The Critique of Pure Reason

PREFACE TO THE FIRST EDITION 1781

Human reason, in one sphere of its cognition, is called upon to consider
questions, which it cannot decline, as they are presented by its own nature,
but which it cannot answer, as they transcend every faculty of the mind.

It falls into this difficulty without any fault of its own. It begins with
principles, which cannot be dispensed with in the field of experience, and the
truth and sufficiency of which are, at the same time, insured by experience.
With these principles it rises, in obedience to the laws of its own nature, to
ever higher and more remote conditions. But it quickly discovers that, in this
way, its labours must remain ever incomplete, because new questions never cease
to present themselves; and thus it finds itself compelled to have recourse to
principles which transcend the region of experience, while they are regarded by
common sense without distrust. It thus falls into confusion and contradictions,
from which it conjectures the presence of latent errors, which, however, it is
unable to discover, because the principles it employs, transcending the limits
of experience, cannot be tested by that criterion. The arena of these endless
contests is called Metaphysic.

Time was, when she was the queen of all the sciences; and, if we take
the will for the deed, she certainly deserves, so far as regards the high
importance of her object-matter, this title of honour. Now, it is the fashion
of the time to heap contempt and scorn upon her; and the matron mourns, forlorn
and forsaken, like Hecuba:

Modo maxima rerum,
Tot generis, natisque potens…
Nunc trahor exul, inops.
—Ovid, Metamorphoses. xiii

At first, her government, under the administration of the dogmatists,
was an absolute despotism. But, as the legislative continued to show
traces of the ancient barbaric rule, her empire gradually broke up, and
intestine wars introduced the reign of anarchy; while the
sceptics, like nomadic tribes, who hate a permanent habitation and
settled mode of living, attacked from time to time those who had organized
themselves into civil communities. But their number was, very happily, small;
and thus they could not entirely put a stop to the exertions of those who
persisted in raising new edifices, although on no settled or uniform plan. In
recent times the hope dawned upon us of seeing those disputes settled, and the
legitimacy of her claims established by a kind of physiology of the
human understanding—that of the celebrated Locke. But it was found
that—although it was affirmed that this so-called queen could not refer
her descent to any higher source than that of common experience, a circumstance
which necessarily brought suspicion on her claims—as this
genealogy was incorrect, she persisted in the advancement of her claims
to sovereignty. Thus metaphysics necessarily fell back into the antiquated and
rotten constitution of dogmatism, and again became obnoxious to the
contempt from which efforts had been made to save it. At present, as all
methods, according to the general persuasion, have been tried in vain, there
reigns nought but weariness and complete indifferentism—the mother
of chaos and night in the scientific world, but at the same time the source of,
or at least the prelude to, the re-creation and reinstallation of a science,
when it has fallen into confusion, obscurity, and disuse from ill directed
effort.

For it is in reality vain to profess indifference in regard to such
inquiries, the object of which cannot be indifferent to humanity. Besides,
these pretended indifferentists, however much they may try to disguise
themselves by the assumption of a popular style and by changes on the language
of the schools, unavoidably fall into metaphysical declarations and
propositions, which they profess to regard with so much contempt. At the same
time, this indifference, which has arisen in the world of science, and which
relates to that kind of knowledge which we should wish to see destroyed the
last, is a phenomenon that well deserves our attention and reflection. It is
plainly not the effect of the levity, but of the matured judgement^[1]
of the age, which refuses to be any longer entertained with illusory knowledge,
It is, in fact, a call to reason, again to undertake the most laborious of all
tasks—that of self-examination, and to establish a tribunal, which may
secure it in its well-grounded claims, while it pronounces against all baseless
assumptions and pretensions, not in an arbitrary manner, but according to its
own eternal and unchangeable laws. This tribunal is nothing less than the
Critical Investigation of Pure Reason.

[1]
We very often hear complaints of the shallowness of the present age, and of the
decay of profound science. But I do not think that those which rest upon a
secure foundation, such as mathematics, physical science, etc., in the least
deserve this reproach, but that they rather maintain their ancient fame, and in
the latter case, indeed, far surpass it. The same would be the case with the
other kinds of cognition, if their principles were but firmly established. In
the absence of this security, indifference, doubt, and finally, severe
criticism are rather signs of a profound habit of thought. Our age is the age
of criticism, to which everything must be subjected. The sacredness of
religion, and the authority of legislation, are by many regarded as grounds of
exemption from the examination of this tribunal. But, if they are exempted,
they become the subjects of just suspicion, and cannot lay claim to sincere
respect, which reason accords only to that which has stood the test of a free
and public examination.

I do not mean by this a criticism of books and systems, but a critical inquiry
into the faculty of reason, with reference to the cognitions to which it
strives to attain without the aid of experience; in other words, the
solution of the question regarding the possibility or impossibility of
metaphysics, and the determination of the origin, as well as of the extent and
limits of this science. All this must be done on the basis of principles.

This path—the only one now remaining—has been entered upon by me;
and I flatter myself that I have, in this way, discovered the cause
of—and consequently the mode of removing—all the errors which have
hitherto set reason at variance with itself, in the sphere of non-empirical
thought. I have not returned an evasive answer to the questions of reason, by
alleging the inability and limitation of the faculties of the mind; I have, on
the contrary, examined them completely in the light of principles, and, after
having discovered the cause of the doubts and contradictions into which reason
fell, have solved them to its perfect satisfaction. It is true, these questions
have not been solved as dogmatism, in its vain fancies and desires, had
expected; for it can only be satisfied by the exercise of magical arts, and of
these I have no knowledge. But neither do these come within the compass of our
mental powers; and it was the duty of philosophy to destroy the illusions which
had their origin in misconceptions, whatever darling hopes and valued
expectations may be ruined by its explanations. My chief aim in this work has
been thoroughness; and I make bold to say that there is not a single
metaphysical problem that does not find its solution, or at least the key to
its solution, here. Pure reason is a perfect unity; and therefore, if the
principle presented by it prove to be insufficient for the solution of even a
single one of those questions to which the very nature of reason gives birth,
we must reject it, as we could not be perfectly certain of its sufficiency in
the case of the others.

While I say this, I think I see upon the countenance of the reader signs of
dissatisfaction mingled with contempt, when he hears declarations which sound
so boastful and extravagant; and yet they are beyond comparison more moderate
than those advanced by the commonest author of the commonest philosophical
programme, in which the dogmatist professes to demonstrate the simple nature of
the soul, or the necessity of a primal being. Such a dogmatist promises to
extend human knowledge beyond the limits of possible experience; while I humbly
confess that this is completely beyond my power. Instead of any such attempt, I
confine myself to the examination of reason alone and its pure thought; and I
do not need to seek far for the sum-total of its cognition, because it has its
seat in my own mind. Besides, common logic presents me with a complete and
systematic catalogue of all the simple operations of reason; and it is my task
to answer the question how far reason can go, without the material presented
and the aid furnished by experience.

So much for the completeness and thoroughness necessary in the execution of the
present task. The aims set before us are not arbitrarily proposed, but are
imposed upon us by the nature of cognition itself.

The above remarks relate to the matter of our critical inquiry. As
regards the form, there are two indispensable conditions, which any one
who undertakes so difficult a task as that of a critique of pure reason, is
bound to fulfil. These conditions are certitude and clearness.

As regards certitude, I have fully convinced myself that, in this sphere
of thought, opinion is perfectly inadmissible, and that everything which
bears the least semblance of an hypothesis must be excluded, as of no value in
such discussions. For it is a necessary condition of every cognition that is to
be established upon à priori grounds that it shall be held to be
absolutely necessary; much more is this the case with an attempt to determine
all pure à priori cognition, and to furnish the standard—and
consequently an example—of all apodeictic (philosophical) certitude.
Whether I have succeeded in what I professed to do, it is for the reader to
determine; it is the author’s business merely to adduce grounds and
reasons, without determining what influence these ought to have on the mind of
his judges. But, lest anything he may have said may become the innocent cause
of doubt in their minds, or tend to weaken the effect which his arguments might
otherwise produce—he may be allowed to point out those passages which may
occasion mistrust or difficulty, although these do not concern the main purpose
of the present work. He does this solely with the view of removing from the
mind of the reader any doubts which might affect his judgement of the work as a
whole, and in regard to its ultimate aim.

I know no investigations more necessary for a full insight into the nature of
the faculty which we call understanding, and at the same time for the
determination of the rules and limits of its use, than those undertaken in the
second chapter of the “Transcendental Analytic,” under the title of
Deduction of the Pure Conceptions of the Understanding; and they have
also cost me by far the greatest labour—labour which, I hope, will not
remain uncompensated. The view there taken, which goes somewhat deeply into the
subject, has two sides. The one relates to the objects of the pure
understanding, and is intended to demonstrate and to render comprehensible the
objective validity of its à priori conceptions; and it forms for this
reason an essential part of the Critique. The other considers the pure
understanding itself, its possibility and its powers of cognition—that
is, from a subjective point of view; and, although this exposition is of great
importance, it does not belong essentially to the main purpose of the work,
because the grand question is what and how much can reason and understanding,
apart from experience, cognize, and not, how is the faculty of thought
itself possible? As the latter is an inquiry into the cause of a given effect,
and has thus in it some semblance of an hypothesis (although, as I shall show
on another occasion, this is really not the fact), it would seem that, in the
present instance, I had allowed myself to enounce a mere opinion, and
that the reader must therefore be at liberty to hold a different
opinion. But I beg to remind him that, if my subjective deduction does
not produce in his mind the conviction of its certitude at which I aimed, the
objective deduction, with which alone the present work is properly concerned,
is in every respect satisfactory.

As regards clearness, the reader has a right to demand, in the first
place, discursive or logical clearness, that is, on the basis of
conceptions, and, secondly, intuitive or æsthetic clearness, by means of
intuitions, that is, by examples or other modes of illustration in
concreto. I have done what I could for the first kind of intelligibility.
This was essential to my purpose; and it thus became the accidental cause of my
inability to do complete justice to the second requirement. I have been almost
always at a loss, during the progress of this work, how to settle this
question. Examples and illustrations always appeared to me necessary, and, in
the first sketch of the Critique, naturally fell into their proper places. But
I very soon became aware of the magnitude of my task, and the numerous problems
with which I should be engaged; and, as I perceived that this critical
investigation would, even if delivered in the driest scholastic manner,
be far from being brief, I found it unadvisable to enlarge it still more with
examples and explanations, which are necessary only from a popular point
of view. I was induced to take this course from the consideration also that the
present work is not intended for popular use, that those devoted to science do
not require such helps, although they are always acceptable, and that they
would have materially interfered with my present purpose. Abbé Terrasson
remarks with great justice that, if we estimate the size of a work, not from
the number of its pages, but from the time which we require to make ourselves
master of it, it may be said of many a book—that it would be much
shorter, if it were not so short. On the other hand, as regards the
comprehensibility of a system of speculative cognition, connected under a
single principle, we may say with equal justice: many a book would have been
much clearer, if it had not been intended to be so very clear. For explanations
and examples, and other helps to intelligibility, aid us in the comprehension
of parts, but they distract the attention, dissipate the mental power of
the reader, and stand in the way of his forming a clear conception of the
whole; as he cannot attain soon enough to a survey of the system, and
the colouring and embellishments bestowed upon it prevent his observing its
articulation or organization—which is the most important consideration
with him, when he comes to judge of its unity and stability.

