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Immanuel Kant's Critique of Pure Reason,

translated by Norman Kemp Smith



THERE can be no doubt that all our knowledge begins with experience. For
how should our faculty of knowledge be awakened into action did not objects
affecting our senses partly of themselves produce representations, partly arouse
the activity of our understanding to compare these representations, and, by
combining or separating them, work up the raw material of the sensible
impressions into that knowledge of objects which is entitled experience? In the
order of time, therefore, we have no knowledge antecedent to experience, and
with experience all our knowledge begins.

But though all our knowledge begins with experience, it does not
follow that it all arises out of experience. For it [42] may well be that even our
empirical knowledge is made up of what we receive through impressions and
of what our own faculty of knowledge (sensible impressions serving merely as
the occasion) supplies from itself. If our faculty of knowledge makes any such
addition, it may be that we are not in a position to distinguish it from the raw
material, until with long practice of attention we have become skilled in
separating it. This, then, is a question which at least calls for closer
examination, and does not allow of any off-hand answer: -- whether there is
any knowledge that is thus independent of experience and even of all
impressions of the senses. Such knowledge is entitled a priori, and
distinguished from the [43] empirical, which has its sources a posteriori, that
is, in experience.

The expression 'a priori' does not, however, indicate with sufficient
precision the full meaning of our question. For it has been customary to say,
even of much knowledge that is derived from empirical sources, that we have it
or are capable of having it a priori, meaning thereby that we do not derive it
immediately from experience, but from a universal rule -- a rule which is itself,
however, borrowed by us from experience. Thus we would say of a man who
undermined the foundations of his house, that he might have known a priori
that it would fall, that is, that he need not have waited for the experience of its
actual falling. But still he could not know this completely a priori. For he had
first to learn through experience that bodies are heavy, and therefore fall when
their supports are withdrawn.

In what follows, therefore, we shall understand by a priori knowledge,
not knowledge independent of this or that experience, but knowledge
absolutely independent of all experience. Opposed to it is empirical
knowledge, which is knowledge possible only a posteriori, that is, through
experience. A priori modes of knowledge are entitled pure when there is no
admixture of anything empirical. Thus, for instance, the proposition, 'every
alteration has its cause', while an a priori proposition, is not a pure
proposition, because alteration is a concept which can be derived only from


What we here require is a criterion by which to distinguish with
certainty between pure and empirical knowledge. Experience teaches us that a
thing is so and so, but not that it cannot be otherwise. First, then, if we have a
proposition which in being thought is thought as necessary, it is an a priori
judgment; and if, besides, it is not derived from any proposition except one
which also has the validity of a necessary judgment, it is an absolutely a
priori judgment. Secondly, [44] experience never confers on its judgments true
or strict but only assumed and comparative universality, through induction.
We can properly only say, therefore, that so far as we have hitherto observed,
there is no exception to this or that rule. If, then, a judgment is thought with
strict universality, that is, in such manner that no exception is allowed as
possible, it is not derived from experience, but is valid absolutely a priori.
Empirical universality is only an arbitrary extension of a validity holding in
most cases to one which holds in all, for instance, in the proposition, 'all
bodies are heavy'. When, on the other hand, strict universality is essential to a
a judgment, this indicates a special source of knowledge, namely, a faculty of
a priori knowledge. Necessity and strict universality are thus sure criteria of
a priori knowledge, and are inseparable from one another. But since in the
employment of these criteria the contingency of judgments is sometimes more
easily shown than their empirical limitation, or, as sometimes also happens,
their unlimited universality can be more convincingly proved than their
necessity, it is advisable to use the two criteria separately, each by itself being

