other [series of] appearances, or whether my perceptions can belong, in their general connection, to more than one possible experience. The understanding, in accordance with the subjective and formal conditions of sensibility as well as of apperception, prescribes a priori to experience in general the rules which alone make experience possible. Other forms of intuition than space and time, other forms of understanding than the discursive forms of thought, or of knowledge through concepts, even if they should be possible, we cannot render in any way conceivable and comprehensible to ourselves; and even assuming that we could do so, they still would not belong to experience—the only kind of knowledge in which objects are given to us. Whether other perceptions than those belonging to our whole possible experience, and therefore a quite different field of matter, may exist, the understanding is not in a position to decide. It can deal only with the synthesis of that which is given. Moreover, the poverty of the customary inferences through which we throw open a great realm of possibility, of which all that is actual (the objects of experience) is only a small part, is patently obvious. Everything actual is possible; from this proposition there naturally follows, in accordance with the logical rules of conversion, the merely particular proposition, that some possible is actual; and this would seem to mean that much is possible which is not actual. It does indeed seem as if we were justified in extending the number of possible things beyond that of the actual, on the ground that something must be added to the possible to constitute the actual. But this [alleged] process of adding to the possible I refuse to allow. For that which would have to be added to the possible, over and above the possible, would be impossible What can be added is only a relation to my understanding, namely, that in addition to agreement with the formal conditions of experience there should be connection with some perception. But whatever is connected with perception in accordance with empirical laws is actual, even although it is not immediately perceived. That yet another series of appearances in thoroughgoing connection with that which is given in perception, and consequently that more than one all-embracing experience is possible, cannot be inferred from what is given; and still less can any such inference be drawn independently of anything being given—since without material nothing whatsoever can be thought. What is possible only under conditions which themselves are merely possible is not in all respects possible. But such [absolute] possibility is in question when it is asked whether the possibility of things extends further than experience can reach.

I have made mention of these questions only in order to omit nothing which is ordinarily reckoned among the concepts of understanding. But as a matter of fact absolute possibility, that which is in all respects valid, is no mere concept of understanding, and can never be employed empirically. It belongs exclusively to reason, which transcends all possible empirical employment of the understanding. We have therefore had to content ourselves with some merely critical remarks; the matter must otherwise be left in obscurity until we come to the proper occasion for its further treatment.

Before concluding this fourth section, and therewith the system of all principles of pure understanding, I must explain why I have entitled the principles of modality postulates. I interpret this expression not in the sense which some recent philosophical writers, wresting it from its proper mathematical significance, have given to it, namely, that to postulate should mean to treat a proposition as immediately certain, without justification or proof. For if, in dealing with synthetic propositions, we are to recognise them as possessing unconditioned validity, independently of deduction, on the evidence [merely] of their own claims, then no matter how evident they may be, all critique of understanding is given up. And since there is no lack of audacious pretensions, and these are supported by common belief (though that is no credential of their truth), the understanding lies open to every fancy, and is in no position to withhold approval of those assertions which, though illegitimate, yet press upon us, in the same confident tone, their claims to be accepted as actual axioms. Whenever, therefore, an a priori determination is synthetically added to the concept of a thing, it is indispensable that, if not a proof, at least a deduction of the legitimacy of such an assertion should be supplied.

The principles of modality are not, however, objectively synthetic. For the predicates of possibility, actuality, and necessity do not in the least enlarge the concept of which they are affirmed, adding something to the representation of the object. But since they are none the less synthetic, they are so subjectively only, that is, they add to the concept of a thing (of something real), of which otherwise they say nothing, the cognitive faculty from which it springs and in which it has its seat. Thus if it is in connection only with the formal conditions of experience, and so merely in the understanding, its object is called possible. If it stands in connection with perception, that is, with sensation as material supplied by the senses, and through perception is determined by means of the understanding, the object is actual. If it is determined through the connection of perceptions according to concepts, the object is entitled necessary. The principles of modality thus predicate of a concept nothing but the action of the faculty of knowledge through which it is generated. Now in mathematics a postulate means the practical proposition which contains nothing save the synthesis through which we first give ourselves an object and generate its concept—for instance, with a given line, to describe a circle on a plane from a given point. Such a proposition cannot be proved, since the procedure which it demands is exactly that through which we first generate the concept of such a figure. With exactly the same right we may postulate the principles of modality, since they do not increase our concept of things, but only show the manner in which it is connected with the faculty of knowledge.

That the possibility of a thing cannot be determined from the category alone, and that in order to exhibit the objective reality of the pure concept of understanding we must always have an intuition, is a very noteworthy fact. Take, for instance, the categories of relation. We cannot determine from mere concepts how (1) something can exist as subject only, and not as a mere determination of other things, that is, how a thing can be substance, or (2) how, because something is, something else must be, and how, therefore, a thing can be a cause, or (3) when several things exist, how because one of them is there, something follows in regard to the others and vice versa, and how in this way there can be a community of substances. This likewise applies to the other categories; for example, how a thing can be equal to a number of things taken together, that is, can be a quantity. So long as intuition is lacking, we do not know whether through the categories we are thinking an object, and whether indeed there can anywhere be an object suited to them. In all these ways, then, we obtain confirmation that the categories are not in themselves knowledge, but are merely forms of thought for the making of knowledge from given intuitions.