The reader must naturally have a strong inducement to co-operate with the
present author, if he has formed the intention of erecting a complete and solid
edifice of metaphysical science, according to the plan now laid before him.
Metaphysics, as here represented, is the only science which admits of
completion—and with little labour, if it is united, in a short time; so
that nothing will be left to future generations except the task of illustrating
and applying it didactically. For this science is nothing more than the
inventory of all that is given us by pure reason, systematically
arranged. Nothing can escape our notice; for what reason produces from itself
cannot lie concealed, but must be brought to the light by reason itself, so
soon as we have discovered the common principle of the ideas we seek. The
perfect unity of this kind of cognitions, which are based upon pure
conceptions, and uninfluenced by any empirical element, or any peculiar
intuition leading to determinate experience, renders this completeness not only
practicable, but also necessary.

Tecum habita, et nôris quam sit tibi curta supellex.
—Persius. Satirae iv. 52.

Such a system of pure speculative reason I hope to be able to publish under the
title of Metaphysic of Nature^[2]. The content of this work (which will not
be half so long) will be very much richer than that of the present Critique,
which has to discover the sources of this cognition and expose the conditions
of its possibility, and at the same time to clear and level a fit foundation
for the scientific edifice. In the present work, I look for the patient hearing
and the impartiality of a judge; in the other, for the good-will and
assistance of a co-labourer. For, however complete the list of
principles for this system may be in the Critique, the correctness of
the system requires that no deduced conceptions should be absent. These
cannot be presented à priori, but must be gradually discovered; and,
while the synthesis of conceptions has been fully exhausted in the
Critique, it is necessary that, in the proposed work, the same should be the
case with their analysis. But this will be rather an amusement than a
labour.

[2]
In contradistinction to the Metaphysic of Ethics. This work was never
published.

PREFACE TO THE SECOND EDITION 1787

Whether the treatment of that portion of our knowledge which lies within the
province of pure reason advances with that undeviating certainty which
characterizes the progress of science, we shall be at no loss to
determine. If we find those who are engaged in metaphysical pursuits, unable to
come to an understanding as to the method which they ought to follow; if we
find them, after the most elaborate preparations, invariably brought to a stand
before the goal is reached, and compelled to retrace their steps and strike
into fresh paths, we may then feel quite sure that they are far from having
attained to the certainty of scientific progress and may rather be said to be
merely groping about in the dark. In these circumstances we shall render an
important service to reason if we succeed in simply indicating the path along
which it must travel, in order to arrive at any results—even if it should
be found necessary to abandon many of those aims which, without reflection,
have been proposed for its attainment.

That Logic has advanced in this sure course, even from the earliest
times, is apparent from the fact that, since Aristotle, it has been unable to
advance a step and, thus, to all appearance has reached its completion. For, if
some of the moderns have thought to enlarge its domain by introducing
psychological discussions on the mental faculties, such as imagination
and wit, metaphysical, discussions on the origin of knowledge and the
different kinds of certitude, according to the difference of the objects
(idealism, scepticism, and so on), or anthropological discussions on
prejudices, their causes and remedies: this attempt, on the part of these
authors, only shows their ignorance of the peculiar nature of logical science.
We do not enlarge but disfigure the sciences when we lose sight of their
respective limits and allow them to run into one another. Now logic is enclosed
within limits which admit of perfectly clear definition; it is a science which
has for its object nothing but the exposition and proof of the formal
laws of all thought, whether it be à priori or empirical, whatever be
its origin or its object, and whatever the difficulties—natural or
accidental—which it encounters in the human mind.

The early success of logic must be attributed exclusively to the narrowness of
its field, in which abstraction may, or rather must, be made of all the objects
of cognition with their characteristic distinctions, and in which the
understanding has only to deal with itself and with its own forms. It is,
obviously, a much more difficult task for reason to strike into the sure path
of science, where it has to deal not simply with itself, but with objects
external to itself. Hence, logic is properly only a
propædeutic—forms, as it were, the vestibule of the sciences; and
while it is necessary to enable us to form a correct judgement with regard to
the various branches of knowledge, still the acquisition of real, substantive
knowledge is to be sought only in the sciences properly so called, that is, in
the objective sciences.

Now these sciences, if they can be termed rational at all, must contain
elements of à priori cognition, and this cognition may stand in a
twofold relation to its object. Either it may have to determine the
conception of the object—which must be supplied extraneously, or it may
have to establish its reality. The former is theoretical, the
latter practical, rational cognition. In both, the pure or à
priori element must be treated first, and must be carefully distinguished
from that which is supplied from other sources. Any other method can only lead
to irremediable confusion.

Mathematics and physics are the two theoretical sciences which
have to determine their objects à priori. The former is purely à
priori, the latter is partially so, but is also dependent on other sources
of cognition.

In the earliest times of which history affords us any record,
mathematics had already entered on the sure course of science, among
that wonderful nation, the Greeks. Still it is not to be supposed that it was
as easy for this science to strike into, or rather to construct for itself,
that royal road, as it was for logic, in which reason has only to deal with
itself. On the contrary, I believe that it must have remained
long—chiefly among the Egyptians—in the stage of blind groping
after its true aims and destination, and that it was revolutionized by the
happy idea of one man, who struck out and determined for all time the path
which this science must follow, and which admits of an indefinite advancement.
The history of this intellectual revolution—much more important in its
results than the discovery of the passage round the celebrated Cape of Good
Hope—and of its author, has not been preserved. But Diogenes Laertius, in
naming the supposed discoverer of some of the simplest elements of geometrical
demonstration—elements which, according to the ordinary opinion, do not
even require to be proved—makes it apparent that the change introduced by
the first indication of this new path, must have seemed of the utmost
importance to the mathematicians of that age, and it has thus been secured
against the chance of oblivion. A new light must have flashed on the mind of
the first man (Thales, or whatever may have been his name) who
demonstrated the properties of the isosceles triangle. For he found that
it was not sufficient to meditate on the figure, as it lay before his eyes, or
the conception of it, as it existed in his mind, and thus endeavour to get at
the knowledge of its properties, but that it was necessary to produce these
properties, as it were, by a positive à priori construction; and that,
in order to arrive with certainty at à priori cognition, he must not
attribute to the object any other properties than those which necessarily
followed from that which he had himself, in accordance with his conception,
placed in the object.

A much longer period elapsed before Physics entered on the highway of
science. For it is only about a century and a half since the wise
BACON gave a new direction to physical studies, or
rather—as others were already on the right track—imparted fresh
vigour to the pursuit of this new direction. Here, too, as in the case of
mathematics, we find evidence of a rapid intellectual revolution. In the
remarks which follow I shall confine myself to the empirical side of
natural science.

When GALILEI experimented with balls of a definite weight on the
inclined plane, when TORRICELLI caused the air to sustain a
weight which he had calculated beforehand to be equal to that of a definite
column of water, or when STAHL, at a later period, converted
metals into lime, and reconverted lime into metal, by the addition and
subtraction of certain elements;^[3] a light broke upon all natural
philosophers. They learned that reason only perceives that which it produces
after its own design; that it must not be content to follow, as it were, in the
leading-strings of nature, but must proceed in advance with principles of
judgement according to unvarying laws, and compel nature to reply its
questions. For accidental observations, made according to no preconceived plan,
cannot be united under a necessary law. But it is this that reason seeks for
and requires. It is only the principles of reason which can give to concordant
phenomena the validity of laws, and it is only when experiment is directed by
these rational principles that it can have any real utility. Reason must
approach nature with the view, indeed, of receiving information from it, not,
however, in the character of a pupil, who listens to all that his master
chooses to tell him, but in that of a judge, who compels the witnesses to reply
to those questions which he himself thinks fit to propose. To this single idea
must the revolution be ascribed, by which, after groping in the dark for so
many centuries, natural science was at length conducted into the path of
certain progress.

[3] I do
not here follow with exactness the history of the experimental method, of
which, indeed, the first steps are involved in some obscurity.

We come now to metaphysics, a purely speculative science, which occupies
a completely isolated position and is entirely independent of the teachings of
experience. It deals with mere conceptions—not, like mathematics, with
conceptions applied to intuition—and in it, reason is the pupil of itself
alone. It is the oldest of the sciences, and would still survive, even if all
the rest were swallowed up in the abyss of an all-destroying barbarism. But it
has not yet had the good fortune to attain to the sure scientific method. This
will be apparent; if we apply the tests which we proposed at the outset. We
find that reason perpetually comes to a stand, when it attempts to gain à
priori the perception even of those laws which the most common experience
confirms. We find it compelled to retrace its steps in innumerable instances,
and to abandon the path on which it had entered, because this does not lead to
the desired result. We find, too, that those who are engaged in metaphysical
pursuits are far from being able to agree among themselves, but that, on the
contrary, this science appears to furnish an arena specially adapted for the
display of skill or the exercise of strength in mock-contests—a field in
which no combatant ever yet succeeded in gaining an inch of ground, in which,
at least, no victory was ever yet crowned with permanent possession.

This leads us to inquire why it is that, in metaphysics, the sure path of
science has not hitherto been found. Shall we suppose that it is impossible to
discover it? Why then should nature have visited our reason with restless
aspirations after it, as if it were one of our weightiest concerns? Nay, more,
how little cause should we have to place confidence in our reason, if it
abandons us in a matter about which, most of all, we desire to know the
truth—and not only so, but even allures us to the pursuit of vain
phantoms, only to betray us in the end? Or, if the path has only hitherto been
missed, what indications do we possess to guide us in a renewed investigation,
and to enable us to hope for greater success than has fallen to the lot of our
predecessors?

It appears to me that the examples of mathematics and natural philosophy,
which, as we have seen, were brought into their present condition by a sudden
revolution, are sufficiently remarkable to fix our attention on the essential
circumstances of the change which has proved so advantageous to them, and to
induce us to make the experiment of imitating them, so far as the analogy
which, as rational sciences, they bear to metaphysics may permit. It has
hitherto been assumed that our cognition must conform to the objects; but all
attempts to ascertain anything about these objects à priori, by means of
conceptions, and thus to extend the range of our knowledge, have been rendered
abortive by this assumption. Let us then make the experiment whether we may not
be more successful in metaphysics, if we assume that the objects must conform
to our cognition. This appears, at all events, to accord better with the
possibility of our gaining the end we have in view, that is to say, of
arriving at the cognition of objects à priori, of determining something
with respect to these objects, before they are given to us. We here propose to
do just what COPERNICUS did in attempting to explain the
celestial movements. When he found that he could make no progress by assuming
that all the heavenly bodies revolved round the spectator, he reversed the
process, and tried the experiment of assuming that the spectator revolved,
while the stars remained at rest. We may make the same experiment with regard
to the intuition of objects. If the intuition must conform to the nature of the
objects, I do not see how we can know anything of them à priori. If, on
the other hand, the object conforms to the nature of our faculty of intuition,
I can then easily conceive the possibility of such an à priori
knowledge. Now as I cannot rest in the mere intuitions, but—if they are
to become cognitions—must refer them, as representations, to
something, as object, and must determine the latter by means of the
former, here again there are two courses open to me. Either, first, I
may assume that the conceptions, by which I effect this determination, conform
to the object—and in this case I am reduced to the same perplexity as
before; or secondly, I may assume that the objects, or, which is the
same thing, that experience, in which alone as given objects they are
cognized, conform to my conceptions—and then I am at no loss how to
proceed. For experience itself is a mode of cognition which requires
understanding. Before objects, are given to me, that is, à priori, I
must presuppose in myself laws of the understanding which are expressed in
conceptions à priori. To these conceptions, then, all the objects of
experience must necessarily conform. Now there are objects which reason
thinks, and that necessarily, but which cannot be given in experience,
or, at least, cannot be given so as reason thinks them. The attempt to
think these objects will hereafter furnish an excellent test of the new method
of thought which we have adopted, and which is based on the principle that we
only cognize in things à priori that which we ourselves place in them.^[4]

[4] This
method, accordingly, which we have borrowed from the natural philosopher,
consists in seeking for the elements of pure reason in that which admits of
confirmation or refutation by experiment. Now the propositions of pure
reason, especially when they transcend the limits of possible experience, do
not admit of our making any experiment with their objects, as in natural
science. Hence, with regard to those conceptions and principles
which we assume à priori, our only course will be to view them from two
different sides. We must regard one and the same conception, on the one
hand, in relation to experience as an object of the senses and of the
understanding, on the other hand, in relation to reason, isolated and
transcending the limits of experience, as an object of mere thought. Now if we
find that, when we regard things from this double point of view, the result is
in harmony with the principle of pure reason, but that, when we regard them
from a single point of view, reason is involved in self-contradiction, then the
experiment will establish the correctness of this distinction.

