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conjoined a priori in one conception, conformably to the unity of

apperception.

Without entering upon a dry and tedious analysis of the essential

requisites of transcendental schemata of the pure conceptions of the

understanding, we shall rather proceed at once to give an

explanation of them according to the order of the categories, and in

connection therewith.

For the external sense the pure image of all quantities

(quantorum) is space; the pure image of all objects of sense in

general, is time. But the pure schema of quantity (quantitatis) as a

conception of the understanding, is number, a representation which

comprehends the successive addition of one to one (homogeneous

quantities). Thus, number is nothing else than the unity of the

synthesis of the manifold in a homogeneous intuition, by means of my

generating time itself in my apprehension of the intuition.

Reality, in the pure conception of the understanding, is that

which corresponds to a sensation in general; that, consequently, the

conception of which indicates a being (in time). Negation is that

the conception of which represents a not-being (in time). The

opposition of these two consists therefore in the difference of one

and the same time, as a time filled or a time empty. Now as time is

only the form of intuition, consequently of objects as phenomena, that

which in objects corresponds to sensation is the transcendental matter

of all objects as things in themselves (Sachheit, reality). Now

every sensation has a degree or quantity by which it can fill time,

that is to say, the internal sense in respect of the representation of

an object, more or less, until it vanishes into nothing (= 0 =

negatio). Thus there is a relation and connection between reality

and negation, or rather a transition from the former to the latter,

which makes every reality representable to us as a quantum; and the

schema of a reality as the quantity of something in so far as it fills

time, is exactly this continuous and uniform generation of the reality

in time, as we descend in time from the sensation which has a

certain degree, down to the vanishing thereof, or gradually ascend

from negation to the quantity thereof.

The schema of substance is the permanence of the real in time;

that is, the representation of it as a substratum of the empirical

determination of time; a substratum which therefore remains, whilst

all else changes. (Time passes not, but in it passes the existence

of the changeable. To time, therefore, which is itself unchangeable

and permanent, corresponds that which in the phenomenon is

unchangeable in existence, that is, substance, and it is only by it

that the succession and coexistence of phenomena can be determined

in regard to time.)

The schema of cause and of the causality of a thing is the real

which, when posited, is always followed by something else. It

consists, therefore, in the succession of the manifold, in so far as

that succession is subjected to a rule.

The schema of community (reciprocity of action and reaction), or the

reciprocal causality of substances in respect of their accidents, is

the coexistence of the determinations of the one with those of the

other, according to a general rule.

The schema of possibility is the accordance of the synthesis of

different representations with the conditions of time in general

(as, for example, opposites cannot exist together at the same time

in the same thing, but only after each other), and is therefore the

determination of the representation of a thing at any time.

The schema of reality is existence in a determined time.

The schema of necessity is the existence of an object in all time.

It is clear, from all this, that the schema of the category of

quantity contains and represents the generation (synthesis) of time

itself, in the successive apprehension of an object; the schema of

quality the synthesis of sensation with the representation of time, or

the filling up of time; the schema of relation the relation of

perceptions to each other in all time (that is, according to a rule of

the determination of time): and finally, the schema of modality and

its categories, time itself, as the correlative of the determination

of an object- whether it does belong to time, and how. The schemata,

therefore, are nothing but a priori determinations of time according

to rules, and these, in regard to all possible objects, following

the arrangement of the categories, relate to the series in time, the

content in time, the order in time, and finally, to the complex or

totality in time.

Hence it is apparent that the schematism of the understanding, by

means of the transcendental synthesis of the imagination, amounts to

nothing else than the unity of the manifold of intuition in the

internal sense, and thus indirectly to the unity of apperception, as a

function corresponding to the internal sense (a receptivity). Thus,

the schemata of the pure conceptions of the understanding are the true

and only conditions whereby our understanding receives an

application to objects, and consequently significance. Finally,

therefore, the categories are only capable of empirical use,

inasmuch as they serve merely to subject phenomena to the universal

rules of synthesis, by means of an a priori necessary unity (on

account of the necessary union of all consciousness in one original

apperception); and so to render them susceptible of a complete

connection in one experience. But within this whole of possible

experience lie all our cognitions, and in the universal relation to

this experience consists transcendental truth, which antecedes all

empirical truth, and renders the latter possible.

It is, however, evident at first sight, that although the schemata

of sensibility are the sole agents in realizing the categories, they

do, nevertheless, also restrict them, that is, they limit the

categories by conditions which lie beyond the sphere of understanding-

namely, in sensibility. Hence the schema is properly only the

phenomenon, or the sensuous conception of an object in harmony with

the category. (Numerus est quantitas phaenomenon- sensatio realitas

phaenomenon; constans et perdurabile rerum substantia phaenomenon-

aeternitas, necessitas, phaenomena, etc.) Now, if we remove a

restrictive condition, we thereby amplify, it appears, the formerly

limited conception. In this way, the categories in their pure

signification, free from all conditions of sensibility, ought to be

valid of things as they are, and not, as the schemata represent

them, merely as they appear; and consequently the categories must have

a significance far more extended, and wholly independent of all

schemata. In truth, there does always remain to the pure conceptions

of the understanding, after abstracting every sensuous condition, a

value and significance, which is, however, merely logical. But in this

case, no object is given them, and therefore they have no meaning

sufficient to afford us a conception of an object. The notion of

substance, for example, if we leave out the sensuous determination

of permanence, would mean nothing more than a something which can be

cogitated as subject, without the possibility of becoming a

predicate to anything else. Of this representation I can make nothing,

inasmuch as it does not indicate to me what determinations the thing

possesses which must thus be valid as premier subject. Consequently,

the categories, without schemata are merely functions of the

understanding for the production of conceptions, but do not

represent any object. This significance they derive from

sensibility, which at the same time realizes the understanding and

restricts it.