For the same reason it follows that no synthetic proposition can be made from mere categories. For instance, we are not in a position to say that in all existence there is substance, that is, something which can exist only as subject and not as mere predicate; or that everything is a quantum, etc. For if intuition be lacking, there is nothing which can enable us to go out beyond a given concept, and to connect another with it. No one, therefore, has ever yet succeeded in proving a synthetic proposition merely from pure concepts of the understanding—as, for instance, that everything which exists contingently has a cause. We can never get further than proving, that without this relation we are unable to comprehend the existence of the contingent, that is, are unable a priori through the understanding to know the existence of such a thing—from which it does not, however, follow that this is also a condition of the possibility of the things themselves. If the reader will go back to our proof of the principle of causality—that everything which happens, that is, every event, presupposes a cause—he will observe that we were able to prove it only of objects of possible experience; and even so, not from pure concepts, but only as a principle of the possibility of experience, and therefore of the knowledge of an object given in empirical intuition. We cannot, indeed, deny that the proposition, that everything contingent must have a cause, is patent to everyone from mere concepts. But the concept of the contingent is then being apprehended as containing, not the category of modality (as something the not-being of which can be thought), but that of relation (as something which can exist only as consequence of something else); and it is then, of course, an identical proposition—that which can exist only as consequence has a cause. As a matter of fact, when we are required to cite examples of contingent existence, we invariably have recourse to alterations, and not merely to the possibility of entertaining the opposite in thought! Now alteration is an event which, as such, is possible only through a cause, and the not-being of which is therefore in itself possible. In other words, we recognise contingency in and through the fact that something can exist only as the effect of a cause; and if, therefore, a thing is assumed to be contingent, it is an analytic proposition to say that it has a cause.

But it is an even more noteworthy fact, that in order to understand the possibility of things in conformity with the categories, and so to demonstrate the objective reality of the latter, we need, not merely intuitions, but intuitions that are in all cases outer intuitions. When, for instance, we take the pure concepts of relation, we find, firstly, that in order to obtain something permanent in intuition corresponding to the concept of substance, and so to demonstrate the objective reality of this concept, we require an intuition in space (of matter). For space alone is determined as permanent, while time, and therefore everything that is in inner sense, is in constant flux. Secondly, in order to exhibit alteration as the intuition corresponding to the concept of causality, we must take as our example motion, that is, alteration in space. Only in this way can we obtain the intuition of alterations, the possibility of which can never be comprehended through any pure understanding. For alteration is combination of contradictorily opposed determinations in the existence of one and the same thing. Now how it is possible that from a given state of a thing an opposite state should follow, not only cannot be conceived by reason without an example, but is actually incomprehensible to reason without intuition. The intuition required is the intuition of the movement of a point in space. The presence of the point in different locations (as a sequence of opposite determinations) is what alone first yields to us an intuition of alteration. For in order that we may afterwards make inner alterations likewise thinkable, we must represent time (the form of inner sense) figuratively as a line, and the inner alteration through the drawing of this line (motion), and so in this manner by means of outer intuition make comprehensible the successive existence of ourselves in different states. The reason of this is that all alteration, if it is to be perceived as alteration, presupposes something permanent in intuition, and that in inner sense no permanent intuition is to be met with. Lastly, the possibility of the category of community cannot be comprehended through mere reason alone; and consequently its objective reality is only to be determined through intuition, and indeed through outer intuition in space. For how are we to think it to be possible, when several substances exist, that, from the existence of one, something (as effect) can follow in regard to the existence of the others, and vice versa; in other words, that because there is something in the one there must also in the others be something which is not to be understood solely from the existence of these others? For this is what is required in order that there be community; community is not conceivable as holding between things each of which, through its subsistence, stands in complete isolation. Leibniz, in attributing to the substances of the world, as thought through the understanding alone, a community, had therefore to resort to the mediating intervention of a Deity. For, as he justly recognised, a community of substances is utterly inconceivable as arising simply from their existence. We can, however, render the possibility of community—of substances as appearances—perfectly comprehensible, if we represent them to ourselves in space, that is, in outer intuition. For this already contains in itself a priori formal outer relations as conditions of the possibility of the real relations of action and reaction, and therefore of the possibility of community.

Similarly, it can easily be shown that the possibility of things as quantities, and therefore the objective reality of quantity, can be exhibited only in outer intuition, and that only through the mediation of outer intuition can it be applied also to inner sense. But, to avoid prolixity, I must leave the reader to supply his own examples of this.

These remarks are of great importance, not only in confirmation of our previous refutation of idealism, but even more, when we come to treat of self-knowledge by mere inner consciousness, that is, by determination of our nature without the aid of outer empirical intuitions—as showing us the limits of the possibility of this kind of knowledge.

The final outcome of this whole section is therefore this: all principles of the pure understanding are nothing more than principles a priori of the possibility of experience, and to experience alone do all a priori synthetic propositions relate—indeed, their possibility itself rests entirely on this relation.