Now it is easy to show that there actually are in human knowledge
judgments which are necessary and in the strictest sense universal, and which
are therefore pure a priori judgments. If an example from the sciences be
desired, we have only to look to any of the propositions of mathematics; if we
seek an example from the understanding in its quite ordinary employment, the
proposition, 'every alteration must have a cause', will serve our purpose. In the
latter case, indeed, the very concept of a cause so manifestly contains the
concept of a necessity of connection with an effect and of the strict universality
of the rule, that the concept would be altogether lost if we attempted to derive
it, as Hume has done, from a repeated association of that which happens with
that which precedes, and from a custom of connecting representations, a
custom originating in this repeated association, and constituting therefore a
merely subjective necessity. Even without appealing [45] to such examples, it
is possible to show that pure a priori principles are indispensable for the
possibility of experience, and so to prove their existence a priori. For whence
could experience derive its certainty, if all the rules, according to which it
proceeds, were always themselves empirical, and therefore contingent? Such
rules could hardly be regarded as first principles. At present, however, we may
be content to have established the fact that our faculty of knowledge does have
a pure employment, and to have shown what are the criteria of such an

Such a priori origin is manifest in certain concepts, no less than in
judgments. If we remove from our empirical concept of a body, one by one,
every feature in it which is [merely] empirical, the color, the hardness or
softness, the weight, even the impenetrability, there still remains the space
which the body (now entirely vanished) occupied, and this cannot be removed.
Again, if we remove from our empirical concept of any object, corporeal or
incorporeal, all properties which experience has taught us, we yet cannot take
away that property through which the object is thought as substance or as
inhering in a substance (although this concept of substance is more
determinate than that of an object in general). Owing, therefore, to the
necessity with which this concept of substance forces itself upon us, we have no
option save to admit that it has its seat in our faculty of a priori knowledge.


But what is still more extraordinary than all the preceding is this, that
certain modes of knowledge leave the field of all possible experiences and have
the appearance of extending the scope of our judgments beyond all limits of
experience, and this by means of concepts to which no corresponding object
can ever be given in experience.

It is precisely by means of the latter modes of knowledge, in a realm
beyond the world of the senses, where experience [46] can yield neither
guidance nor correction, that our reason carries on those enquiries which
owing to their importance we consider to be far more excellent, and in their
purpose far more lofty, than all that the understanding can learn in the field of
appearances. Indeed we prefer to run every risk of error rather than desist from
such urgent enquiries, on the ground of their dubious character, or from
disdain and indifference. These unavoidable problems set by pure reason itself
are God, freedom, and immortality. The science which, with all its
preparations, is in its final intention directed solely to their solution is
metaphysics; and its procedure is at first dogmatic, that is, it confidently sets
itself to this task without any previous examination of the capacity or
incapacity of reason for so great an undertaking.

Now it does indeed seem natural that, as soon as we have left the
ground of experience, we should, through careful enquiries, assure ourselves as
to the foundations of any building that we propose to erect, not making use of
any knowledge that we possess without first determining whence it has come,
and not trusting to principles without knowing their origin. It is natural, that
is to say, that the question should first be considered, how the understanding
can arrive at all this knowledge a priori, and what extent, validity, and worth
it may have. Nothing, indeed, could be more natural, if by the term 'natural'
we signify what fittingly and reasonably ought to happen. But if we mean by
'natural' what ordinarily happens, then on the contrary nothing is more
natural and more intelligible than the fact that this enquiry has been so long
neglected. For one part of this knowledge, the mathematical, has long been of
established reliability, and so gives rise to a favorable presumption as regards
the other part, which may yet be of quite different nature. Besides, once we are
outside the circle of experience, we can be sure of not being contradicted by
experience. The charm of extending our knowledge is so great that nothing
short of encountering a direct contradiction can suffice to arrest us in our
course; and this can be avoided, if we are careful in our fabrications -- which
none the less will still remain fabrications. Mathematics gives us a shining
[47] example of how far, independently of experience, we can progress in a
priori knowledge. It does, indeed, occupy itself with objects and with
knowledge solely in so far as they allow of being exhibited in intuition. But
this circumstance is easily overlooked, since the intuition, in being thought,
can itself be given a priori, and is therefore hardly to be distinguished from a
bare and pure concept. Misled by such a proof of the power of reason, the
demand for the extension of knowledge recognizes no limits. The light dove,
cleaving the air in her free flight, and feeling its resistance, might imagine that
its flight would be still easier in empty space. It was thus that Plato left the
world of the senses, as setting too narrow limits to the understanding, and
ventured out beyond it on the wings of the ideas, in the empty space of the pure
understanding. He did not observe that with all his efforts he made no advance
-- meeting no resistance that might, as it were, serve as a support upon which
he could take a stand, to which he could apply his powers, and so set his
understanding in motion. It is, indeed, the common fate of human reason to
complete its speculative structures as speedily as may be, and only afterwards
to enquire whether the foundations are reliable. All sorts of excuses will then
be appealed to, in order to reassure us of their solidity, or rather indeed to
enable us to dispense altogether with so late and so dangerous an enquiry. But
what keeps us, during the actual building, free from all apprehension and
suspicion, and flatters us with a seeming thoroughness, is this other
circumstance, namely, that a great, perhaps the greatest, part of the business of
our reason consists in analysis of the concepts which we already have of
objects. This analysis supplies us with a considerable body of knowledge,
which, while nothing but explanation or elucidation of what has already been
thought in our concepts, though in a confused manner, is yet prized as being,
at least as regards its form, new insight. But so far as the matter or content is
concerned, there has been no extension of our previously possessed concepts,
but only an analysis of them. Since this procedure yields real knowledge a
priori, which [48] progresses in an assured and useful fashion, reason is so far
misled as surreptitiously to introduce, without itself being aware of so doing,
assertions of an entirely different order, in which it attaches to given concepts
others completely foreign to them, and moreover attaches them a priori. And
yet it is not known how reason can be in position to do this. Such a question is
never so much as thought of. I shall therefore at once proceed to deal with the
difference between these two kinds of knowledge.


