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in most cases, to that which is asserted of a proposition which

holds good in all; as, for example, in the affirmation, "All bodies

are heavy." When, on the contrary, strict universality characterizes a

judgement, it necessarily indicates another peculiar source of

knowledge, namely, a faculty of cognition a priori. Necessity and

strict universality, therefore, are infallible tests for

distinguishing pure from empirical knowledge, and are inseparably

connected with each other. But as in the use of these criteria the

empirical limitation is sometimes more easily detected than the

contingency of the judgement, or the unlimited universality which we

attach to a judgement is often a more convincing proof than its

necessity, it may be advisable to use the criteria separately, each

being by itself infallible.

Now, that in the sphere of human cognition we have judgements

which are necessary, and in the strictest sense universal,

consequently pure a priori, it will be an easy matter to show. If we

desire an example from the sciences, we need only take any proposition

in mathematics. If we cast our eyes upon the commonest operations of

the understanding, the proposition, "Every change must have a

cause," will amply serve our purpose. In the latter case, indeed,

the conception of a cause so plainly involves the conception of a

necessity of connection with an effect, and of a strict universality

of the law, that the very notion of a cause would entirely

disappear, were we to derive it, like Hume, from a frequent

association of what happens with that which precedes; and the habit

thence originating of connecting representations- the necessity

inherent in the judgement being therefore merely subjective.

Besides, without seeking for such examples of principles existing a

priori in cognition, we might easily show that such principles are the

indispensable basis of the possibility of experience itself, and

consequently prove their existence a priori. For whence could our

experience itself acquire certainty, if all the rules on which it

depends were themselves empirical, and consequently fortuitous? No

one, therefore, can admit the validity of the use of such rules as

first principles. But, for the present, we may content ourselves

with having established the fact, that we do possess and exercise a

faculty of pure a priori cognition; and, secondly, with having pointed

out the proper tests of such cognition, namely, universality and

necessity.

Not only in judgements, however, but even in conceptions, is an a

priori origin manifest. For example, if we take away by degrees from

our conceptions of a body all that can be referred to mere sensuous

experience- colour, hardness or softness, weight, even

impenetrability- the body will then vanish; but the space which it

occupied still remains, and this it is utterly impossible to

annihilate in thought. Again, if we take away, in like manner, from

our empirical conception of any object, corporeal or incorporeal,

all properties which mere experience has taught us to connect with it,

still we cannot think away those through which we cogitate it as

substance, or adhering to substance, although our conception of

substance is more determined than that of an object. Compelled,

therefore, by that necessity with which the conception of substance

forces itself upon us, we must confess that it has its seat in our

faculty of cognition a priori.

III. Philosophy stands in need of a Science which shall

Determine the Possibility, Principles, and Extent of

Human Knowledge "a priori"

Of far more importance than all that has been above said, is the

consideration that certain of our cognitions rise completely above the

sphere of all possible experience, and by means of conceptions, to

which there exists in the whole extent of experience no

corresponding object, seem to extend the range of our judgements

beyond its bounds. And just in this transcendental or supersensible

sphere, where experience affords us neither instruction nor

guidance, lie the investigations of reason, which, on account of their

importance, we consider far preferable to, and as having a far more

elevated aim than, all that the understanding can achieve within the

sphere of sensuous phenomena. So high a value do we set upon these

investigations, that even at the risk of error, we persist in

following them out, and permit neither doubt nor disregard nor

indifference to restrain us from the pursuit. These unavoidable

problems of mere pure reason are God, freedom (of will), and

immortality. The science which, with all its preliminaries, has for

its especial object the solution of these problems is named

metaphysics- a science which is at the very outset dogmatical, that

is, it confidently takes upon itself the execution of this task

without any previous investigation of the ability or inability of

reason for such an undertaking.

Now the safe ground of experience being thus abandoned, it seems

nevertheless natural that we should hesitate to erect a building

with the cognitions we possess, without knowing whence they come,

and on the strength of principles, the origin of which is

undiscovered. Instead of thus trying to build without a foundation, it

is rather to be expected that we should long ago have put the

question, how the understanding can arrive at these a priori

cognitions, and what is the extent, validity, and worth which they may

possess? We say, "This is natural enough," meaning by the word

natural, that which is consistent with a just and reasonable way of

thinking; but if we understand by the term, that. which usually

happens, nothing indeed could be more natural and more

comprehensible than that this investigation should be left long

unattempted. For one part of our pure knowledge, the science of

mathematics, has been long firmly established, and thus leads us to

form flattering expectations with regard to others, though these may

be of quite a different nature. Besides, when we get beyond the bounds

of experience, we are of course safe from opposition in that

quarter; and the charm of widening the range of our knowledge is so

great that, unless we are brought to a standstill by some evident

contradiction, we hurry on undoubtingly in our course. This,

however, may be avoided, if we are sufficiently cautious in the

construction of our fictions, which are not the less fictions on

that account.

