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namely, space and time. To the consideration of these we shall now

proceed.

SECTION I. Of Space.

SS 2. Metaphysical Exposition of this Conception.

By means of the external sense (a property of the mind), we

represent to ourselves objects as without us, and these all in

space. Herein alone are their shape, dimensions, and relations to each

other determined or determinable. The internal sense, by means of

which the mind contemplates itself or its internal state, gives,

indeed, no intuition of the soul as an object; yet there is

nevertheless a determinate form, under which alone the contemplation

of our internal state is possible, so that all which relates to the

inward determinations of the mind is represented in relations of time.

Of time we cannot have any external intuition, any more than we can

have an internal intuition of space. What then are time and space? Are

they real existences? Or, are they merely relations or

determinations of things, such, however, as would equally belong to

these things in themselves, though they should never become objects of

intuition; or, are they such as belong only to the form of

intuition, and consequently to the subjective constitution of the

mind, without which these predicates of time and space could not be

attached to any object? In order to become informed on these points,

we shall first give an exposition of the conception of space. By

exposition, I mean the clear, though not detailed, representation of

that which belongs to a conception; and an exposition is

metaphysical when it contains that which represents the conception

as given a priori.

1. Space is not a conception which has been derived from outward

experiences. For, in order that certain sensations may relate to

something without me (that is, to something which occupies a different

part of space from that in which I am); in like manner, in order

that I may represent them not merely as without, of, and near to

each other, but also in separate places, the representation of space

must already exist as a foundation. Consequently, the representation

of space cannot be borrowed from the relations of external phenomena

through experience; but, on the contrary, this external experience

is itself only possible through the said antecedent representation.

2. Space then is a necessary representation a priori, which serves

for the foundation of all external intuitions. We never can imagine or

make a representation to ourselves of the non-existence of space,

though we may easily enough think that no objects are found in it.

It must, therefore, be considered as the condition of the

possibility of phenomena, and by no means as a determination dependent

on them, and is a representation a priori, which necessarily

supplies the basis for external phenomena.

3. Space is no discursive, or as we say, general conception of the

relations of things, but a pure intuition. For, in the first place, we

can only represent to ourselves one space, and, when we talk of divers

spaces, we mean only parts of one and the same space. Moreover,

these parts cannot antecede this one all-embracing space, as the

component parts from which the aggregate can be made up, but can be

cogitated only as existing in it. Space is essentially one, and

multiplicity in it, consequently the general notion of spaces, of this

or that space, depends solely upon limitations. Hence it follows

that an a priori intuition (which is not empirical) lies at the root

of all our conceptions of space. Thus, moreover, the principles of

geometry- for example, that "in a triangle, two sides together are

greater than the third," are never deduced from general conceptions of

line and triangle, but from intuition, and this a priori, with

apodeictic certainty.

4. Space is represented as an infinite given quantity. Now every

conception must indeed be considered as a representation which is

contained in an infinite multitude of different possible

representations, which, therefore, comprises these under itself; but

no conception, as such, can be so conceived, as if it contained within

itself an infinite multitude of representations. Nevertheless, space

is so conceived of, for all parts of space are equally capable of

being produced to infinity. Consequently, the original

representation of space is an intuition a priori, and not a

conception.

SS 3. Transcendental Exposition of the Conception of Space.

By a transcendental exposition, I mean the explanation of a

conception, as a principle, whence can be discerned the possibility of

other synthetical a priori cognitions. For this purpose, it is

requisite, firstly, that such cognitions do really flow from the given

conception; and, secondly, that the said cognitions are only

possible under the presupposition of a given mode of explaining this

conception.

Geometry is a science which determines the properties of space

synthetically, and yet a priori. What, then, must be our

representation of space, in order that such a cognition of it may be

possible? It must be originally intuition, for from a mere conception,

no propositions can be deduced which go out beyond the conception, and

yet this happens in geometry. (Introd. V.) But this intuition must

be found in the mind a priori, that is, before any perception of

objects, consequently must be pure, not empirical, intuition. For

geometrical principles are always apodeictic, that is, united with the

consciousness of their necessity, as: "Space has only three

dimensions." But propositions of this kind cannot be empirical

judgements, nor conclusions from them. (Introd. II.) Now, how can an

external intuition anterior to objects themselves, and in which our

conception of objects can be determined a priori, exist in the human

mind? Obviously not otherwise than in so far as it has its seat in the

subject only, as the formal capacity of the subject's being affected

by objects, and thereby of obtaining immediate representation, that

is, intuition; consequently, only as the form of the external sense in

general.

Thus it is only by means of our explanation that the possibility

of geometry, as a synthetical science a priori, becomes

comprehensible. Every mode of explanation which does not show us

this possibility, although in appearance it may be similar to ours,

can with the utmost certainty be distinguished from it by these marks.

SS 4. Conclusions from the foregoing Conceptions.

(a) Space does Space does not represent any property of objects as

things in themselves, nor does it represent them in their relations to

each other; in other words, space does not represent to us any

determination of objects such as attaches to the objects themselves,

and would remain, even though all subjective conditions of the

intuition were abstracted. For neither absolute nor relative

determinations of objects can be intuited prior to the existence of

the things to which they belong, and therefore not a priori.

