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like the preceding is quite foreign to its true purpose. The

misunderstanding arises in this way. We first of all separate a

predicate of a thing from the conception of the thing, and

afterwards connect with this predicate its opposite, and hence do

not establish any contradiction with the subject, but only with its

predicate, which has been conjoined with the subject synthetically-

a contradiction, moreover, which obtains only when the first and

second predicate are affirmed in the same time. If I say: "A man who

is ignorant is not learned," the condition "at the same time" must

be added, for he who is at one time ignorant, may at another be

learned. But if I say: "No ignorant man is a learned man," the

proposition is analytical, because the characteristic ignorance is now

a constituent part of the conception of the subject; and in this

case the negative proposition is evident immediately from the

proposition of contradiction, without the necessity of adding the

condition "the same time." This is the reason why I have altered the

formula of this principle- an alteration which shows very clearly

the nature of an analytical proposition.

SECTION II. Of the Supreme Principle of all Synthetical Judgements.

The explanation of the possibility of synthetical judgements is a

task with which general logic has nothing to do; indeed she needs

not even be acquainted with its name. But in transcendental logic it

is the most important matter to be dealt with- indeed the only one, if

the question is of the possibility of synthetical judgements a priori,

the conditions and extent of their validity. For when this question is

fully decided, it can reach its aim with perfect ease, the

determination, to wit, of the extent and limits of the pure

understanding.

In an analytical judgement I do not go beyond the given

conception, in order to arrive at some decision respecting it. If

the judgement is affirmative, I predicate of the conception only

that which was already cogitated in it; if negative, I merely

exclude from the conception its contrary. But in synthetical

judgements, I must go beyond the given conception, in order to

cogitate, in relation with it, something quite different from that

which was cogitated in it, a relation which is consequently never

one either of identity or contradiction, and by means of which the

truth or error of the judgement cannot be discerned merely from the

judgement itself.

Granted, then, that we must go out beyond a given conception, in

order to compare it synthetically with another, a third thing is

necessary, in which alone the synthesis of two conceptions can

originate. Now what is this tertium quid that is to be the medium of

all synthetical judgements? It is only a complex in which all our

representations are contained, the internal sense to wit, and its form

a priori, time.

The synthesis of our representations rests upon the imagination;

their synthetical unity (which is requisite to a judgement), upon

the unity of apperception. In this, therefore, is to be sought the

possibility of synthetical judgements, and as all three contain the

sources of a priori representations, the possibility of pure

synthetical judgements also; nay, they are necessary upon these

grounds, if we are to possess a knowledge of objects, which rests

solely upon the synthesis of representations.

If a cognition is to have objective reality, that is, to relate to

an object, and possess sense and meaning in respect to it, it is

necessary that the object be given in some way or another. Without

this, our conceptions are empty, and we may indeed have thought by

means of them, but by such thinking we have not, in fact, cognized

anything, we have merely played with representation. To give an

object, if this expression be understood in the sense of "to

present" the object, not mediately but immediately in intuition, means

nothing else than to apply the representation of it to experience,

be that experience real or only possible. Space and time themselves,

pure as these conceptions are from all that is empirical, and

certain as it is that they are represented fully a priori in the mind,

would be completely without objective validity, and without sense

and significance, if their necessary use in the objects of

experience were not shown. Nay, the representation of them is a mere

schema, that always relates to the reproductive imagination, which

calls up the objects of experience, without which they have no

meaning. And so it is with all conceptions without distinction.

The possibility of experience is, then, that which gives objective

reality to all our a priori cognitions. Now experience depends upon

the synthetical unity of phenomena, that is, upon a synthesis

according to conceptions of the object of phenomena in general, a

synthesis without which experience never could become knowledge, but

would be merely a rhapsody of perceptions, never fitting together into

any connected text, according to rules of a thoroughly united

(possible) consciousness, and therefore never subjected to the

transcendental and necessary unity of apperception. Experience has

therefore for a foundation, a priori principles of its form, that is

to say, general rules of unity in the synthesis of phenomena, the

objective reality of which rules, as necessary conditions even of

the possibility of experience can which rules, as necessary

conditions- even of the possibility of experience- can always be shown

in experience. But apart from this relation, a priori synthetical

propositions are absolutely impossible, because they have no third

term, that is, no pure object, in which the synthetical unity can

exhibit the objective reality of its conceptions.

Although, then, respecting space, or the forms which productive

imagination describes therein, we do cognize much a priori in

synthetical judgements, and are really in no need of experience for

this purpose, such knowledge would nevertheless amount to nothing

but a busy trifling with a mere chimera, were not space to be

considered as the condition of the phenomena which constitute the

material of external experience. Hence those pure synthetical

judgements do relate, though but mediately, to possible experience, or

rather to the possibility of experience, and upon that alone is

founded the objective validity of their synthesis.

While then, on the one hand, experience, as empirical synthesis,

is the only possible mode of cognition which gives reality to all

other synthesis; on the other hand, this latter synthesis, as

cognition a priori, possesses truth, that is, accordance with its

object, only in so far as it contains nothing more than what is

necessary to the synthetical unity of experience.