Mathematical science affords us a brilliant example, how far,

independently of all experience, we may carry our a priori

knowledge. It is true that the mathematician occupies himself with

objects and cognitions only in so far as they can be represented by

means of intuition. But this circumstance is easily overlooked,

because the said intuition can itself be given a priori, and therefore

is hardly to be distinguished from a mere pure conception. Deceived by

such a proof of the power of reason, we can perceive no limits to

the extension of our knowledge. The light dove cleaving in free flight

the thin air, whose resistance it feels, might imagine that her

movements would be far more free and rapid in airless space. just in

the same way did Plato, abandoning the world of sense because of the

narrow limits it sets to the understanding, venture upon the wings

of ideas beyond it, into the void space of pure intellect. He did

not reflect that he made no real progress by all his efforts; for he

met with no resistance which might serve him for a support, as it

were, whereon to rest, and on which he might apply his powers, in

order to let the intellect acquire momentum for its progress. It is,

indeed, the common fate of human reason in speculation, to finish

the imposing edifice of thought as rapidly as possible, and then for

the first time to begin to examine whether the foundation is a solid

one or no. Arrived at this point, all sorts of excuses are sought

after, in order to console us for its want of stability, or rather,

indeed, to enable Us to dispense altogether with so late and dangerous

an investigation. But what frees us during the process of building

from all apprehension or suspicion, and flatters us into the belief of

its solidity, is this. A great part, perhaps the greatest part, of the

business of our reason consists in the analysation of the

conceptions which we already possess of objects. By this means we gain

a multitude of cognitions, which although really nothing more than

elucidations or explanations of that which (though in a confused

manner) was already thought in our conceptions, are, at least in

respect of their form, prized as new introspections; whilst, so far as

regards their matter or content, we have really made no addition to

our conceptions, but only disinvolved them. But as this process does

furnish a real priori knowledge, which has a sure progress and

useful results, reason, deceived by this, slips in, without being

itself aware of it, assertions of a quite different kind; in which, to

given conceptions it adds others, a priori indeed, but entirely

foreign to them, without our knowing how it arrives at these, and,

indeed, without such a question ever suggesting itself. I shall

therefore at once proceed to examine the difference between these

two modes of knowledge.

IV. Of the Difference Between Analytical and Synthetical Judgements.

In all judgements wherein the relation of a subject to the predicate

is cogitated (I mention affirmative judgements only here; the

application to negative will be very easy), this relation is

possible in two different ways. Either the predicate B belongs to

the subject A, as somewhat which is contained (though covertly) in the

conception A; or the predicate B lies completely out of the conception

A, although it stands in connection with it. In the first instance,

I term the judgement analytical, in the second, synthetical.

Analytical judgements (affirmative) are therefore those in which the

connection of the predicate with the subject is cogitated through

identity; those in which this connection is cogitated without

identity, are called synthetical judgements. The former may be

called explicative, the latter augmentative judgements; because the

former add in the predicate nothing to the conception of the

subject, but only analyse it into its constituent conceptions, which

were thought already in the subject, although in a confused manner;

the latter add to our conceptions of the subject a predicate which was

not contained in it, and which no analysis could ever have

discovered therein. For example, when I say, "All bodies are

extended," this is an analytical judgement. For I need not go beyond

the conception of body in order to find extension connected with it,

but merely analyse the conception, that is, become conscious of the

manifold properties which I think in that conception, in order to

discover this predicate in it: it is therefore an analytical

judgement. On the other hand, when I say, "All bodies are heavy,"

the predicate is something totally different from that which I think

in the mere conception of a body. By the addition of such a predicate,

therefore, it becomes a synthetical judgement.

Judgements of experience, as such, are always synthetical. For it

would be absurd to think of grounding an analytical judgement on

experience, because in forming such a judgement I need not go out of

the sphere of my conceptions, and therefore recourse to the

testimony of experience is quite unnecessary. That "bodies are

extended" is not an empirical judgement, but a proposition which

stands firm a priori. For before addressing myself to experience, I

already have in my conception all the requisite conditions for the

judgement, and I have only to extract the predicate from the

conception, according to the principle of contradiction, and thereby

at the same time become conscious of the necessity of the judgement, a

necessity which I could never learn from experience. On the other

hand, though at first I do not at all include the predicate of

weight in my conception of body in general, that conception still

indicates an object of experience, a part of the totality of

experience, to which I can still add other parts; and this I do when I

recognize by observation that bodies are heavy. I can cognize

beforehand by analysis the conception of body through the

characteristics of extension, impenetrability, shape, etc., all

which are cogitated in this conception. But now I extend my knowledge,

and looking back on experience from which I had derived this

conception of body, I find weight at all times connected with the

above characteristics, and therefore I synthetically add to my

conceptions this as a predicate, and say, "All bodies are heavy." Thus

it is experience upon which rests the possibility of the synthesis

of the predicate of weight with the conception of body, because both

conceptions, although the one is not contained in the other, still

belong to one another (only contingently, however), as parts of a

whole, namely, of experience, which is itself a synthesis of

intuitions.

But to synthetical judgements a priori, such aid is entirely

wanting. If I go out of and beyond the conception A, in order to

recognize another B as connected with it, what foundation have I to

rest on, whereby to render the synthesis possible? I have here no

longer the advantage of looking out in the sphere of experience for

what I want. Let us take, for example, the proposition, "Everything

that happens has a cause." In the conception of "something that

happens," I indeed think an existence which a certain time

antecedes, and from this I can derive analytical judgements. But the

conception of a cause lies quite out of the above conception, and

indicates something entirely different from "that which happens,"

and is consequently not contained in that conception. How then am I

able to assert concerning the general conception- "that which

happens"- something entirely different from that conception, and to