第 7 页

recognize the conception of cause although not contained in it, yet as

belonging to it, and even necessarily? what is here the unknown = X,

upon which the understanding rests when it believes it has found,

out of the conception A a foreign predicate B, which it nevertheless

considers to be connected with it? It cannot be experience, because

the principle adduced annexes the two representations, cause and

effect, to the representation existence, not only with universality,

which experience cannot give, but also with the expression of

necessity, therefore completely a priori and from pure conceptions.

Upon such synthetical, that is augmentative propositions, depends

the whole aim of our speculative knowledge a priori; for although

analytical judgements are indeed highly important and necessary,

they are so, only to arrive at that clearness of conceptions which

is requisite for a sure and extended synthesis, and this alone is a

real acquisition.

V. In all Theoretical Sciences of Reason, Synthetical Judgements

"a priori" are contained as Principles.

1. Mathematical judgements are always synthetical. Hitherto this

fact, though incontestably true and very important in its

consequences, seems to have escaped the analysts of the human mind,

nay, to be in complete opposition to all their conjectures. For as

it was found that mathematical conclusions all proceed according to

the principle of contradiction (which the nature of every apodeictic

certainty requires), people became persuaded that the fundamental

principles of the science also were recognized and admitted in the

same way. But the notion is fallacious; for although a synthetical

proposition can certainly be discerned by means of the principle of

contradiction, this is possible only when another synthetical

proposition precedes, from which the latter is deduced, but never of

itself which

Before all, be it observed, that proper mathematical propositions

are always judgements a priori, and not empirical, because they

carry along with them the conception of necessity, which cannot be

given by experience. If this be demurred to, it matters not; I will

then limit my assertion to pure mathematics, the very conception of

which implies that it consists of knowledge altogether non-empirical

and a priori.

We might, indeed at first suppose that the proposition 7 + 5 = 12 is

a merely analytical proposition, following (according to the principle

of contradiction) from the conception of a sum of seven and five.

But if we regard it more narrowly, we find that our conception of

the sum of seven and five contains nothing more than the uniting of

both sums into one, whereby it cannot at all be cogitated what this

single number is which embraces both. The conception of twelve is by

no means obtained by merely cogitating the union of seven and five;

and we may analyse our conception of such a possible sum as long as we

will, still we shall never discover in it the notion of twelve. We

must go beyond these conceptions, and have recourse to an intuition

which corresponds to one of the two- our five fingers, for example, or

like Segner in his Arithmetic five points, and so by degrees, add

the units contained in the five given in the intuition, to the

conception of seven. For I first take the number 7, and, for the

conception of 5 calling in the aid of the fingers of my hand as

objects of intuition, I add the units, which I before took together to

make up the number 5, gradually now by means of the material image

my hand, to the number 7, and by this process, I at length see the

number 12 arise. That 7 should be added to 5, I have certainly

cogitated in my conception of a sum = 7 + 5, but not that this sum was

equal to 12. Arithmetical propositions are therefore always

synthetical, of which we may become more clearly convinced by trying

large numbers. For it will thus become quite evident that, turn and

twist our conceptions as we may, it is impossible, without having

recourse to intuition, to arrive at the sum total or product by

means of the mere analysis of our conceptions. just as little is any

principle of pure geometry analytical. "A straight line between two

points is the shortest," is a synthetical proposition. For my

conception of straight contains no notion of quantity, but is merely

qualitative. The conception of the shortest is therefore fore wholly

an addition, and by no analysis can it be extracted from our

conception of a straight line. Intuition must therefore here lend

its aid, by means of which, and thus only, our synthesis is possible.

Some few principles preposited by geometricians are, indeed,

really analytical, and depend on the principle of contradiction.

They serve, however, like identical propositions, as links in the

chain of method, not as principles- for example, a = a, the whole is

equal to itself, or (a+b) > a, the whole is greater than its part. And

yet even these principles themselves, though they derive their

validity from pure conceptions, are only admitted in mathematics

because they can be presented in intuition. What causes us here

commonly to believe that the predicate of such apodeictic judgements

is already contained in our conception, and that the judgement is

therefore analytical, is merely the equivocal nature of the

expression. We must join in thought a certain predicate to a given

conception, and this necessity cleaves already to the conception.

But the question is, not what we must join in thought to the given

conception, but what we really think therein, though only obscurely,

and then it becomes manifest that the predicate pertains to these

conceptions, necessarily indeed, yet not as thought in the

conception itself, but by virtue of an intuition, which must be

added to the conception.

2. The science of natural philosophy (physics) contains in itself

synthetical judgements a priori, as principles. I shall adduce two

propositions. For instance, the proposition, "In all changes of the

material world, the quantity of matter remains unchanged"; or, that,

"In all communication of motion, action and reaction must always be

equal." In both of these, not only is the necessity, and therefore

their origin a priori clear, but also that they are synthetical

propositions. For in the conception of matter, I do not cogitate its

permanency, but merely its presence in space, which it fills. I

therefore really go out of and beyond the conception of matter, in

order to think on to it something a priori, which I did not think in

it. The proposition is therefore not analytical, but synthetical,

and nevertheless conceived a priori; and so it is with regard to the

other propositions of the pure part of natural philosophy.

3. As to metaphysics, even if we look upon it merely as an attempted

science, yet, from the nature of human reason, an indispensable one,

we find that it must contain synthetical propositions a priori. It

is not merely the duty of metaphysics to dissect, and thereby

analytically to illustrate the conceptions which we form a priori of

things; but we seek to widen the range of our a priori knowledge.