This attempt succeeds as well as we could desire, and promises to metaphysics,
in its first part—that is, where it is occupied with conceptions à
priori, of which the corresponding objects may be given in
experience—the certain course of science. For by this new method we are
enabled perfectly to explain the possibility of à priori cognition, and,
what is more, to demonstrate satisfactorily the laws which lie à priori
at the foundation of nature, as the sum of the objects of
experience—neither of which was possible according to the procedure
hitherto followed. But from this deduction of the faculty of à priori
cognition in the first part of metaphysics, we derive a surprising result, and
one which, to all appearance, militates against the great end of metaphysics,
as treated in the second part. For we come to the conclusion that our faculty
of cognition is unable to transcend the limits of possible experience; and yet
this is precisely the most essential object of this science. The estimate of
our rational cognition à priori at which we arrive is that it has only
to do with phenomena, and that things in themselves, while possessing a real
existence, lie beyond its sphere. Here we are enabled to put the justice of
this estimate to the test. For that which of necessity impels us to transcend
the limits of experience and of all phenomena is the unconditioned,
which reason absolutely requires in things as they are in themselves, in order
to complete the series of conditions. Now, if it appears that when, on the one
hand, we assume that our cognition conforms to its objects as things in
themselves, the unconditioned cannot be thought without contradiction,
and that when, on the other hand, we assume that our representation of things
as they are given to us, does not conform to these things as they are in
themselves, but that these objects, as phenomena, conform to our mode of
representation, the contradiction disappears: we shall then be convinced
of the truth of that which we began by assuming for the sake of experiment; we
may look upon it as established that the unconditioned does not lie in things
as we know them, or as they are given to us, but in things as they are in
themselves, beyond the range of our cognition.^[5]

[5] This
experiment of pure reason has a great similarity to that of the
Chemists, which they term the experiment of reduction, or, more
usually, the synthetic process. The analysis of the metaphysician
separates pure cognition à priori into two heterogeneous elements, viz.,
the cognition of things as phenomena, and of things in themselves.
Dialectic combines these again into harmony with the necessary rational
idea of the unconditioned, and finds that this harmony never results except
through the above distinction, which is, therefore, concluded to be just.

But, after we have thus denied the power of speculative reason to make any
progress in the sphere of the supersensible, it still remains for our
consideration whether data do not exist in practical cognition which may
enable us to determine the transcendent conception of the unconditioned, to
rise beyond the limits of all possible experience from a practical point
of view, and thus to satisfy the great ends of metaphysics. Speculative reason
has thus, at least, made room for such an extension of our knowledge: and, if
it must leave this space vacant, still it does not rob us of the liberty to
fill it up, if we can, by means of practical data—nay, it even challenges
us to make the attempt.^[6]

[6] So
the central laws of the movements of the heavenly bodies established the truth
of that which Copernicus, first, assumed only as a hypothesis, and, at the same
time, brought to light that invisible force (Newtonian attraction) which holds
the universe together. The latter would have remained forever undiscovered, if
Copernicus had not ventured on the experiment—contrary to the senses but
still just—of looking for the observed movements not in the heavenly
bodies, but in the spectator. In this Preface I treat the new metaphysical
method as a hypothesis with the view of rendering apparent the first attempts
at such a change of method, which are always hypothetical. But in the Critique
itself it will be demonstrated, not hypothetically, but apodeictically, from
the nature of our representations of space and time, and from the elementary
conceptions of the understanding.

This attempt to introduce a complete revolution in the procedure of
metaphysics, after the example of the geometricians and natural
philosophers, constitutes the aim of the Critique of Pure Speculative Reason.
It is a treatise on the method to be followed, not a system of the science
itself. But, at the same time, it marks out and defines both the external
boundaries and the internal structure of this science. For pure speculative
reason has this peculiarity, that, in choosing the various objects of thought,
it is able to define the limits of its own faculties, and even to give a
complete enumeration of the possible modes of proposing problems to itself, and
thus to sketch out the entire system of metaphysics. For, on the one hand, in
cognition à priori, nothing must be attributed to the objects but what
the thinking subject derives from itself; and, on the other hand, reason is, in
regard to the principles of cognition, a perfectly distinct, independent unity,
in which, as in an organized body, every member exists for the sake of the
others, and all for the sake of each, so that no principle can be viewed, with
safety, in one relationship, unless it is, at the same time, viewed in relation
to the total use of pure reason. Hence, too, metaphysics has this singular
advantage—an advantage which falls to the lot of no other science which
has to do with objects—that, if once it is conducted into the sure
path of science, by means of this criticism, it can then take in the whole
sphere of its cognitions, and can thus complete its work, and leave it for the
use of posterity, as a capital which can never receive fresh accessions. For
metaphysics has to deal only with principles and with the limitations of its
own employment as determined by these principles. To this perfection it is,
therefore, bound, as the fundamental science, to attain, and to it the maxim
may justly be applied:

Nil actum reputans, si quid superesset agendum.

But, it will be asked, what kind of a treasure is this that we propose to
bequeath to posterity? What is the real value of this system of metaphysics,
purified by criticism, and thereby reduced to a permanent condition? A cursory
view of the present work will lead to the supposition that its use is merely
negative, that it only serves to warn us against venturing, with
speculative reason, beyond the limits of experience. This is, in fact, its
primary use. But this, at once, assumes a positive value, when we
observe that the principles with which speculative reason endeavours to
transcend its limits lead inevitably, not to the extension, but to the
contraction of the use of reason, inasmuch as they threaten to extend
the limits of sensibility, which is their proper sphere, over the entire realm
of thought and, thus, to supplant the pure (practical) use of reason. So far,
then, as this criticism is occupied in confining speculative reason within its
proper bounds, it is only negative; but, inasmuch as it thereby, at the same
time, removes an obstacle which impedes and even threatens to destroy the use
of practical reason, it possesses a positive and very important value. In order
to admit this, we have only to be convinced that there is an absolutely
necessary use of pure reason—the moral use—in which it inevitably
transcends the limits of sensibility, without the aid of speculation, requiring
only to be insured against the effects of a speculation which would involve it
in contradiction with itself. To deny the positive advantage of the service
which this criticism renders us would be as absurd as to maintain that the
system of police is productive of no positive benefit, since its main business
is to prevent the violence which citizen has to apprehend from citizen, that so
each may pursue his vocation in peace and security. That space and time are
only forms of sensible intuition, and hence are only conditions of the
existence of things as phenomena; that, moreover, we have no conceptions of the
understanding, and, consequently, no elements for the cognition of things,
except in so far as a corresponding intuition can be given to these
conceptions; that, accordingly, we can have no cognition of an object, as a
thing in itself, but only as an object of sensible intuition, that is, as
phenomenon—all this is proved in the analytical part of the Critique; and
from this the limitation of all possible speculative cognition to the mere
objects of experience, follows as a necessary result. At the same time,
it must be carefully borne in mind that, while we surrender the power of
cognizing, we still reserve the power of thinking objects, as
things in themselves.^[7] For, otherwise, we should require to
affirm the existence of an appearance, without something that
appears—which would be absurd. Now let us suppose, for a moment, that we
had not undertaken this criticism and, accordingly, had not drawn the necessary
distinction between things as objects of experience and things as they are in
themselves. The principle of causality, and, by consequence, the mechanism of
nature as determined by causality, would then have absolute validity in
relation to all things as efficient causes. I should then be unable to assert,
with regard to one and the same being, e.g., the human soul, that its will is
free, and yet, at the same time, subject to natural necessity, that is,
not free, without falling into a palpable contradiction, for in both
propositions I should take the soul in the same signification, as a
thing in general, as a thing in itself—as, without previous criticism, I
could not but take it. Suppose now, on the other hand, that we have
undertaken this criticism, and have learnt that an object may be taken in
two senses, first, as a phenomenon, secondly, as a thing in itself; and
that, according to the deduction of the conceptions of the understanding, the
principle of causality has reference only to things in the first sense. We then
see how it does not involve any contradiction to assert, on the one hand, that
the will, in the phenomenal sphere—in visible action—is necessarily
obedient to the law of nature, and, in so far, not free; and, on the
other hand, that, as belonging to a thing in itself, it is not subject to that
law, and, accordingly, is free. Now, it is true that I cannot, by means
of speculative reason, and still less by empirical observation, cognize
my soul as a thing in itself and consequently, cannot cognize liberty as the
property of a being to which I ascribe effects in the world of sense. For, to
do so, I must cognize this being as existing, and yet not in time,
which—since I cannot support my conception by any intuition—is
impossible. At the same time, while I cannot cognize, I can quite well
think freedom, that is to say, my representation of it involves at least
no contradiction, if we bear in mind the critical distinction of the two modes
of representation (the sensible and the intellectual) and the consequent
limitation of the conceptions of the pure understanding and of the principles
which flow from them. Suppose now that morality necessarily presupposed
liberty, in the strictest sense, as a property of our will; suppose that reason
contained certain practical, original principles à priori, which were
absolutely impossible without this presupposition; and suppose, at the same
time, that speculative reason had proved that liberty was incapable of being
thought at all. It would then follow that the moral presupposition must give
way to the speculative affirmation, the opposite of which involves an obvious
contradiction, and that liberty and, with it, morality must yield to the
mechanism of nature; for the negation of morality involves no
contradiction, except on the presupposition of liberty. Now morality does not
require the speculative cognition of liberty; it is enough that I can think it,
that its conception involves no contradiction, that it does not interfere with
the mechanism of nature. But even this requirement we could not satisfy, if we
had not learnt the twofold sense in which things may be taken; and it is only
in this way that the doctrine of morality and the doctrine of nature are
confined within their proper limits. For this result, then, we are indebted to
a criticism which warns us of our unavoidable ignorance with regard to things
in themselves, and establishes the necessary limitation of our theoretical
cognition to mere phenomena.

[7] In
order to cognize an object, I must be able to prove its possibility,
either from its reality as attested by experience, or à priori, by means
of reason. But I can think what I please, provided only I do not
contradict myself; that is, provided my conception is a possible thought,
though I may be unable to answer for the existence of a corresponding object in
the sum of possibilities. But something more is required before I can attribute
to such a conception objective validity, that is real possibility—the
other possibility being merely logical. We are not, however, confined to
theoretical sources of cognition for the means of satisfying this additional
requirement, but may derive them from practical sources.

The positive value of the critical principles of pure reason in relation to the
conception of God and of the simple nature of the soul,
admits of a similar exemplification; but on this point I shall not dwell. I
cannot even make the assumption—as the practical interests of morality
require—of God, freedom, and immortality, if I do not deprive speculative
reason of its pretensions to transcendent insight. For to arrive at these, it
must make use of principles which, in fact, extend only to the objects of
possible experience, and which cannot be applied to objects beyond this sphere
without converting them into phenomena, and thus rendering the practical
extension of pure reason impossible. I must, therefore, abolish
knowledge, to make room for belief. The dogmatism of metaphysics,
that is, the presumption that it is possible to advance in metaphysics without
previous criticism, is the true source of the unbelief (always dogmatic) which
militates against morality.