In all judgments in which the relation of a subject to the predicate is
thought (I take into consideration affirmative judgments only, the subsequent
application to negative judgments being easily made), this relation is possible
in two different ways. Either the predicate to the subject A, as something
which is (covertly) contained in this concept A; or outside the concept A,
although it does indeed stand in connection with it. In the one case I entitle the
judgment analytic, in the other synthetic. Analytic judgments (affirmative) are
therefore those in which the connection of the predicate with the subject is
thought through identity; those in which this connection is thought without
identity should be entitled synthetic. The former, as adding nothing through
the predicate to the concept of the subject, but merely breaking it up into those
constituent concepts that have all along been thought in it, although
confusedly, can also be entitled explicative. The latter, on the other hand, add
to the concept of the subject a predicate which has not been in any wise
thought in it, and which no analysis could possibly extract from it; and they
may therefore be entitled ampliative. If I say, for instance, 'All bodies are
extended', this is an analytic judgment. For I do not require to go beyond the
concept which I connect with 'body' in order to find extension as bound up
with it. To [49] meet with this predicate, I have merely to analyze the concept,
that is, to become conscious to myself of the manifold which I always think in
that concept. The judgment is therefore analytic. But when I say, 'All bodies
are heavy', the predicate is something quite different from anything that I
think in the mere concept of body in general; and the addition of such a
predicate therefore yields a synthetic judgment.

{2} Judgments of experience, as such, are one and all synthetic. For it
would be absurd to found an analytic judgment on experience. Since, in
framing the judgment, I must not go outside my concept, there is no need to
appeal to the testimony of experience in its support. That a body is extended is
a proposition that holds a priori and is not empirical. For, before appealing to
experience, I have already in the concept of body all the conditions required for
my judgment. I have only to extract from it, in accordance with the principle of
contradiction, the required predicate, and in so doing can at the same time
become conscious of the necessity of the judgment -- and that is what
experience could never have taught me. On the other hand, though I do not
include in the concept of a body in general the predicate 'weight', none the less
this concept indicates an object of experience through one of its parts, and I can
add to that part other parts of this same experience, as in this way belonging
together with the concept. From the start [50] I can apprehend the concept of
body analytically through the characters of extension, impenetrability, figure,
etc. , all of which are thought in the concept. Now, however, looking back on
the experience from which I have derived this concept of body, and finding
weight to be invariably connected with the above characters, I attach it as a
predicate to the concept; and in doing so I attach it synthetically, and am
therefore extending my knowledge. The possibility of the synthesis of the
predicate 'weight' with the concept of 'body' thus rests upon experience. While
the one concept is not contained in the other, they yet belong to one another,
though only contingently, as parts of a whole, namely, of an experience which
is itself a synthetic combination of intuitions.