CHAPTER II. System of all Principles of the Pure Understanding.

In the foregoing chapter we have merely considered the general

conditions under which alone the transcendental faculty of judgement

is justified in using the pure conceptions of the understanding for

synthetical judgements. Our duty at present is to exhibit in

systematic connection those judgements which the understanding

really produces a priori. For this purpose, our table of the

categories will certainly afford us the natural and safe guidance. For

it is precisely the categories whose application to possible

experience must constitute all pure a priori cognition of the

understanding; and the relation of which to sensibility will, on

that very account, present us with a complete and systematic catalogue

of all the transcendental principles of the use of the understanding.

Principles a priori are so called, not merely because they contain

in themselves the grounds of other judgements, but also because they

themselves are not grounded in higher and more general cognitions.

This peculiarity, however, does not raise them altogether above the

need of a proof. For although there could be found no higher

cognition, and therefore no objective proof, and although such a

principle rather serves as the foundation for all cognition of the

object, this by no means hinders us from drawing a proof from the

subjective sources of the possibility of the cognition of an object.

Such a proof is necessary, moreover, because without it the

principle might be liable to the imputation of being a mere gratuitous

assertion.

In the second place, we shall limit our investigations to those

principles which relate to the categories. For as to the principles of

transcendental aesthetic, according to which space and time are the

conditions of the possibility of things as phenomena, as also the

restriction of these principles, namely, that they cannot be applied

to objects as things in themselves- these, of course, do not fall

within the scope of our present inquiry. In like manner, the

principles of mathematical science form no part of this system,

because they are all drawn from intuition, and not from the pure

conception of the understanding. The possibility of these

principles, however, will necessarily be considered here, inasmuch

as they are synthetical judgements a priori, not indeed for the

purpose of proving their accuracy and apodeictic certainty, which is

unnecessary, but merely to render conceivable and deduce the

possibility of such evident a priori cognitions.

But we shall have also to speak of the principle of analytical

judgements, in opposition to synthetical judgements, which is the

proper subject of our inquiries, because this very opposition will

free the theory of the latter from all ambiguity, and place it clearly

before our eyes in its true nature.

SYSTEM OF THE PRINCIPLES OF THE PURE UNDERSTANDING.

SECTION I. Of the Supreme Principle of all Analytical Judgements.

Whatever may be the content of our cognition, and in whatever manner

our cognition may be related to its object, the universal, although

only negative conditions of all our judgements is that they do not

contradict themselves; otherwise these judgements are in themselves

(even without respect to the object) nothing. But although there may

exist no contradiction in our judgement, it may nevertheless connect

conceptions in such a manner that they do not correspond to the

object, or without any grounds either a priori or a posteriori for

arriving at such a judgement, and thus, without being

self-contradictory, a judgement may nevertheless be either false or

groundless.

Now, the proposition: "No subject can have a predicate that

contradicts it," is called the principle of contradiction, and is a

universal but purely negative criterion of all truth. But it belongs

to logic alone, because it is valid of cognitions, merely as

cognitions and without respect to their content, and declares that the

contradiction entirely nullifies them. We can also, however, make a

positive use of this principle, that is, not merely to banish

falsehood and error (in so far as it rests upon contradiction), but

also for the cognition of truth. For if the judgement is analytical,

be it affirmative or negative, its truth must always be recognizable

by means of the principle of contradiction. For the contrary of that

which lies and is cogitated as conception in the cognition of the

object will be always properly negatived, but the conception itself

must always be affirmed of the object, inasmuch as the contrary

thereof would be in contradiction to the object.

We must therefore hold the principle of contradiction to be the

universal and fully sufficient Principle of all analytical

cognition. But as a sufficient criterion of truth, it has no further

utility or authority. For the fact that no cognition can be at

variance with this principle without nullifying itself, constitutes

this principle the sine qua non, but not the determining ground of the

truth of our cognition. As our business at present is properly with

the synthetical part of our knowledge only, we shall always be on

our guard not to transgress this inviolable principle; but at the same

time not to expect from it any direct assistance in the

establishment of the truth of any synthetical proposition.

There exists, however, a formula of this celebrated principle- a

principle merely formal and entirely without content- which contains a

synthesis that has been inadvertently and quite unnecessarily mixed up

with it. It is this: "It is impossible for a thing to be and not to be

at the same time." Not to mention the superfluousness of the

addition of the word impossible to indicate the apodeictic

certainty, which ought to be self-evident from the proposition itself,

the proposition is affected by the condition of time, and as it were

says: "A thing = A, which is something = B, cannot at the same time be

non-B." But both, B as well as non-B, may quite well exist in

succession. For example, a man who is young cannot at the same time be

old; but the same man can very well be at one time young, and at

another not young, that is, old. Now the principle of contradiction as

a merely logical proposition must not by any means limit its

application merely to relations of time, and consequently a formula