Thus, while it may be no very difficult task to bequeath a legacy to posterity,
in the shape of a system of metaphysics constructed in accordance with the
Critique of Pure Reason, still the value of such a bequest is not to be
depreciated. It will render an important service to reason, by substituting the
certainty of scientific method for that random groping after results without
the guidance of principles, which has hitherto characterized the pursuit of
metaphysical studies. It will render an important service to the inquiring mind
of youth, by leading the student to apply his powers to the cultivation of
genuine science, instead of wasting them, as at present, on speculations which
can never lead to any result, or on the idle attempt to invent new ideas and
opinions. But, above all, it will confer an inestimable benefit on morality and
religion, by showing that all the objections urged against them may be silenced
for ever by the Socratic method, that is to say, by proving the
ignorance of the objector. For, as the world has never been, and, no doubt,
never will be without a system of metaphysics of one kind or another, it is the
highest and weightiest concern of philosophy to render it powerless for harm,
by closing up the sources of error.

This important change in the field of the sciences, this loss of its fancied
possessions, to which speculative reason must submit, does not prove in any way
detrimental to the general interests of humanity. The advantages which the
world has derived from the teachings of pure reason are not at all impaired.
The loss falls, in its whole extent, on the monopoly of the schools, but
does not in the slightest degree touch the interests of mankind. I
appeal to the most obstinate dogmatist, whether the proof of the continued
existence of the soul after death, derived from the simplicity of its
substance; of the freedom of the will in opposition to the general mechanism of
nature, drawn from the subtle but impotent distinction of subjective and
objective practical necessity; or of the existence of God, deduced from the
conception of an ens realissimum—the contingency of the
changeable, and the necessity of a prime mover, has ever been able to pass
beyond the limits of the schools, to penetrate the public mind, or to exercise
the slightest influence on its convictions. It must be admitted that this has
not been the case and that, owing to the unfitness of the common understanding
for such subtle speculations, it can never be expected to take place. On the
contrary, it is plain that the hope of a future life arises from the
feeling, which exists in the breast of every man, that the temporal is
inadequate to meet and satisfy the demands of his nature. In like manner, it
cannot be doubted that the clear exhibition of duties in opposition to all the
claims of inclination, gives rise to the consciousness of freedom, and
that the glorious order, beauty, and providential care, everywhere displayed in
nature, give rise to the belief in a wise and great Author of the Universe.
Such is the genesis of these general convictions of mankind, so far as they
depend on rational grounds; and this public property not only remains
undisturbed, but is even raised to greater importance, by the doctrine that the
schools have no right to arrogate to themselves a more profound insight into a
matter of general human concernment than that to which the great mass of men,
ever held by us in the highest estimation, can without difficulty attain, and
that the schools should, therefore, confine themselves to the elaboration of
these universally comprehensible and, from a moral point of view, amply
satisfactory proofs. The change, therefore, affects only the arrogant
pretensions of the schools, which would gladly retain, in their own exclusive
possession, the key to the truths which they impart to the public.

Quod mecum nescit, solus vult scire videri.

At the same time it does not deprive the speculative philosopher of his just
title to be the sole depositor of a science which benefits the public without
its knowledge—I mean, the Critique of Pure Reason. This can never become
popular and, indeed, has no occasion to be so; for finespun arguments in favour
of useful truths make just as little impression on the public mind as the
equally subtle objections brought against these truths. On the other hand,
since both inevitably force themselves on every man who rises to the height of
speculation, it becomes the manifest duty of the schools to enter upon a
thorough investigation of the rights of speculative reason and, thus, to
prevent the scandal which metaphysical controversies are sure, sooner or later,
to cause even to the masses. It is only by criticism that metaphysicians (and,
as such, theologians too) can be saved from these controversies and from the
consequent perversion of their doctrines. Criticism alone can strike a blow at
the root of materialism, fatalism, atheism, free-thinking, fanaticism, and
superstition, which are universally injurious—as well as of idealism and
scepticism, which are dangerous to the schools, but can scarcely pass over to
the public. If governments think proper to interfere with the affairs of the
learned, it would be more consistent with a wise regard for the interests of
science, as well as for those of society, to favour a criticism of this kind,
by which alone the labours of reason can be established on a firm basis, than
to support the ridiculous despotism of the schools, which raise a loud cry of
danger to the public over the destruction of cobwebs, of which the public has
never taken any notice, and the loss of which, therefore, it can never feel.

This critical science is not opposed to the dogmatic procedure of reason
in pure cognition; for pure cognition must always be dogmatic, that is, must
rest on strict demonstration from sure principles à priori—but to
dogmatism, that is, to the presumption that it is possible to make any
progress with a pure cognition, derived from (philosophical) conceptions,
according to the principles which reason has long been in the habit of
employing—without first inquiring in what way and by what right reason
has come into the possession of these principles. Dogmatism is thus the
dogmatic procedure of pure reason without previous criticism of its own
powers, and in opposing this procedure, we must not be supposed to lend any
countenance to that loquacious shallowness which arrogates to itself the name
of popularity, nor yet to scepticism, which makes short work with the whole
science of metaphysics. On the contrary, our criticism is the necessary
preparation for a thoroughly scientific system of metaphysics which must
perform its task entirely à priori, to the complete satisfaction of
speculative reason, and must, therefore, be treated, not popularly, but
scholastically. In carrying out the plan which the Critique prescribes, that
is, in the future system of metaphysics, we must have recourse to the strict
method of the celebrated WOLF, the greatest of all dogmatic
philosophers. He was the first to point out the necessity of establishing fixed
principles, of clearly defining our conceptions, and of subjecting our
demonstrations to the most severe scrutiny, instead of rashly jumping at
conclusions. The example which he set served to awaken that spirit of profound
and thorough investigation which is not yet extinct in Germany. He would have
been peculiarly well fitted to give a truly scientific character to
metaphysical studies, had it occurred to him to prepare the field by a
criticism of the organum, that is, of pure reason itself. That he failed
to perceive the necessity of such a procedure must be ascribed to the dogmatic
mode of thought which characterized his age, and on this point the philosophers
of his time, as well as of all previous times, have nothing to reproach each
other with. Those who reject at once the method of Wolf, and of the Critique of
Pure Reason, can have no other aim but to shake off the fetters of
science, to change labour into sport, certainty into opinion, and
philosophy into philodoxy.

In this second edition, I have endeavoured, as far as possible, to
remove the difficulties and obscurity which, without fault of mine perhaps,
have given rise to many misconceptions even among acute thinkers. In the
propositions themselves, and in the demonstrations by which they are supported,
as well as in the form and the entire plan of the work, I have found nothing to
alter; which must be attributed partly to the long examination to which I had
subjected the whole before offering it to the public and partly to the nature
of the case. For pure speculative reason is an organic structure in which there
is nothing isolated or independent, but every Single part is essential to all
the rest; and hence, the slightest imperfection, whether defect or positive
error, could not fail to betray itself in use. I venture, further, to hope,
that this system will maintain the same unalterable character for the future. I
am led to entertain this confidence, not by vanity, but by the evidence which
the equality of the result affords, when we proceed, first, from the simplest
elements up to the complete whole of pure reason and, and then, backwards from
the whole to each part. We find that the attempt to make the slightest
alteration, in any part, leads inevitably to contradictions, not merely in this
system, but in human reason itself. At the same time, there is still much room
for improvement in the exposition of the doctrines contained in this
work. In the present edition, I have endeavoured to remove misapprehensions of
the æsthetical part, especially with regard to the conception of time; to clear
away the obscurity which has been found in the deduction of the conceptions of
the understanding; to supply the supposed want of sufficient evidence in the
demonstration of the principles of the pure understanding; and, lastly, to
obviate the misunderstanding of the paralogisms which immediately precede the
Rational Psychology. Beyond this point—the end of the second main
division of the “Transcendental Dialectic”—I have not
extended my alterations,^[8] partly from want of time, and partly
because I am not aware that any portion of the remainder has given rise to
misconceptions among intelligent and impartial critics, whom I do not here
mention with that praise which is their due, but who will find that their
suggestions have been attended to in the work itself.

[8] The
only addition, properly so called—and that only in the method of
proof—which I have made in the present edition, consists of a new
refutation of psychological Idealism, and a strict
demonstration—the only one possible, as I believe—of the objective
reality of external intuition. However harmless idealism may be
considered—although in reality it is not so—in regard to the
essential ends of metaphysics, it must still remain a scandal to philosophy and
to the general human reason to be obliged to assume, as an article of mere
belief, the existence of things external to ourselves (from which, yet, we
derive the whole material of cognition for the internal sense), and not to be
able to oppose a satisfactory proof to any one who may call it in question. As
there is some obscurity of expression in the demonstration as it stands in the
text, I propose to alter the passage in question as follows: “But this
permanent cannot be an intuition in me. For all the determining grounds of my
existence which can be found in me are representations and, as such, do
themselves require a permanent, distinct from them, which may determine my
existence in relation to their changes, that is, my existence in time, wherein
they change.” It may, probably, be urged in opposition to this proof
that, after all, I am only conscious immediately of that which is in me, that
is, of my representation of external things, and that, consequently, it
must always remain uncertain whether anything corresponding to this
representation does or does not exist externally to me. But I am conscious,
through internal experience, of my existence in time
(consequently, also, of the determinability of the former in the latter), and
that is more than the simple consciousness of my representation. It is, in
fact, the same as the empirical consciousness of my existence, which can
only be determined in relation to something, which, while connected with my
existence, is external to me. This consciousness of my existence in time
is, therefore, identical with the consciousness of a relation to something
external to me, and it is, therefore, experience, not fiction, sense, not
imagination, which inseparably connects the external with my internal sense.
For the external sense is, in itself, the relation of intuition to something
real, external to me; and the reality of this something, as opposed to the mere
imagination of it, rests solely on its inseparable connection with internal
experience as the condition of its possibility. If with the intellectual
consciousness of my existence, in the representation: I am, which
accompanies all my judgements, and all the operations of my understanding, I
could, at the same time, connect a determination of my existence by
intellectual intuition, then the consciousness of a relation to
something external to me would not be necessary. But the internal intuition in
which alone my existence can be determined, though preceded by that purely
intellectual consciousness, is itself sensible and attached to the condition of
time. Hence this determination of my existence, and consequently my internal
experience itself, must depend on something permanent which is not in me, which
can be, therefore, only in something external to me, to which I must look upon
myself as being related. Thus the reality of the external sense is necessarily
connected with that of the internal, in order to the possibility of experience
in general; that is, I am just as certainly conscious that there are things
external to me related to my sense as I am that I myself exist as determined in
time. But in order to ascertain to what given intuitions objects, external me,
really correspond, in other words, what intuitions belong to the external sense
and not to imagination, I must have recourse, in every particular case, to
those rules according to which experience in general (even internal experience)
is distinguished from imagination, and which are always based on the
proposition that there really is an external experience.—We may add the
remark that the representation of something permanent in existence, is
not the same thing as the permanent representation; for a representation
may be very variable and changing—as all our representations, even that
of matter, are—and yet refer to something permanent, which must,
therefore, be distinct from all my representations and external to me, the
existence of which is necessarily included in the determination of my own
existence, and with it constitutes one experience—an experience
which would not even be possible internally, if it were not also at the same
time, in part, external. To the question How? we are no more able to
reply, than we are, in general, to think the stationary in time, the
coexistence of which with the variable, produces the conception of change.