But in a priori synthetic judgments this help is entirely lacking. [I do
not here have the advantage of looking around in the field of experience.] Upon
what, then, am I to rely, when I seek to go beyond the concept A, and to know
that another concept B is connected with it? Through what is the synthesis
made possible? Let us take the proposition, 'Everything which happens has its
cause'. In the concept of 'something which happens', I do indeed think an
existence which is preceded by a time, etc. , and from this concept analytic
judgments may be obtained. But the concept of a 'cause' lies entirely outside
the other concept, and signifies something different [51] from 'that which
happens', and is not therefore in any way contained in this latter
representation. How come I then to predicate of that which happens something
quite different, and to apprehend that the concept of cause, though not
contained in it, yet belongs, and indeed necessarily belongs to it? What is here
the unknown = X which gives support to the understanding when it believes
that it can discover outside the concept A a predicate B foreign to this concept,
which it yet at the same time considers to be connected with it? It cannot be
experience, because the suggested principle has connected the second
representation with the first, not only with greater universality, but also with
the character of necessity, and therefore completely a priori and on the basis of
mere concepts. Upon such synthetic, that is, ampliative principles, all our a
priori speculative knowledge must ultimately rest; analytic judgments are
very important, and indeed necessary, but only for obtaining that clearness in
the concepts which is requisite for such a sure and wide synthesis as will lead
to a genuinely new addition to all previous knowledge.{3}



1. All mathematical judgments, without exception, are synthetic. This fact,
though incontestably certain and in its consequences very important, has
hitherto escaped the notice of those who are engaged in the analysis of human
reason, and is, indeed, directly opposed to all their conjectures. For as it was
found that all mathematical inferences proceed in accordance with the
principle of contradiction (which the nature of all apodeictic certainty
requires), it was supposed that the fundamental propositions of the science can
themselves be known to be true through that principle. This is an erroneous
view. For though a synthetic proposition can indeed be discerned in
accordance with the principle of contradiction, this can only be if another
synthetic proposition is presupposed, and if it can then be apprehended as
following from this other proposition; it can never be so discerned in and by

First of all, it has to be noted that mathematical propositions, strictly
so called, are always judgments a priori, not empirical; because they carry
with them necessity, which cannot be derived from experience. If this be
demurred to, I am willing to limit my statement to pure mathematics, the very
concept of which implies that it does not contain empirical, but only pure a
priori knowledge.

We might, indeed, at first suppose that the proposition 7 & 5 = 12 is a
merely analytic proposition, and follows by the principle of contradiction from
the concept of a sum of 7 and 5. But if we look more closely we find that the
concept of the sum of 7 and 5 contains nothing save the union of the two
numbers into one, and in this no thought is being taken [53] as to what that
single number may be which combines both. The concept of 12 is by no means
already thought in merely thinking this union of 7 and 5; and I may analyze
my concept of such a possible sum as long as I please, still I shall never find
the 12 in it. We have to go outside these concepts, and call in the aid of the
intuition which corresponds to one of them, our five fingers, for instance, or, as
Segner does in his Arithmetic, five points, adding to the concept of 7, unit by
unit, the five given in intuition. For starting with the number 7, and for the
concept of 5 calling in the aid of the fingers of my hand as intuition, I now add
one by one to the number 7 the units which I previously took together to form
the number 5, and with the aid of that figure [the hand] see the number 12
come into being. That 5 should be added to 7, I have indeed already thought in
the concept of a sum = 7 & 5, but not that this sum is equivalent to the number
12. Arithmetical propositions are therefore always synthetic. This is still more
evident if we take larger numbers. For it is then obvious that, however we
might turn and twist our concepts, we could never, by the mere analysis of
them, and without the aid of intuition, discover what [the number is that] is
the sum.