Accordingly, the supreme principle of all synthetical judgements is:

"Every object is subject to the necessary conditions of the

synthetical unity of the manifold of intuition in a possible

experience."

A priori synthetical judgements are possible when we apply the

formal conditions of the a priori intuition, the synthesis of the

imagination, and the necessary unity of that synthesis in a

transcendental apperception, to a possible cognition of experience,

and say: "The conditions of the possibility of experience in general

are at the same time conditions of the possibility of the objects of

experience, and have, for that reason, objective validity in an a

priori synthetical judgement."

SECTION III. Systematic Representation of all Synthetical

Principles of the Pure Understanding.

That principles exist at all is to be ascribed solely to the pure

understanding, which is not only the faculty of rules in regard to

that which happens, but is even the source of principles according

to which everything that can be presented to us as an object is

necessarily subject to rules, because without such rules we never

could attain to cognition of an object. Even the laws of nature, if

they are contemplated as principles of the empirical use of the

understanding, possess also a characteristic of necessity, and we

may therefore at least expect them to be determined upon grounds which

are valid a priori and antecedent to all experience. But all laws of

nature, without distinction, are subject to higher principles of the

understanding, inasmuch as the former are merely applications of the

latter to particular cases of experience. These higher principles

alone therefore give the conception, which contains the necessary

condition, and, as it were, the exponent of a rule; experience, on the

other hand, gives the case which comes under the rule.

There is no danger of our mistaking merely empirical principles

for principles of the pure understanding, or conversely; for the

character of necessity, according to conceptions which distinguish the

latter, and the absence of this in every empirical proposition, how

extensively valid soever it may be, is a perfect safeguard against

confounding them. There are, however, pure principles a priori,

which nevertheless I should not ascribe to the pure understanding- for

this reason, that they are not derived from pure conceptions, but

(although by the mediation of the understanding) from pure intuitions.

But understanding is the faculty of conceptions. Such principles

mathematical science possesses, but their application to experience,

consequently their objective validity, nay the possibility of such a

priori synthetical cognitions (the deduction thereof) rests entirely

upon the pure understanding.

On this account, I shall not reckon among my principles those of

mathematics; though I shall include those upon the possibility and

objective validity a priori, of principles of the mathematical

science, which, consequently, are to be looked upon as the principle

of these, and which proceed from conceptions to intuition, and not

from intuition to conceptions.

In the application of the pure conceptions of the understanding to

possible experience, the employment of their synthesis is either

mathematical or dynamical, for it is directed partly on the

intuition alone, partly on the existence of a phenomenon. But the a

priori conditions of intuition are in relation to a possible

experience absolutely necessary, those of the existence of objects

of a possible empirical intuition are in themselves contingent.

Hence the principles of the mathematical use of the categories will

possess a character of absolute necessity, that is, will be

apodeictic; those, on the other hand, of the dynamical use, the

character of an a priori necessity indeed, but only under the

condition of empirical thought in an experience, therefore only

mediately and indirectly. Consequently they will not possess that

immediate evidence which is peculiar to the former, although their

application to experience does not, for that reason, lose its truth

and certitude. But of this point we shall be better able to judge at

the conclusion of this system of principles.

The table of the categories is naturally our guide to the table of

principles, because these are nothing else than rules for the

objective employment of the former. Accordingly, all principles of the

pure understanding are:

1

Axioms

of Intuition

2 3

Anticipations Analogies

of Perception of Experience

4

Postulates of

Empirical Thought

in general

These appellations I have chosen advisedly, in order that we might

not lose sight of the distinctions in respect of the evidence and

the employment of these principles. It will, however, soon appear

that- a fact which concerns both the evidence of these principles, and

the a priori determination of phenomena- according to the categories

of quantity and quality (if we attend merely to the form of these),

the principles of these categories are distinguishable from those of

the two others, in as much as the former are possessed of an

intuitive, but the latter of a merely discursive, though in both

instances a complete, certitude. I shall therefore call the former

mathematical, and the latter dynamical principles.* It must be

observed, however, that by these terms I mean just as little in the

one case the principles of mathematics as those of general

(physical) dynamics in the other. I have here in view merely the

principles of the pure understanding, in their application to the

internal sense (without distinction of the representations given

therein), by means of which the sciences of mathematics and dynamics

become possible. Accordingly, I have named these principles rather

with reference to their application than their content; and I shall

now proceed to consider them in the order in which they stand in the

table.

*All combination (conjunctio) is either composition (compositio)

or connection (nexus). The former is the synthesis of a manifold,

the parts of which do not necessarily belong to each other. For

example, the two triangles into which a square is divided by a

diagonal, do not necessarily belong to each other, and of this kind is

the synthesis of the homogeneous in everything that can be

mathematically considered. This synthesis can be divided into those of

aggregation and coalition, the former of which is applied to

extensive, the latter to intensive quantities. The second sort of

combination (nexus) is the synthesis of a manifold, in so far as its

parts do belong necessarily to each other; for example, the accident

to a substance, or the effect to the cause. Consequently it is a

synthesis of that which though heterogeneous, is represented as

connected a priori. This combination- not an arbitrary one- I

entitle dynamical because it concerns the connection of the