In attempting to render the exposition of my views as intelligible as possible,
I have been compelled to leave out or abridge various passages which were not
essential to the completeness of the work, but which many readers might
consider useful in other respects, and might be unwilling to miss. This
trifling loss, which could not be avoided without swelling the book beyond due
limits, may be supplied, at the pleasure of the reader, by a comparison with
the first edition, and will, I hope, be more than compensated for by the
greater clearness of the exposition as it now stands.

I have observed, with pleasure and thankfulness, in the pages of various
reviews and treatises, that the spirit of profound and thorough investigation
is not extinct in Germany, though it may have been overborne and silenced for a
time by the fashionable tone of a licence in thinking, which gives itself the
airs of genius, and that the difficulties which beset the paths of criticism
have not prevented energetic and acute thinkers from making themselves masters
of the science of pure reason to which these paths conduct—a science
which is not popular, but scholastic in its character, and which alone can hope
for a lasting existence or possess an abiding value. To these deserving men,
who so happily combine profundity of view with a talent for lucid
exposition—a talent which I myself am not conscious of possessing—I
leave the task of removing any obscurity which may still adhere to the
statement of my doctrines. For, in this case, the danger is not that of being
refuted, but of being misunderstood. For my own part, I must henceforward
abstain from controversy, although I shall carefully attend to all suggestions,
whether from friends or adversaries, which may be of use in the future
elaboration of the system of this Propædeutic. As, during these labours, I have
advanced pretty far in years this month I reach my sixty-fourth year—it
will be necessary for me to economize time, if I am to carry out my plan of
elaborating the metaphysics of nature as well as of morals, in confirmation of
the correctness of the principles established in this Critique of Pure Reason,
both speculative and practical; and I must, therefore, leave the task of
clearing up the obscurities of the present work—inevitable, perhaps, at
the outset—as well as, the defence of the whole, to those deserving men,
who have made my system their own. A philosophical system cannot come forward
armed at all points like a mathematical treatise, and hence it may be quite
possible to take objection to particular passages, while the organic structure
of the system, considered as a unity, has no danger to apprehend. But few
possess the ability, and still fewer the inclination, to take a comprehensive
view of a new system. By confining the view to particular passages, taking
these out of their connection and comparing them with one another, it is easy
to pick out apparent contradictions, especially in a work written with any
freedom of style. These contradictions place the work in an unfavourable light
in the eyes of those who rely on the judgement of others, but are easily
reconciled by those who have mastered the idea of the whole. If a theory
possesses stability in itself, the action and reaction which seemed at first to
threaten its existence serve only, in the course of time, to smooth down any
superficial roughness or inequality, and—if men of insight, impartiality,
and truly popular gifts, turn their attention to it—to secure to it, in a
short time, the requisite elegance also.

KÖNIGSBERG, April 1787.

Introduction

I. Of the difference between Pure and Empirical
Knowledge

That all our knowledge begins with experience there can be no doubt. For how is
it possible that the faculty of cognition should be awakened into exercise
otherwise than by means of objects which affect our senses, and partly of
themselves produce representations, partly rouse our powers of understanding
into activity, to compare to connect, or to separate these, and so to convert
the raw material of our sensuous impressions into a knowledge of objects, which
is called experience? In respect of time, therefore, no knowledge of ours is
antecedent to experience, but begins with it.

But, though all our knowledge begins with experience, it by no means follows
that all arises out of experience. For, on the contrary, it is quite possible
that our empirical knowledge is a compound of that which we receive through
impressions, and that which the faculty of cognition supplies from itself
(sensuous impressions giving merely the occasion), an addition which we cannot
distinguish from the original element given by sense, till long practice has
made us attentive to, and skilful in separating it. It is, therefore, a
question which requires close investigation, and not to be answered at first
sight, whether there exists a knowledge altogether independent of experience,
and even of all sensuous impressions? Knowledge of this kind is called à
priori, in contradistinction to empirical knowledge, which has its sources à
posteriori, that is, in experience.

But the expression, “à priori,” is not as yet definite enough
adequately to indicate the whole meaning of the question above started. For, in
speaking of knowledge which has its sources in experience, we are wont to say,
that this or that may be known à priori, because we do not derive this
knowledge immediately from experience, but from a general rule, which, however,
we have itself borrowed from experience. Thus, if a man undermined his house,
we say, “he might know à priori that it would have fallen;” that
is, he needed not to have waited for the experience that it did actually fall.
But still, à priori, he could not know even this much. For, that bodies are
heavy, and, consequently, that they fall when their supports are taken away,
must have been known to him previously, by means of experience.

By the term “knowledge à priori,” therefore, we shall in the sequel
understand, not such as is independent of this or that kind of experience, but
such as is absolutely so of all experience. Opposed to this is empirical
knowledge, or that which is possible only à posteriori, that is, through
experience. Knowledge à priori is either pure or impure. Pure knowledge à
priori is that with which no empirical element is mixed up. For example, the
proposition, “Every change has a cause,” is a proposition à priori,
but impure, because change is a conception which can only be derived from
experience.

II. The Human Intellect, even in an Unphilosophical
State, is in Possession of Certain Cognitions “à priori”.

The question now is as to a criterion, by which we may securely distinguish a
pure from an empirical cognition. Experience no doubt teaches us that this or
that object is constituted in such and such a manner, but not that it could not
possibly exist otherwise. Now, in the first place, if we have a proposition
which contains the idea of necessity in its very conception, it is priori. If,
moreover, it is not derived from any other proposition, unless from one equally
involving the idea of necessity, it is absolutely priori. Secondly, an
empirical judgement never exhibits strict and absolute, but only assumed and
comparative universality (by induction); therefore, the most we can say
is—so far as we have hitherto observed, there is no exception to this or
that rule. If, on the other hand, a judgement carries with it strict and
absolute universality, that is, admits of no possible exception, it is not
derived from experience, but is valid absolutely à priori.

Empirical universality is, therefore, only an arbitrary extension of validity,
from that which may be predicated of a proposition valid 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 à 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 à 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 à 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 à 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 à 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 à 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 à priori.

III. Philosophy stands in need of a Science which
shall Determine the Possibility, Principles, and Extent of Human Knowledge
“à 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 à 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 à 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 à 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, à 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 à 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 à 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
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 à priori and from pure conceptions. Upon
such synthetical, that is augmentative propositions, depends the whole aim of
our speculative knowledge à 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 “à 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.

Before all, be it observed, that proper mathematical propositions are always
judgements à 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 à 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 à 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 à 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 à priori, which I did not think in
it. The proposition is therefore not analytical, but synthetical, and
nevertheless conceived à 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 à priori. It is not merely the duty of
metaphysics to dissect, and thereby analytically to illustrate the conceptions
which we form à priori of things; but we seek to widen the range of our à
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 à 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 à
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 à 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 à 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 à 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 à 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 à 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.^[9] 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.

[9]
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.

We may and must, therefore, regard the attempts hitherto made to establish
metaphysical science dogmatically as non-existent. For what of analysis, that
is, mere dissection of conceptions, is contained in one or other, is not the
aim of, but only a preparation for metaphysics proper, which has for its object
the extension, by means of synthesis, of our à priori knowledge. And for this
purpose, mere analysis is of course useless, because it only shows what is
contained in these conceptions, but not how we arrive, à priori, at them; and
this it is her duty to show, in order to be able afterwards to determine their
valid use in regard to all objects of experience, to all knowledge in general.
But little self-denial, indeed, is needed to give up these pretensions, seeing
the undeniable, and in the dogmatic mode of procedure, inevitable
contradictions of Reason with herself, have long since ruined the reputation of
every system of metaphysics that has appeared up to this time. It will require
more firmness to remain undeterred by difficulty from within, and opposition
from without, from endeavouring, by a method quite opposed to all those
hitherto followed, to further the growth and fruitfulness of a science
indispensable to human reason—a science from which every branch it has
borne may be cut away, but whose roots remain indestructible.

VII. Idea and Division of a Particular Science, under
the Name of a Critique of Pure Reason.

From all that has been said, there results the idea of a particular science,
which may be called the Critique of Pure Reason. For reason is the faculty
which furnishes us with the principles of knowledge à priori. Hence, pure
reason is the faculty which contains the principles of cognizing anything
absolutely à priori. An organon of pure reason would be a compendium of those
principles according to which alone all pure cognitions à priori can be
obtained. The completely extended application of such an organon would afford
us a system of pure reason. As this, however, is demanding a great deal, and it
is yet doubtful whether any extension of our knowledge be here possible, or, if
so, in what cases; we can regard a science of the mere criticism of pure
reason, its sources and limits, as the propædeutic to a system of pure reason.
Such a science must not be called a doctrine, but only a critique of pure
reason; and its use, in regard to speculation, would be only negative, not to
enlarge the bounds of, but to purify, our reason, and to shield it against
error—which alone is no little gain. I apply the term transcendental to
all knowledge which is not so much occupied with objects as with the mode of
our cognition of these objects, so far as this mode of cognition is possible à
priori. A system of such conceptions would be called transcendental philosophy.
But this, again, is still beyond the bounds of our present essay. For as such a
science must contain a complete exposition not only of our synthetical à
priori, but of our analytical à priori knowledge, it is of too wide a range for
our present purpose, because we do not require to carry our analysis any
farther than is necessary to understand, in their full extent, the principles
of synthesis à priori, with which alone we have to do. This investigation,
which we cannot properly call a doctrine, but only a transcendental critique,
because it aims not at the enlargement, but at the correction and guidance, of
our knowledge, and is to serve as a touchstone of the worth or worthlessness of
all knowledge à priori, is the sole object of our present essay. Such a
critique is consequently, as far as possible, a preparation for an organon; and
if this new organon should be found to fail, at least for a canon of pure
reason, according to which the complete system of the philosophy of pure
reason, whether it extend or limit the bounds of that reason, might one day be
set forth both analytically and synthetically. For that this is possible, nay,
that such a system is not of so great extent as to preclude the hope of its
ever being completed, is evident. For we have not here to do with the nature of
outward objects, which is infinite, but solely with the mind, which judges of
the nature of objects, and, again, with the mind only in respect of its
cognition à priori. And the object of our investigations, as it is not to be
sought without, but, altogether within, ourselves, cannot remain concealed, and
in all probability is limited enough to be completely surveyed and fairly
estimated, according to its worth or worthlessness. Still less let the reader
here expect a critique of books and systems of pure reason; our present object
is exclusively a critique of the faculty of pure reason itself. Only when we
make this critique our foundation, do we possess a pure touchstone for
estimating the philosophical value of ancient and modern writings on this
subject; and without this criterion, the incompetent historian or judge decides
upon and corrects the groundless assertions of others with his own, which have
themselves just as little foundation.

Transcendental philosophy is the idea of a science, for which the Critique of
Pure Reason must sketch the whole plan architectonically, that is, from
principles, with a full guarantee for the validity and stability of all the
parts which enter into the building. It is the system of all the principles of
pure reason. If this Critique itself does not assume the title of
transcendental philosophy, it is only because, to be a complete system, it
ought to contain a full analysis of all human knowledge à priori. Our critique
must, indeed, lay before us a complete enumeration of all the radical
conceptions which constitute the said pure knowledge. But from the complete
analysis of these conceptions themselves, as also from a complete investigation
of those derived from them, it abstains with reason; partly because it would be
deviating from the end in view to occupy itself with this analysis, since this
process is not attended with the difficulty and insecurity to be found in the
synthesis, to which our critique is entirely devoted, and partly because it
would be inconsistent with the unity of our plan to burden this essay with the
vindication of the completeness of such an analysis and deduction, with which,
after all, we have at present nothing to do. This completeness of the analysis
of these radical conceptions, as well as of the deduction from the conceptions
à priori which may be given by the analysis, we can, however, easily attain,
provided only that we are in possession of all these radical conceptions, which
are to serve as principles of the synthesis, and that in respect of this main
purpose nothing is wanting.

