Front Page Titles (by Subject) Section I: Of Space - Critique of Pure Reason
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Section I: Of Space - Friedrich Max Müller, Critique of Pure Reason 
Immanuel Kant’s Critique of Pure Reason. In Commemoration of the Centenary of its First Publication. Translated into English by F. Max Mueller (2nd revised ed.) (New York: Macmillan, 1922).
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By means of our external sense, a property of our mind (Gemüth), we represent to ourselves objects as external or outside ourselves, and all of these in space. It is within space that their form, size, and relative position are fixed or can be fixed. The internal sense by means of which the mind perceives itself or its internal state, does not give an intuition (Anschauung) of the soul (Seele) itself, as an object, but it is nevertheless a fixed form under which alone an intuition of its internal state is [p. 23] possible, so that whatever belongs to its internal determinations (Bestimmungen) must be represented in relations of time. Time cannot be perceived (angeschaut) externally, as little as space can be perceived as something within us.
What then are space and time? Are they real beings? Or, if not that, are they determinations or relations of things, but such as would belong to them even if they were not perceived? Or lastly, are they determinations and relations which are inherent in the form of intuition only, and therefore in the subjective nature of our mind, without which such predicates as space and time would never be ascribed to anything?
In order to understand this more clearly, let us first consider space.
1. Space is not an empirical concept which has been derived from external experience. For in order that certain sensations should be referred to something outside myself, i.e. to something in a different part of space from that where I am; again, in order that I may be able to represent them (vorstellen) as side by side, that is, not only as different, but as in different places, the representation (Vorstellung) of space must already be there. Therefore the representation of space cannot be borrowed through experience from relations of external phenomena, but, on the contrary, this external experience becomes possible only by means of the representation of space.
2. Space is a necessary representation a priori, forming the very foundation of all external intuitions. [p. 24] It is impossible to imagine that there should be no space, though one might very well imagine that there should be space without objects to fill it. Space is therefore regarded as a condition of the possibility of phenomena, not as a determination produced by them; it is a representation a priori which necessarily precedes all external phenomena.
[3. On this necessity of an a priori representation of space rests the apodictic certainty of all geometrical principles, and the possibility of their construction a priori. For if the intuition of space were a concept gained a posteriori, borrowed from general external experience, the first principles of mathematical definition would be nothing but perceptions. They would be exposed to all the accidents of perception, and there being but one straight line between two points would not be a necessity, but only something taught in each case by experience. Whatever is derived from experience possesses a relative generality only, based on induction. We should therefore not be able to say more than that, so far as hitherto observed, no space has yet been found having more than three dimensions.]
4. Space is not a discursive or so-called general [p. 25] concept of the relations of things in general, but a pure intuition. For, first of all, we can imagine one space only and if we speak of many spaces, we mean parts only of one and the same space. Nor can these parts be considered as antecedent to the one and all-embracing space and, as it were, its component parts out of which an aggregate is formed, but they can be thought of as existing within it only. Space is essentially one; its multiplicity, and therefore the general concept of spaces in general, arises entirely from limitations. Hence it follows that, with respect to space, an intuition a priori, which is not empirical, must form the foundation of all conceptions of space. In the same manner all geometrical principles, e.g. ‘that in every triangle two sides together are greater than the third,’ are never to be derived from the general concepts of side and triangle, but from an intuition, and that a priori, with apodictic certainty.
[5. Space is represented as an infinite quantity. Now a general concept of space, which is found in a foot as well as in an ell, could tell us nothing in respect to the quantity of the space. If there were not infinity in the progression of intuition, no concept of relations of space could ever contain a principle of infinity.1 ]
Conclusions from the Foregoing Concepts [p. 26]
a. Space does not represent any quality of objects by themselves, or objects in their relation to one another; i.e. space does not represent any determination which is inherent in the objects themselves, and would remain, even if all subjective conditions of intuition were removed. For no determinations of objects, whether belonging to them absolutely or in relation to others, can enter into our intuition before the actual existence of the objects themselves, that is to say, they can never be intuitions a priori.
b. Space is nothing but the form of all phenomena of the external senses; it is the subjective condition of our sensibility, without which no external intuition is possible for us. If then we consider that the receptivity of the subject, its capacity of being affected by objects, must necessarily precede all intuition of objects, we shall understand how the form of all phenomena may be given before all real perceptions, may be, in fact, a priori in the soul, and may, as a pure intuition, by which all objects must be determined, contain, prior to all experience, principles regulating their relations.