(b) Space is nothing else than the form of all phenomena of the

external sense, that is, the subjective condition of the

sensibility, under which alone external intuition is possible. Now,

because the receptivity or capacity of the subject to be affected by

objects necessarily antecedes all intuitions of these objects, it is

easily understood how the form of all phenomena can be given in the

mind previous to all actual perceptions, therefore a priori, and how

it, as a pure intuition, in which all objects must be determined,

can contain principles of the relations of these objects prior to

all experience.

It is therefore from the human point of view only that we can

speak of space, extended objects, etc. If we depart from the

subjective condition, under which alone we can obtain external

intuition, or, in other words, by means of which we are affected by

objects, the representation of space has no meaning whatsoever. This

predicate is only applicable to things in so far as they appear to us,

that is, are objects of sensibility. The constant form of this

receptivity, which we call sensibility, is a necessary condition of

all relations in which objects can be intuited as existing without us,

and when abstraction of these objects is made, is a pure intuition, to

which we give the name of space. It is clear that we cannot make the

special conditions of sensibility into conditions of the possibility

of things, but only of the possibility of their existence as far as

they are phenomena. And so we may correctly say that space contains

all which can appear to us externally, but not all things considered

as things in themselves, be they intuited or not, or by whatsoever

subject one will. As to the intuitions of other thinking beings, we

cannot judge whether they are or are not bound by the same

conditions which limit our own intuition, and which for us are

universally valid. If we join the limitation of a judgement to the

conception of the subject, then the judgement will possess

unconditioned validity. For example, the proposition, "All objects are

beside each other in space," is valid only under the limitation that

these things are taken as objects of our sensuous intuition. But if

I join the condition to the conception and say, "All things, as

external phenomena, are beside each other in space," then the rule

is valid universally, and without any limitation. Our expositions,

consequently, teach the reality (i.e., the objective validity) of

space in regard of all which can be presented to us externally as

object, and at the same time also the ideality of space in regard to

objects when they are considered by means of reason as things in

themselves, that is, without reference to the constitution of our

sensibility. We maintain, therefore, the empirical reality of space in

regard to all possible external experience, although we must admit its

transcendental ideality; in other words, that it is nothing, so soon

as we withdraw the condition upon which the possibility of all

experience depends and look upon space as something that belongs to

things in themselves.

But, with the exception of space, there is no representation,

subjective and ref erring to something external to us, which could

be called objective a priori. For there are no other subjective

representations from which we can deduce synthetical propositions a

priori, as we can from the intuition of space. (See SS 3.)

Therefore, to speak accurately, no ideality whatever belongs to these,

although they agree in this respect with the representation of

space, that they belong merely to the subjective nature of the mode of

sensuous perception; such a mode, for example, as that of sight, of

hearing, and of feeling, by means of the sensations of colour,

sound, and heat, but which, because they are only sensations and not

intuitions, do not of themselves give us the cognition of any

object, least of all, an a priori cognition. My purpose, in the

above remark, is merely this: to guard any one against illustrating

the asserted ideality of space by examples quite insufficient, for

example, by colour, taste, etc.; for these must be contemplated not as

properties of things, but only as changes in the subject, changes

which may be different in different men. For, in such a case, that

which is originally a mere phenomenon, a rose, for example, is taken

by the empirical understanding for a thing in itself, though to

every different eye, in respect of its colour, it may appear

different. On the contrary, the transcendental conception of phenomena

in space is a critical admonition, that, in general, nothing which

is intuited in space is a thing in itself, and that space is not a

form which belongs as a property to things; but that objects are quite

unknown to us in themselves, and what we call outward objects, are

nothing else but mere representations of our sensibility, whose form

is space, but whose real correlate, the thing in itself, is not

known by means of these representations, nor ever can be, but

respecting which, in experience, no inquiry is ever made.

SECTION II. Of Time.

SS 5 Metaphysical Exposition of this Conception.

1. Time is not an empirical conception. For neither coexistence

nor succession would be perceived by us, if the representation of time

did not exist as a foundation a priori. Without this presupposition we

could not represent to ourselves that things exist together at one and

the same time, or at different times, that is, contemporaneously, or

in succession.

2. Time is a necessary representation, lying at the foundation of

all our intuitions. With regard to phenomena in general, we cannot

think away time from them, and represent them to ourselves as out of

and unconnected with time, but we can quite well represent to

ourselves time void of phenomena. Time is therefore given a priori. In

it alone is all reality of phenomena possible. These may all be

annihilated in thought, but time itself, as the universal condition of

their possibility, cannot be so annulled.

3. On this necessity a priori is also founded the possibility of

apodeictic principles of the relations of time, or axioms of time in

general, such as: "Time has only one dimension," "Different times

are not coexistent but successive" (as different spaces are not

successive but coexistent). These principles cannot be derived from

experience, for it would give neither strict universality, nor

apodeictic certainty. We should only be able to say, "so common

experience teaches us," but not "it must be so." They are valid as

rules, through which, in general, experience is possible; and they

instruct us respecting experience, and not by means of it.

4. Time is not a discursive, or as it is called, general conception,

but a pure form of the sensuous intuition. Different times are

merely parts of one and the same time. But the representation which

can only be given by a single object is an intuition. Besides, the