To the Critique of Pure Reason, therefore, belongs all that constitutes
transcendental philosophy; and it is the complete idea of transcendental
philosophy, but still not the science itself; because it only proceeds so far
with the analysis as is necessary to the power of judging completely of our
synthetical knowledge à priori.

The principal thing we must attend to, in the division of the parts of a
science like this, is that no conceptions must enter it which contain aught
empirical; in other words, that the knowledge à priori must be completely pure.
Hence, although the highest principles and fundamental conceptions of morality
are certainly cognitions à priori, yet they do not belong to transcendental
philosophy; because, though they certainly do not lay the conceptions of pain,
pleasure, desires, inclinations, etc. (which are all of empirical origin), at
the foundation of its precepts, yet still into the conception of duty—as
an obstacle to be overcome, or as an incitement which should not be made into a
motive—these empirical conceptions must necessarily enter, in the
construction of a system of pure morality. Transcendental philosophy is
consequently a philosophy of the pure and merely speculative reason. For all
that is practical, so far as it contains motives, relates to feelings, and
these belong to empirical sources of cognition.

If we wish to divide this science from the universal point of view of a science
in general, it ought to comprehend, first, a Doctrine of the Elements, and,
secondly, a Doctrine of the Method of pure reason. Each of these main divisions
will have its subdivisions, the separate reasons for which we cannot here
particularize. Only so much seems necessary, by way of introduction of
premonition, that there are two sources of human knowledge (which probably
spring from a common, but to us unknown root), namely, sense and understanding.
By the former, objects are given to us; by the latter, thought. So far as the
faculty of sense may contain representations à priori, which form the
conditions under which objects are given, in so far it belongs to
transcendental philosophy. The transcendental doctrine of sense must form the
first part of our science of elements, because the conditions under which alone
the objects of human knowledge are given must precede those under which they
are thought.

I. TRANSCENDENTAL DOCTRINE OF ELEMENTS.

FIRST PART. TRANSCENDENTAL ÆSTHETIC.

§ I. Introductory.

In whatsoever mode, or by whatsoever means, our knowledge may relate to
objects, it is at least quite clear that the only manner in which it
immediately relates to them is by means of an intuition. To this as the
indispensable groundwork, all thought points. But an intuition can take place
only in so far as the object is given to us. This, again, is only possible, to
man at least, on condition that the object affect the mind in a certain manner.
The capacity for receiving representations (receptivity) through the mode in
which we are affected by objects, objects, is called sensibility. By means of
sensibility, therefore, objects are given to us, and it alone furnishes us with
intuitions; by the understanding they are thought, and from it arise
conceptions. But an thought must directly, or indirectly, by means of certain
signs, relate ultimately to intuitions; consequently, with us, to sensibility,
because in no other way can an object be given to us.

The effect of an object upon the faculty of representation, so far as we are
affected by the said object, is sensation. That sort of intuition which relates
to an object by means of sensation is called an empirical intuition. The
undetermined object of an empirical intuition is called phenomenon. That which
in the phenomenon corresponds to the sensation, I term its matter; but that
which effects that the content of the phenomenon can be arranged under certain
relations, I call its form. But that in which our sensations are merely
arranged, and by which they are susceptible of assuming a certain form, cannot
be itself sensation. It is, then, the matter of all phenomena that is given to
us à posteriori; the form must lie ready à priori for them in the mind, and
consequently can be regarded separately from all sensation.

I call all representations pure, in the transcendental meaning of the word,
wherein nothing is met with that belongs to sensation. And accordingly we find
existing in the mind à priori, the pure form of sensuous intuitions in general,
in which all the manifold content of the phenomenal world is arranged and
viewed under certain relations. This pure form of sensibility I shall call pure
intuition. Thus, if I take away from our representation of a body all that the
understanding thinks as belonging to it, as substance, force, divisibility,
etc., and also whatever belongs to sensation, as impenetrability, hardness,
colour, etc.; yet there is still something left us from this empirical
intuition, namely, extension and shape. These belong to pure intuition, which
exists à priori in the mind, as a mere form of sensibility, and without any
real object of the senses or any sensation.

The science of all the principles of sensibility à priori, I call
transcendental æsthetic.^[10] There must, then, be such a science
forming the first part of the transcendental doctrine of elements, in
contradistinction to that part which contains the principles of pure thought,
and which is called transcendental logic.

[10]
The Germans are the only people who at present use this word to indicate what
others call the critique of taste. At the foundation of this term lies the
disappointed hope, which the eminent analyst, Baumgarten, conceived, of
subjecting the criticism of the beautiful to principles of reason, and so of
elevating its rules into a science. But his endeavours were vain. For the said
rules or criteria are, in respect to their chief sources, merely empirical,
consequently never can serve as determinate laws à priori, by which our
judgement in matters of taste is to be directed. It is rather our judgement
which forms the proper test as to the correctness of the principles. On this
account it is advisable to give up the use of the term as designating the
critique of taste, and to apply it solely to that doctrine, which is true
science—the science of the laws of sensibility—and thus come nearer
to the language and the sense of the ancients in their well-known division of
the objects of cognition into aiotheta kai noeta, or to share it with
speculative philosophy, and employ it partly in a transcendental, partly in a
psychological signification.

In the science of transcendental æsthetic accordingly, we shall first isolate
sensibility or the sensuous faculty, by separating from it all that is annexed
to its perceptions by the conceptions of understanding, so that nothing be left
but empirical intuition. In the next place we shall take away from this
intuition all that belongs to sensation, so that nothing may remain but pure
intuition, and the mere form of phenomena, which is all that the sensibility
can afford à priori. From this investigation it will be found that there are
two pure forms of sensuous intuition, as principles of knowledge à priori,
namely, space and time. To the consideration of these we shall now proceed.

SECTION I. Of Space.

§ 2. Metaphysical Exposition of this Conception.

By means of the external sense (a property of the mind), we represent to
ourselves objects as without us, and these all in space. Herein alone are their
shape, dimensions, and relations to each other determined or determinable. The
internal sense, by means of which the mind contemplates itself or its internal
state, gives, indeed, no intuition of the soul as an object; yet there is
nevertheless a determinate form, under which alone the contemplation of our
internal state is possible, so that all which relates to the inward
determinations of the mind is represented in relations of time. Of time we
cannot have any external intuition, any more than we can have an internal
intuition of space. What then are time and space? Are they real existences? Or,
are they merely relations or determinations of things, such, however, as would
equally belong to these things in themselves, though they should never become
objects of intuition; or, are they such as belong only to the form of
intuition, and consequently to the subjective constitution of the mind, without
which these predicates of time and space could not be attached to any object?
In order to become informed on these points, we shall first give an exposition
of the conception of space. By exposition, I mean the clear, though not
detailed, representation of that which belongs to a conception; and an
exposition is metaphysical when it contains that which represents the
conception as given à priori.

1. Space is not a conception which has been derived from outward experiences.
For, in order that certain sensations may relate to something without me (that
is, to something which occupies a different part of space from that in which I
am); in like manner, in order that I may represent them not merely as without,
of, and near to each other, but also in separate places, the representation of
space must already exist as a foundation. Consequently, the representation of
space cannot be borrowed from the relations of external phenomena through
experience; but, on the contrary, this external experience is itself only
possible through the said antecedent representation.

2. Space then is a necessary representation à priori, which serves for the
foundation of all external intuitions. We never can imagine or make a
representation to ourselves of the non-existence of space, though we may easily
enough think that no objects are found in it. It must, therefore, be considered
as the condition of the possibility of phenomena, and by no means as a
determination dependent on them, and is a representation à priori, which
necessarily supplies the basis for external phenomena.

3. Space is no discursive, or as we say, general conception of the relations of
things, but a pure intuition. For, in the first place, we can only represent to
ourselves one space, and, when we talk of divers spaces, we mean only parts of
one and the same space. Moreover, these parts cannot antecede this one
all-embracing space, as the component parts from which the aggregate can be
made up, but can be cogitated only as existing in it. Space is essentially one,
and multiplicity in it, consequently the general notion of spaces, of this or
that space, depends solely upon limitations. Hence it follows that an à priori
intuition (which is not empirical) lies at the root of all our conceptions of
space. Thus, moreover, the principles of geometry—for example, that
“in a triangle, two sides together are greater than the third,” are
never deduced from general conceptions of line and triangle, but from
intuition, and this à priori, with apodeictic certainty.

4. Space is represented as an infinite given quantity. Now every conception
must indeed be considered as a representation which is contained in an infinite
multitude of different possible representations, which, therefore, comprises
these under itself; but no conception, as such, can be so conceived, as if it
contained within itself an infinite multitude of representations. Nevertheless,
space is so conceived of, for all parts of space are equally capable of being
produced to infinity. Consequently, the original representation of space is an
intuition à priori, and not a conception.

§ 3. Transcendental Exposition of the Conception of
Space.

By a transcendental exposition, I mean the explanation of a conception, as a
principle, whence can be discerned the possibility of other synthetical à
priori cognitions. For this purpose, it is requisite, firstly, that such
cognitions do really flow from the given conception; and, secondly, that the
said cognitions are only possible under the presupposition of a given mode of
explaining this conception.

Geometry is a science which determines the properties of space synthetically,
and yet à priori. What, then, must be our representation of space, in order
that such a cognition of it may be possible? It must be originally intuition,
for from a mere conception, no propositions can be deduced which go out beyond
the conception, and yet this happens in geometry. (Introd. V.) But this
intuition must be found in the mind à priori, that is, before any perception of
objects, consequently must be pure, not empirical, intuition. For geometrical
principles are always apodeictic, that is, united with the consciousness of
their necessity, as: “Space has only three dimensions.” But
propositions of this kind cannot be empirical judgements, nor conclusions from
them. (Introd. II.) Now, how can an external intuition anterior to objects
themselves, and in which our conception of objects can be determined à priori,
exist in the human mind? Obviously not otherwise than in so far as it has its
seat in the subject only, as the formal capacity of the subject’s being
affected by objects, and thereby of obtaining immediate representation, that
is, intuition; consequently, only as the form of the external sense in general.

Thus it is only by means of our explanation that the possibility of geometry,
as a synthetical science à priori, becomes comprehensible. Every mode of
explanation which does not show us this possibility, although in appearance it
may be similar to ours, can with the utmost certainty be distinguished from it
by these marks.

§ 4. Conclusions from the foregoing Conceptions.

(a) Space does not represent any property of objects as things in themselves,
nor does it represent them in their relations to each other; in other words,
space does not represent to us any determination of objects such as attaches to
the objects themselves, and would remain, even though all subjective conditions
of the intuition were abstracted. For neither absolute nor relative
determinations of objects can be intuited prior to the existence of the things
to which they belong, and therefore not à priori.

(b) Space is nothing else than the form of all phenomena of the external sense,
that is, the subjective condition of the sensibility, under which alone
external intuition is possible. Now, because the receptivity or capacity of the
subject to be affected by objects necessarily antecedes all intuitions of these
objects, it is easily understood how the form of all phenomena can be given in
the mind previous to all actual perceptions, therefore à priori, and how it, as
a pure intuition, in which all objects must be determined, can contain
principles of the relations of these objects prior to all experience.