Just as little is any fundamental proposition of pure geometry analytic.
That the straight line between two points is the shortest, is a synthetic
proposition. For my concept of straight contains nothing of quantity, but only
of quality. The concept of the shortest is wholly an addition, and cannot be
derived, through any process of analysis, from the concept of the straight line.
Intuition, therefore, must here be called in; only by its aid is the synthesis
possible. What here causes us commonly to believe that the predicate of such
apodeictic judgments is already contained in our concept, and that the
judgment is therefore analytic, is merely the ambiguous character of the terms
used. We are required to join in thought a certain predicate to a given concept,
and this necessity [54] is inherent in the concepts themselves. But the question
is not what we ought to join in thought to the given concept, but what we
actually think in it, even if only obscurely; and it is then manifest that, while
the predicate is indeed attached necessarily to the concept, it is so in virtue of
an intuition which must be added to the concept, not as thought in the concept

Some few fundamental propositions, presupposed by the geometrician,
are, indeed, really analytic, and rest on the principle of contradiction. But, as
identical propositions, they serve only as links in the chain of method and not
as principles; for instance, a = a; the whole is equal to itself; or (a & b) a,
that is, the whole is greater than its part. And even these propositions, though
they are valid according to pure concepts, are only admitted in mathematics
because they can be exhibited in intuition.

2. Natural science (physics) contains a priori synthetic judgments as
principles. I need cite only two such judgments: that in all changes of the
material world the quantity of matter remains unchanged; and that in all
communication of motion, action and reaction must always be equal. Both
propositions, it is evident, are not only necessary, and therefore in their origin
a priori, but also synthetic. For in the concept of matter I do not think its
permanence, but only its presence in the space which it occupies. I go outside
and beyond the concept of matter, joining to it a priori in thought something
which I have not thought in it. The proposition is not, therefore, analytic, but
synthetic, and yet is thought a priori; and so likewise are the other
propositions of the pure part of natural science.

3. Metaphysics, even if we look upon it as having hitherto failed in all
its endeavors, is yet, owing to the nature of human reason, a quite
indispensable science, and ought to contain a priori synthetic knowledge. For
its business is not merely to analyze concepts which we make for ourselves a
priori of things, and thereby to clarify them analytically, but to extend our a
priori knowledge. And for this purpose we must employ principles which add
to the given concept something that was not contained in it, and through a
priori synthetic judgments venture out so far that experience is quite [55]
unable to follow us, as, for instance, in the proposition, that the world must
have a first beginning, and such like. Thus metaphysics consists, at least in
intention, entirely of a priori synthetic propositions.


Much is already gained if we can bring a number of investigations
under the formula of a single problem. For we not only lighten our own task,
by defining it accurately, but make it easier for others, who would test our
results, to judge whether or not we have succeeded in what we set out to do.
Now the proper problem of pure reason is contained in the question: How are
a priori synthetic judgments possible?

That metaphysics has hitherto remained in so vacillating a state of
uncertainty and contradiction, is entirely due to the fact that this problem, and
perhaps even the distinction between analytic and synthetic judgments, has
never previously been considered. Upon the solution of this problem, or upon a
sufficient proof that the possibility which it desires to have explained does in
fact not exist at all, depends the success or failure of metaphysics. Among
philosophers, David Hume came nearest to envisaging this problem, but still
was very far from conceiving it with sufficient definiteness and universality.
He occupied himself exclusively with the synthetic proposition regarding the
connection of an effect with its cause (principium causalitatis), and he believed
himself to have shown that such an a priori proposition is entirely impossible.
If we accept his conclusions, then all that we call metaphysics is a mere
delusion whereby we fancy ourselves to have rational insight into what, in
actual fact, is borrowed solely from experience, and under the influence of
custom has taken the illusory semblance of necessity. If he had envisaged our
problem in all its universality, he would never have been guilty of this
statement, so destructive of all pure philosophy. For he would then have
recognized that, according to his own argument, pure mathematics, as
certainly containing a priori synthetic propositions, would also not be
possible; and from such an assertion his good sense would have saved him.