English (NKS 1929): Section I. Space — §2, §3 and the Conclusions
By means of outer sense, a property of our mind, we repre-sent to ourselves objects as outside us, and all without excep-tion in space. In space their shape, magnitude, and relation toone another are determined or determinable. Inner sense,by means of which the mind intuits itself or its inner state,yields indeed no intuition of the soul itself as an object; butthere is nevertheless a determinate form [namely, time] inwhich alone the intuition of inner states is possible, and every-thing which belongs to inner determinations is thereforerepresented in relations of time. Time cannot be outwardlyintuited, any more than space can be intuited as somethingin us. What, then, are space and time? Are they real exist-ences? Are they only determinations or relations of things, yetsuch as would belong to things even if they were not intuited?Or are space and time such that they belong only to the formof intuition, and therefore to the subjective constitution of ourmind, apart from which they could not be ascribed to anythingwhatsoever? In order to obtain light upon these questions,let us first give an exposition of the concept of space. Byexposition (expositio) I mean the clear, though not necessarilyexhaustive, representation of that which belongs to a concept:the exposition is metaphysical when it contains that whichexhibits the concept as given a priori.
1. Space is not an empirical concept which has been de-rived from outer experiences. For in order that certain sensa-tions be referred to something outside me (that is, to somethingin another region of space from that in which I find myself),and similarly in order that I may be able to represent them asoutside and alongside one another, and accordingly as notonly different but as in different places, the representation ofspace must be presupposed. The representation of space can-not, therefore, be empirically obtained from the relations ofouter appearance. On the contrary, this outer experience isitself possible at all only through that representation.
2. Space is a necessary a priori representation, whichunderlies all outer intuitions. We can never represent to our-selves the absence of space, though we can quite well think itas empty of objects. It must therefore be regarded as the con-dition of the possibility of appearances, and not as a determina-tion dependent upon them. It is an a priori representation,which necessarily underlies outer appearances.
3. Space is not a discursive or, as we say, general conceptof relations of things in general, but a pure intuition. For, in thefirst place, we can represent to ourselves only one space; andif we speak of diverse spaces, we mean thereby only parts ofone and the same unique space. Secondly, these parts cannotprecede the one all-embracing space, as being, as it were,constituents out of which it can be composed; on the contrary,they can be thought only as in it. Space is essentially one;the manifold in it, and therefore the general concept of spaces,depends solely on [the introduction of] limitations. Hence itfollows that an a priori, and not an empirical, intuition under-lies all concepts of space. For kindred reasons, geometricalpropositions, that, for instance, in a triangle two sidestogether are greater than the third, can never be derivedfrom the general concepts of line and triangle, but onlyfrom intuition, and this indeed a priori, with apodeicticcertainty.
4. Space is represented as an infinite given magnitude.Now every concept must be thought as a representationwhich is contained in an infinite number of different possiblerepresentations (as their common character), and whichtherefore contains these under itself; but no concept, as such,can be thought as containing an infinite number of representa-tions within itself. It is in this latter way, however, that spaceis thought; for all the parts of space coexist ad infinitum.Consequently, the original representation of space is an apriori intuition, not a concept.
I understand by a transcendental exposition the explana-tion of a concept, as a principle from which the possibilityof other a priori synthetic knowledge can be understood.For this purpose it is required (1) that such knowledge doesreally flow from the given concept, (2) that this knowledge ispossible only on the assumption of a given mode of explainingthe concept.Geometry is a science which determines the propertiesof space synthetically, and yet a priori. What, then, must beour representation of space, in order that such knowledgeof it may be possible? It must in its origin be intuition; forfrom a mere concept no propositions can be obtained whichgo beyond the concept — as happens in geometry (Introduc-tion, V). Further, this intuition must be a priori, that is,it must be found in us prior to any perception of an object,and must therefore be pure, not empirical, intuition. Forgeometrical propositions are one and all apodeictic, that is,are bound up with the consciousness of their necessity; forinstance, that space has only three dimensions. Such pro-positions cannot be empirical or, in other words, judgmentsof experience, nor can they be derived from any such judg-ments (Introduction, II).How, then, can there exist in the mind an outer intui-tion which precedes the objects themselves, and in whichthe concept of these objects can be determined a priori?Manifestly, not otherwise than in so far as the intuition hasits seat in the subject only, as the formal character of thesubject, in virtue of which, in being affected by objects, itobtains immediate representation, that is, intuition, of them;and only in so far, therefore, as it is merely the form of outersense in general.Our explanation is thus the only explanation that makesintelligible the possibility of geometry, as a body of a priorisynthetic knowledge. Any mode of explanation which fails todo this, although it may otherwise seem to be somewhatsimilar, can by this criterion be distinguished from it withthe greatest certainty.