It is therefore from the human point of view only that we can speak of space,
extended objects, etc. If we depart from the subjective condition, under which
alone we can obtain external intuition, or, in other words, by means of which
we are affected by objects, the representation of space has no meaning
whatsoever. This predicate is only applicable to things in so far as they
appear to us, that is, are objects of sensibility. The constant form of this
receptivity, which we call sensibility, is a necessary condition of all
relations in which objects can be intuited as existing without us, and when
abstraction of these objects is made, is a pure intuition, to which we give the
name of space. It is clear that we cannot make the special conditions of
sensibility into conditions of the possibility of things, but only of the
possibility of their existence as far as they are phenomena. And so we may
correctly say that space contains all which can appear to us externally, but
not all things considered as things in themselves, be they intuited or not, or
by whatsoever subject one will. As to the intuitions of other thinking beings,
we cannot judge whether they are or are not bound by the same conditions which
limit our own intuition, and which for us are universally valid. If we join the
limitation of a judgement to the conception of the subject, then the judgement
will possess unconditioned validity. For example, the proposition, “All
objects are beside each other in space,” is valid only under the
limitation that these things are taken as objects of our sensuous intuition.
But if I join the condition to the conception and say, “All things, as
external phenomena, are beside each other in space,” then the rule is
valid universally, and without any limitation. Our expositions, consequently,
teach the reality (i.e., the objective validity) of space in regard of all
which can be presented to us externally as object, and at the same time also
the ideality of space in regard to objects when they are considered by means of
reason as things in themselves, that is, without reference to the constitution
of our sensibility. We maintain, therefore, the empirical reality of space in
regard to all possible external experience, although we must admit its
transcendental ideality; in other words, that it is nothing, so soon as we
withdraw the condition upon which the possibility of all experience depends and
look upon space as something that belongs to things in themselves.

But, with the exception of space, there is no representation, subjective and
referring to something external to us, which could be called objective à
priori. For there are no other subjective representations from which we can
deduce synthetical propositions à priori, as we can from the intuition of
space. (See § 3.) Therefore, to speak accurately, no ideality whatever belongs
to these, although they agree in this respect with the representation of space,
that they belong merely to the subjective nature of the mode of sensuous
perception; such a mode, for example, as that of sight, of hearing, and of
feeling, by means of the sensations of colour, sound, and heat, but which,
because they are only sensations and not intuitions, do not of themselves give
us the cognition of any object, least of all, an à priori cognition. My
purpose, in the above remark, is merely this: to guard any one against
illustrating the asserted ideality of space by examples quite insufficient, for
example, by colour, taste, etc.; for these must be contemplated not as
properties of things, but only as changes in the subject, changes which may be
different in different men. For, in such a case, that which is originally a
mere phenomenon, a rose, for example, is taken by the empirical understanding
for a thing in itself, though to every different eye, in respect of its colour,
it may appear different. On the contrary, the transcendental conception of
phenomena in space is a critical admonition, that, in general, nothing which is
intuited in space is a thing in itself, and that space is not a form which
belongs as a property to things; but that objects are quite unknown to us in
themselves, and what we call outward objects, are nothing else but mere
representations of our sensibility, whose form is space, but whose real
correlate, the thing in itself, is not known by means of these representations,
nor ever can be, but respecting which, in experience, no inquiry is ever made.

SECTION II. Of Time.

§ 5. Metaphysical Exposition of this Conception.

1. Time is not an empirical conception. For neither coexistence nor succession
would be perceived by us, if the representation of time did not exist as a
foundation à priori. Without this presupposition we could not represent to
ourselves that things exist together at one and the same time, or at different
times, that is, contemporaneously, or in succession.

2. Time is a necessary representation, lying at the foundation of all our
intuitions. With regard to phenomena in general, we cannot think away time from
them, and represent them to ourselves as out of and unconnected with time, but
we can quite well represent to ourselves time void of phenomena. Time is
therefore given à priori. In it alone is all reality of phenomena possible.
These may all be annihilated in thought, but time itself, as the universal
condition of their possibility, cannot be so annulled.

3. On this necessity à priori is also founded the possibility of apodeictic
principles of the relations of time, or axioms of time in general, such as:
“Time has only one dimension,” “Different times are not
coexistent but successive” (as different spaces are not successive but
coexistent). These principles cannot be derived from experience, for it would
give neither strict universality, nor apodeictic certainty. We should only be
able to say, “so common experience teaches us,” but not “it
must be so.” They are valid as rules, through which, in general,
experience is possible; and they instruct us respecting experience, and not by
means of it.

4. Time is not a discursive, or as it is called, general conception, but a pure
form of the sensuous intuition. Different times are merely parts of one and the
same time. But the representation which can only be given by a single object is
an intuition. Besides, the proposition that different times cannot be
coexistent could not be derived from a general conception. For this proposition
is synthetical, and therefore cannot spring out of conceptions alone. It is
therefore contained immediately in the intuition and representation of time.

5. The infinity of time signifies nothing more than that every determined
quantity of time is possible only through limitations of one time lying at the
foundation. Consequently, the original representation, time, must be given as
unlimited. But as the determinate representation of the parts of time and of
every quantity of an object can only be obtained by limitation, the complete
representation of time must not be furnished by means of conceptions, for these
contain only partial representations. Conceptions, on the contrary, must have
immediate intuition for their basis.

§ 6 Transcendental Exposition of the Conception of
Time.

I may here refer to what is said above (§ 5, 3), where, for or sake of brevity,
I have placed under the head of metaphysical exposition, that which is properly
transcendental. Here I shall add that the conception of change, and with it the
conception of motion, as change of place, is possible only through and in the
representation of time; that if this representation were not an intuition
(internal) à priori, no conception, of whatever kind, could render
comprehensible the possibility of change, in other words, of a conjunction of
contradictorily opposed predicates in one and the same object, for example, the
presence of a thing in a place and the non-presence of the same thing in the
same place. It is only in time that it is possible to meet with two
contradictorily opposed determinations in one thing, that is, after each other.
Thus our conception of time explains the possibility of so much synthetical
knowledge à priori, as is exhibited in the general doctrine of motion, which is
not a little fruitful.

§ 7. Conclusions from the above Conceptions.

(a) Time is not something which subsists of itself, or which inheres in things
as an objective determination, and therefore remains, when abstraction is made
of the subjective conditions of the intuition of things. For in the former
case, it would be something real, yet without presenting to any power of
perception any real object. In the latter case, as an order or determination
inherent in things themselves, it could not be antecedent to things, as their
condition, nor discerned or intuited by means of synthetical propositions à
priori. But all this is quite possible when we regard time as merely the
subjective condition under which all our intuitions take place. For in that
case, this form of the inward intuition can be represented prior to the
objects, and consequently à priori.

(b) Time is nothing else than the form of the internal sense, that is, of the
intuitions of self and of our internal state. For time cannot be any
determination of outward phenomena. It has to do neither with shape nor
position; on the contrary, it determines the relation of representations in our
internal state. And precisely because this internal intuition presents to us no
shape or form, we endeavour to supply this want by analogies, and represent the
course of time by a line progressing to infinity, the content of which
constitutes a series which is only of one dimension; and we conclude from the
properties of this line as to all the properties of time, with this single
exception, that the parts of the line are coexistent, whilst those of time are
successive. From this it is clear also that the representation of time is
itself an intuition, because all its relations can be expressed in an external
intuition.

(c) Time is the formal condition à priori of all phenomena whatsoever. Space,
as the pure form of external intuition, is limited as a condition à priori to
external phenomena alone. On the other hand, because all representations,
whether they have or have not external things for their objects, still in
themselves, as determinations of the mind, belong to our internal state; and
because this internal state is subject to the formal condition of the internal
intuition, that is, to time—time is a condition à priori of all phenomena
whatsoever—the immediate condition of all internal, and thereby the
mediate condition of all external phenomena. If I can say à priori, “All
outward phenomena are in space, and determined à priori according to the
relations of space,” I can also, from the principle of the internal
sense, affirm universally, “All phenomena in general, that is, all
objects of the senses, are in time and stand necessarily in relations of
time.”

If we abstract our internal intuition of ourselves and all external intuitions,
possible only by virtue of this internal intuition and presented to us by our
faculty of representation, and consequently take objects as they are in
themselves, then time is nothing. It is only of objective validity in regard to
phenomena, because these are things which we regard as objects of our senses.
It no longer objective we, make abstraction of the sensuousness of our
intuition, in other words, of that mode of representation which is peculiar to
us, and speak of things in general. Time is therefore merely a subjective
condition of our (human) intuition (which is always sensuous, that is, so far
as we are affected by objects), and in itself, independently of the mind or
subject, is nothing. Nevertheless, in respect of all phenomena, consequently of
all things which come within the sphere of our experience, it is necessarily
objective. We cannot say, “All things are in time,” because in this
conception of things in general, we abstract and make no mention of any sort of
intuition of things. But this is the proper condition under which time belongs
to our representation of objects. If we add the condition to the conception,
and say, “All things, as phenomena, that is, objects of sensuous
intuition, are in time,” then the proposition has its sound objective
validity and universality à priori.

What we have now set forth teaches, therefore, the empirical reality of time;
that is, its objective validity in reference to all objects which can ever be
presented to our senses. And as our intuition is always sensuous, no object
ever can be presented to us in experience, which does not come under the
conditions of time. On the other hand, we deny to time all claim to absolute
reality; that is, we deny that it, without having regard to the form of our
sensuous intuition, absolutely inheres in things as a condition or property.
Such properties as belong to objects as things in themselves never can be
presented to us through the medium of the senses. Herein consists, therefore,
the transcendental ideality of time, according to which, if we abstract the
subjective conditions of sensuous intuition, it is nothing, and cannot be
reckoned as subsisting or inhering in objects as things in themselves,
independently of its relation to our intuition. This ideality, like that of
space, is not to be proved or illustrated by fallacious analogies with
sensations, for this reason—that in such arguments or illustrations, we
make the presupposition that the phenomenon, in which such and such predicates
inhere, has objective reality, while in this case we can only find such an
objective reality as is itself empirical, that is, regards the object as a mere
phenomenon. In reference to this subject, see the remark in Section I (§ 4)

§ 8. Elucidation.

Against this theory, which grants empirical reality to time, but denies to it
absolute and transcendental reality, I have heard from intelligent men an
objection so unanimously urged that I conclude that it must naturally present
itself to every reader to whom these considerations are novel. It runs thus:
“Changes are real” (this the continual change in our own
representations demonstrates, even though the existence of all external
phenomena, together with their changes, is denied). Now, changes are only
possible in time, and therefore time must be something real. But there is no
difficulty in answering this. I grant the whole argument. Time, no doubt, is
something real, that is, it is the real form of our internal intuition. It
therefore has subjective reality, in reference to our internal experience, that
is, I have really the representation of time and of my determinations therein.
Time, therefore, is not to be regarded as an object, but as the mode of
representation of myself as an object. But if I could intuite myself, or be
intuited by another being, without this condition of sensibility, then those
very determinations which we now represent to ourselves as changes, would
present to us a knowledge in which the representation of time, and consequently
of change, would not appear. The empirical reality of time, therefore, remains,
as the condition of all our experience. But absolute reality, according to what
has been said above, cannot be granted it. Time is nothing but the form of our
internal intuition.^[11] If we take away from it the special
condition of our sensibility, the conception of time also vanishes; and it
inheres not in the objects themselves, but solely in the subject (or mind)
which intuites them.

[11]
I can indeed say “my representations follow one another, or are
successive”; but this means only that we are conscious of them as in a
succession, that is, according to the form of the internal sense. Time,
therefore, is not a thing in itself, nor is it any objective determination
pertaining to, or inherent in things.