It is therefore from the human standpoint only that we can speak of space, extended objects, etc. If we drop the subjective condition under which alone we can gain external intuition, that is, so far as we ourselves may be affected by objects, the representation of space means nothing. For this predicate is applied to objects only in so far as they appear to us, and are objects of our [p. 27] senses. The constant form of this receptivity, which we call sensibility, is a necessary condition of all relations in which objects, as without us, can be perceived; and, when abstraction is made of these objects, what remains is that pure intuition which we call space. As the peculiar conditions of our sensibility cannot be looked upon as conditions of the possibility of the objects themselves, but only of their appearance as phenomena to us, we may say indeed that space comprehends all things which may appear to us externally, but not all things by themselves, whether perceived by us or not, or by any subject whatsoever. We cannot judge whether the intuitions of other thinking beings are subject to the same conditions which determine our intuition, and which for us are generally binding. If we add the limitation of a judgment to a subjective concept, the judgment gains absolute validity. The proposition ‘all things are beside each other in space,’ is valid only under the limitation that things are taken as objects of our sensuous intuition (Anschauung). If I add that limitation to the concept and say ‘all things, as external phenomena, are beside each other in space,’ the rule obtains universal and unlimited validity. Our discussions teach therefore the reality, i.e. the objective validity, of space with regard to all that can come to us externally [p. 28] as an object, but likewise the ideality of space with regard to things, when they are considered in themselves by our reason, and independent of the nature of our senses. We maintain the empirical reality of space, so far as every possible external experience is concerned, but at the same time its transcendental ideality; that is to say, we maintain that space is nothing, if we leave out of consideration the condition of a possible experience, and accept it as something on which things by themselves are in any way dependent.
With the exception of space there is no other subjective representation (Vorstellung) referring to something external, that would be called a priori objective. [This1 subjective condition of all external phenomena cannot therefore be compared to any other. The taste of wine does not belong to the objective determinations of wine, considered as an object, even as a phenomenal object, but to the peculiar nature of the sense belonging to the subject that tastes the wine. Colours are not qualities of a body, though inherent in its intuition, but they are likewise modifications only of the sense of sight, as it is affected in different ways by light. Space, on the contrary, as the very condition of external objects, is essential to their appearance or intuition. Taste and colour are by no means necessary conditions under which alone things [p. 29] can become to us objects of sensuous perception. They are connected with their appearance, as accidentally added effects only of our peculiar organisation. They are not therefore representations a priori, but are dependent on sensation (Empfindung), nay taste even on an affection (Gefühl) of pleasure and pain, which is the result of a sensation. No one can have a priori, an idea (Vorstellung) either of colour or of taste, but space refers to the pure form of intuition only, and involves no kind of sensation, nothing empirical; nay all kinds and determinations of space can and must be represented a priori, if concepts of forms and their relations are to arise. Through it alone is it possible that things should become external objects to us.]
My object in what I have said just now is only to prevent people from imagining that they can elucidate the ideality of space by illustrations which are altogether insufficient, such as colour, taste, etc., which should never be considered as qualities of things, but as modifications of the subject, and which therefore may be different with different people. For in this case that which originally is itself a phenomenon only, as for instance, a rose, is taken by the empirical understanding for a thing by itself, which nevertheless, with regard to colour, may appear [p. 30] different to every eye. The transcendental conception, on the contrary, of all phenomena in space, is a critical warning that nothing which is seen in space is a thing by itself, nor space a form of things supposed to belong to them by themselves, but that objects by themselves are not known to us at all, and that what we call external objects are nothing but representations of our senses, the form of which is space, and the true correlative of which, that is the thing by itself, is not known, nor can be known by these representations, nor do we care to know anything about it in our daily experience.1
[1 ]No. 5 (No. 4) is differently worded in the Second Edition; see Supplement VIII.
[1 ]This passage to ‘my object in what I have said’ is differently worded in the Second Edition; see Supplement IX.
[1 ]In the Second Edition the title is, Metaphysical exposition of the concept of time, with reference to par. 5, Transcendental exposition of the concept of time.