For this purpose, we must avail ourselves of such principles as add

something to the original conception- something not identical with,

nor contained in it, and by means of synthetical judgements a

priori, leave far behind us the limits of experience; for example,

in the proposition, "the world must have a beginning," and such

like. Thus metaphysics, according to the proper aim of the science,

consists merely of synthetical propositions a priori.

VI. The Universal Problem of Pure Reason.

It is extremely advantageous to be able to bring a number of

investigations under the formula of a single problem. For in this

manner, we not only facilitate our own labour, inasmuch as we define

it clearly to ourselves, but also render it more easy for others to

decide whether we have done justice to our undertaking. The proper

problem of pure reason, then, is contained in the question: "How are

synthetical judgements a priori possible?"

That metaphysical science has hitherto remained in so vacillating

a state of uncertainty and contradiction, is only to be attributed

to the fact that this great problem, and perhaps even the difference

between analytical and synthetical judgements, did not sooner

suggest itself to philosophers. Upon the solution of this problem,

or upon sufficient proof of the impossibility of synthetical knowledge

a priori, depends the existence or downfall of the science of

metaphysics. Among philosophers, David Hume came the nearest of all to

this problem; yet it never acquired in his mind sufficient

precision, nor did he regard the question in its universality. On

the contrary, he stopped short at the synthetical proposition of the

connection of an effect with its cause (principium causalitatis),

insisting that such proposition a priori was impossible. According

to his conclusions, then, all that we term metaphysical science is a

mere delusion, arising from the fancied insight of reason into that

which is in truth borrowed from experience, and to which habit has

given the appearance of necessity. Against this assertion, destructive

to all pure philosophy, he would have been guarded, had he had our

problem before his eyes in its universality. For he would then have

perceived that, according to his own argument, there likewise could

not be any pure mathematical science, which assuredly cannot exist

without synthetical propositions a priori- an absurdity from which his

good understanding must have saved him.

In the solution of the above problem is at the same time

comprehended the possibility of the use of pure reason in the

foundation and construction of all sciences which contain

theoretical knowledge a priori of objects, that is to say, the

answer to the following questions:

How is pure mathematical science possible?

How is pure natural science possible?

Respecting these sciences, as they do certainly exist, it may with

propriety be asked, how they are possible?- for that they must be

possible is shown by the fact of their really existing.* But as to

metaphysics, the miserable progress it has hitherto made, and the fact

that of no one system yet brought forward, far as regards its true

aim, can it be said that this science really exists, leaves any one at

liberty to doubt with reason the very possibility of its existence.

*As to the existence of pure natural science, or physics, perhaps

many may still express doubts. But we have only to look at the

different propositions which are commonly treated of at the

commencement of proper (empirical) physical science- those, for

example, relating to the permanence of the same quantity of matter,

the vis inertiae, the equality of action and reaction, etc.- to be

soon convinced that they form a science of pure physics (physica pura,

or rationalis), which well deserves to be separately exposed as a

special science, in its whole extent, whether that be great or

confined.

Yet, in a certain sense, this kind of knowledge must

unquestionably be looked upon as given; in other words, metaphysics

must be considered as really existing, if not as a science,

nevertheless as a natural disposition of the human mind (metaphysica

naturalis). For human reason, without any instigations imputable to

the mere vanity of great knowledge, unceasingly progresses, urged on

by its own feeling of need, towards such questions as cannot be

answered by any empirical application of reason, or principles derived

therefrom; and so there has ever really existed in every man some

system of metaphysics. It will always exist, so soon as reason

awakes to the exercise of its power of speculation. And now the

question arises: "How is metaphysics, as a natural disposition,

possible?" In other words, how, from the nature of universal human

reason, do those questions arise which pure reason proposes to itself,

and which it is impelled by its own feeling of need to answer as

well as it can?

But as in all the attempts hitherto made to answer the questions

which reason is prompted by its very nature to propose to itself,

for example, whether the world had a beginning, or has existed from

eternity, it has always met with unavoidable contradictions, we must

not rest satisfied with the mere natural disposition of the mind to

metaphysics, that is, with the existence of the faculty of pure

reason, whence, indeed, some sort of metaphysical system always

arises; but it must be possible to arrive at certainty in regard to

the question whether we know or do not know the things of which

metaphysics treats. We must be able to arrive at a decision on the

subjects of its questions, or on the ability or inability of reason to

form any judgement respecting them; and therefore either to extend

with confidence the bounds of our pure reason, or to set strictly

defined and safe limits to its action. This last question, which

arises out of the above universal problem, would properly run thus:

"How is metaphysics possible as a science?"

Thus, the critique of reason leads at last, naturally and

necessarily, to science; and, on the other hand, the dogmatical use of

reason without criticism leads to groundless assertions, against which

others equally specious can always be set, thus ending unavoidably

in scepticism.

Besides, this science cannot be of great and formidable prolixity,

because it has not to do with objects of reason, the variety of

which is inexhaustible, but merely with Reason herself and her

problems; problems which arise out of her own bosom, and are not

proposed to her by the nature of outward things, but by her own

nature. And when once Reason has previously become able completely

to understand her own power in regard to objects which she meets

with in experience, it will be easy to determine securely the extent

and limits of her attempted application to objects beyond the confines

of experience.