(a) Space does not represent any property of things inthemselves, nor does it represent them in their relation toone another. That is to say, space does not represent anydetermination that attaches to the objects themselves, andwhich remains even when abstraction has been made of allthe subjective conditions of intuition. For no determina-tions, whether absolute or relative, can be intuited prior tothe existence of the things to which they belong, and none,therefore, can be intuited a priori.
(b) Space is nothing but the form of all appearancesof outer sense. It is the subjective condition of sensibility,under which alone outer intuition is possible for us. Since,then, the receptivity of the subject, its capacity to be affectedby objects, must necessarily precede all intuitions of theseobjects, it can readily be understood how the form of allappearances can be given prior to all actual perceptions, andso exist in the mind a priori, and how, as a pure intuition, inwhich all objects must be determined, it can contain, priorto all experience, principles which determine the relationsof these objects.It is, therefore, solely from the human standpoint thatwe can speak of space, of extended things, etc. If we departfrom the subjective condition under which alone we can haveouter intuition, namely, liability to be affected by objects,the representation of space stands for nothing whatsoever.This predicate can be ascribed to things only in so far as theyappear to us, that is, only to objects of sensibility. The con-stant form of this receptivity, which we term sensibility, is anecessary condition of all the relations in which objects canbe intuited as outside us; and if we abstract from theseobjects, it is a pure intuition, and bears the name of space.Since we cannot treat the special conditions of sensibility asconditions of the possibility of things, but only of their appear-ances, we can indeed say that space comprehends all thingsthat appear to us as external, but not all things in themselves,by whatever subject they are intuited, or whether they beintuited or not. For we cannot judge in regard to the intui-tions of other thinking beings, whether they are bound bythe same conditions as those which limit our intuition andwhich for us are universally valid. If we add to the concept ofthe subject of a judgment the limitation under which the judg-ment is made, the judgment is then unconditionally valid.The proposition, that all things are side by side in space, isvalid under the limitation that these things are viewed asobjects of our sensible intuition. If, now, I add the conditionto the concept, and say that all things, as outer appearances,are side by side in space, the rule is valid universally andwithout limitation. Our exposition therefore establishes thereality, that is, the objective validity, of space in respect ofwhatever can be presented to us outwardly as object, but alsoat the same time the ideality of space in respect of things whenthey are considered in themselves through reason, that is,without regard to the constitution of our sensibility. Weassert, then, the empirical reality of space, as regards allpossible outer experience; and yet at the same time weassert its transcendental ideality — in other words, that itis nothing at all, immediately we withdraw the above con-dition, namely, its limitation to possible experience, and solook upon it as something that underlies things in them-selves.With the sole exception of space there is no subjectiverepresentation, referring to something outer, which could beentitled [at once] objective [and] a priori. For there is no othersubjective representation from which we can derive a priorisynthetic propositions, as we can from intuition in space (§3).Strictly speaking, therefore, these other representations have noideality, although they agree with the representation of space inthis respect, that they belong merely to the subjective constitu-tion of our manner of sensibility, for instance, of sight, hearing,touch, as in the case of the sensations of colours, sounds, andheat, which, since they are mere sensations and not intuitions,do not of themselves yield knowledge of any object, least ofall any a priori knowledge.The above remark is intended only to guard anyone fromsupposing that the ideality of space as here asserted can beillustrated by examples so altogether insufficient as colours,taste, etc. For these cannot rightly be regarded as propertiesof things, but only as changes in the subject, changes whichmay, indeed, be different for different men. In such examplesas these, that which originally is itself only appearance, forinstance, a rose, is being treated by the empirical understand-ing as a thing in itself, which, nevertheless, in respect of itscolour, can appear differently to every observer. The tran-scendental concept of appearances in space, on the other hand,is a critical reminder that nothing intuited in space is a thingin itself, that space is not a form inhering in things in themselvesas their intrinsic property, that objects in themselves arequite unknown to us, and that what we call outer objects arenothing but mere representations of our sensibility, the formof which is space. The true correlate of sensibility, the thingin itself, is not known, and cannot be known, through theserepresentations; and in experience no question is ever askedin regard to it.