But the reason why this objection is so unanimously brought against our
doctrine of time, and that too by disputants who cannot start any intelligible
arguments against the doctrine of the ideality of space, is this—they
have no hope of demonstrating apodeictically the absolute reality of space,
because the doctrine of idealism is against them, according to which the
reality of external objects is not capable of any strict proof. On the other
hand, the reality of the object of our internal sense (that is, myself and my
internal state) is clear immediately through consciousness. The
former—external objects in space—might be a mere delusion, but the
latter—the object of my internal perception—is undeniably real.
They do not, however, reflect that both, without question of their reality as
representations, belong only to the genus phenomenon, which has always two
aspects, the one, the object considered as a thing in itself, without regard to
the mode of intuiting it, and the nature of which remains for this very reason
problematical, the other, the form of our intuition of the object, which must
be sought not in the object as a thing in itself, but in the subject to which
it appears—which form of intuition nevertheless belongs really and
necessarily to the phenomenal object.

Time and space are, therefore, two sources of knowledge, from which, à priori,
various synthetical cognitions can be drawn. Of this we find a striking example
in the cognitions of space and its relations, which form the foundation of pure
mathematics. They are the two pure forms of all intuitions, and thereby make
synthetical propositions à priori possible. But these sources of knowledge
being merely conditions of our sensibility, do therefore, and as such, strictly
determine their own range and purpose, in that they do not and cannot present
objects as things in themselves, but are applicable to them solely in so far as
they are considered as sensuous phenomena. The sphere of phenomena is the only
sphere of their validity, and if we venture out of this, no further objective
use can be made of them. For the rest, this formal reality of time and space
leaves the validity of our empirical knowledge unshaken; for our certainty in
that respect is equally firm, whether these forms necessarily inhere in the
things themselves, or only in our intuitions of them. On the other hand, those
who maintain the absolute reality of time and space, whether as essentially
subsisting, or only inhering, as modifications, in things, must find themselves
at utter variance with the principles of experience itself. For, if they decide
for the first view, and make space and time into substances, this being the
side taken by mathematical natural philosophers, they must admit two
self-subsisting nonentities, infinite and eternal, which exist (yet without
there being anything real) for the purpose of containing in themselves
everything that is real. If they adopt the second view of inherence, which is
preferred by some metaphysical natural philosophers, and regard space and time
as relations (contiguity in space or succession in time), abstracted from
experience, though represented confusedly in this state of separation, they
find themselves in that case necessitated to deny the validity of mathematical
doctrines à priori in reference to real things (for example, in space)—at
all events their apodeictic certainty. For such certainty cannot be found in an
à posteriori proposition; and the conceptions à priori of space and time are,
according to this opinion, mere creations of the imagination, having their
source really in experience, inasmuch as, out of relations abstracted from
experience, imagination has made up something which contains, indeed, general
statements of these relations, yet of which no application can be made without
the restrictions attached thereto by nature. The former of these parties gains
this advantage, that they keep the sphere of phenomena free for mathematical
science. On the other hand, these very conditions (space and time) embarrass
them greatly, when the understanding endeavours to pass the limits of that
sphere. The latter has, indeed, this advantage, that the representations of
space and time do not come in their way when they wish to judge of objects, not
as phenomena, but merely in their relation to the understanding. Devoid,
however, of a true and objectively valid à priori intuition, they can neither
furnish any basis for the possibility of mathematical cognitions à priori, nor
bring the propositions of experience into necessary accordance with those of
mathematics. In our theory of the true nature of these two original forms of
the sensibility, both difficulties are surmounted.

In conclusion, that transcendental æsthetic cannot contain any more than these
two elements—space and time, is sufficiently obvious from the fact that
all other conceptions appertaining to sensibility, even that of motion, which
unites in itself both elements, presuppose something empirical. Motion, for
example, presupposes the perception of something movable. But space considered
in itself contains nothing movable, consequently motion must be something which
is found in space only through experience—in other words, an empirical
datum. In like manner, transcendental æsthetic cannot number the conception of
change among its data à priori; for time itself does not change, but only
something which is in time. To acquire the conception of change, therefore, the
perception of some existing object and of the succession of its determinations,
in one word, experience, is necessary.

§ 9. General Remarks on Transcendental Æsthetic.

I. In order to prevent any misunderstanding, it will be requisite, in the first
place, to recapitulate, as clearly as possible, what our opinion is with
respect to the fundamental nature of our sensuous cognition in general. We have
intended, then, to say that all our intuition is nothing but the representation
of phenomena; that the things which we intuite, are not in themselves the same
as our representations of them in intuition, nor are their relations in
themselves so constituted as they appear to us; and that if we take away the
subject, or even only the subjective constitution of our senses in general,
then not only the nature and relations of objects in space and time, but even
space and time themselves disappear; and that these, as phenomena, cannot exist
in themselves, but only in us. What may be the nature of objects considered as
things in themselves and without reference to the receptivity of our
sensibility is quite unknown to us. We know nothing more than our mode of
perceiving them, which is peculiar to us, and which, though not of necessity
pertaining to every animated being, is so to the whole human race. With this
alone we have to do. Space and time are the pure forms thereof; sensation the
matter. The former alone can we cognize à priori, that is, antecedent to all
actual perception; and for this reason such cognition is called pure intuition.
The latter is that in our cognition which is called cognition à posteriori,
that is, empirical intuition. The former appertain absolutely and necessarily
to our sensibility, of whatsoever kind our sensations may be; the latter may be
of very diversified character. Supposing that we should carry our empirical
intuition even to the very highest degree of clearness, we should not thereby
advance one step nearer to a knowledge of the constitution of objects as things
in themselves. For we could only, at best, arrive at a complete cognition of
our own mode of intuition, that is of our sensibility, and this always under
the conditions originally attaching to the subject, namely, the conditions of
space and time; while the question: “What are objects considered as
things in themselves?” remains unanswerable even after the most thorough
examination of the phenomenal world.

To say, then, that all our sensibility is nothing but the confused
representation of things containing exclusively that which belongs to them as
things in themselves, and this under an accumulation of characteristic marks
and partial representations which we cannot distinguish in consciousness, is a
falsification of the conception of sensibility and phenomenization, which
renders our whole doctrine thereof empty and useless. The difference between a
confused and a clear representation is merely logical and has nothing to do
with content. No doubt the conception of right, as employed by a sound
understanding, contains all that the most subtle investigation could unfold
from it, although, in the ordinary practical use of the word, we are not
conscious of the manifold representations comprised in the conception. But we
cannot for this reason assert that the ordinary conception is a sensuous one,
containing a mere phenomenon, for right cannot appear as a phenomenon; but the
conception of it lies in the understanding, and represents a property (the
moral property) of actions, which belongs to them in themselves. On the other
hand, the representation in intuition of a body contains nothing which could
belong to an object considered as a thing in itself, but merely the phenomenon
or appearance of something, and the mode in which we are affected by that
appearance; and this receptivity of our faculty of cognition is called
sensibility, and remains toto caelo different from the cognition of an object
in itself, even though we should examine the content of the phenomenon to the
very bottom.

It must be admitted that the Leibnitz-Wolfian philosophy has assigned an
entirely erroneous point of view to all investigations into the nature and
origin of our cognitions, inasmuch as it regards the distinction between the
sensuous and the intellectual as merely logical, whereas it is plainly
transcendental, and concerns not merely the clearness or obscurity, but the
content and origin of both. For the faculty of sensibility not only does not
present us with an indistinct and confused cognition of objects as things in
themselves, but, in fact, gives us no knowledge of these at all. On the
contrary, so soon as we abstract in thought our own subjective nature, the
object represented, with the properties ascribed to it by sensuous intuition,
entirely disappears, because it was only this subjective nature that determined
the form of the object as a phenomenon.

In phenomena, we commonly, indeed, distinguish that which essentially belongs
to the intuition of them, and is valid for the sensuous faculty of every human
being, from that which belongs to the same intuition accidentally, as valid not
for the sensuous faculty in general, but for a particular state or organization
of this or that sense. Accordingly, we are accustomed to say that the former is
a cognition which represents the object itself, whilst the latter presents only
a particular appearance or phenomenon thereof. This distinction, however, is
only empirical. If we stop here (as is usual), and do not regard the empirical
intuition as itself a mere phenomenon (as we ought to do), in which nothing
that can appertain to a thing in itself is to be found, our transcendental
distinction is lost, and we believe that we cognize objects as things in
themselves, although in the whole range of the sensuous world, investigate the
nature of its objects as profoundly as we may, we have to do with nothing but
phenomena. Thus, we call the rainbow a mere appearance of phenomenon in a sunny
shower, and the rain, the reality or thing in itself; and this is right enough,
if we understand the latter conception in a merely physical sense, that is, as
that which in universal experience, and under whatever conditions of sensuous
perception, is known in intuition to be so and so determined, and not
otherwise. But if we consider this empirical datum generally, and inquire,
without reference to its accordance with all our senses, whether there can be
discovered in it aught which represents an object as a thing in itself (the
raindrops of course are not such, for they are, as phenomena, empirical
objects), the question of the relation of the representation to the object is
transcendental; and not only are the raindrops mere phenomena, but even their
circular form, nay, the space itself through which they fall, is nothing in
itself, but both are mere modifications or fundamental dispositions of our
sensuous intuition, whilst the transcendental object remains for us utterly
unknown.

The second important concern of our æsthetic is that it does not obtain favour
merely as a plausible hypothesis, but possess as undoubted a character of
certainty as can be demanded of any theory which is to serve for an organon. In
order fully to convince the reader of this certainty, we shall select a case
which will serve to make its validity apparent, and also to illustrate what has
been said in § 3.

Suppose, then, that space and time are in themselves objective, and conditions
of the—possibility of objects as things in themselves. In the first
place, it is evident that both present us, with very many apodeictic and
synthetic propositions à priori, but especially space—and for this reason
we shall prefer it for investigation at present. As the propositions of
geometry are cognized synthetically à priori, and with apodeictic certainty, I
inquire: Whence do you obtain propositions of this kind, and on what basis does
the understanding rest, in order to arrive at such absolutely necessary and
universally valid truths?

There is no other way than through intuitions or conceptions, as such; and
these are given either à priori or à posteriori. The latter, namely, empirical
conceptions, together with the empirical intuition on which they are founded,
cannot afford any synthetical proposition, except such as is itself also
empirical, that is, a proposition of experience. But an empirical proposition
cannot possess the qualities of necessity and absolute universality, which,
nevertheless, are the characteristics of all geometrical propositions. As to
the first and only means to arrive at such cognitions, namely, through mere
conceptions or intuitions à priori, it is quite clear that from mere
conceptions no synthetical cognitions, but only analytical ones, can be
obtained. Take, for example, the proposition: “Two straight lines cannot
enclose a space, and with these alone no figure is possible,” and try to
deduce it from the conception of a straight line and the number two; or take
the proposition: “It is possible to construct a figure with three
straight lines,” and endeavour, in like manner, to deduce it from the
mere conception of a straight line and the number three. All your endeavours
are in vain, and you find yourself forced to have recourse to intuition, as, in
fact, geometry always does. You therefore give yourself an object in intuition.
But of what kind is this intuition? Is it a pure à priori, or is it an
empirical intuition? If the latter, then neither an universally valid, much
less an apodeictic proposition can arise from it, for experience never can give
us any such proposition. You must, therefore, give yourself an object à priori
in intuition, and upon that ground your synthetical proposition. Now if there
did not exist within you a faculty of intuition à priori; if this subjective
condition were not in respect to its form also the universal condition à priori
under which alone the object of this external intuition is itself possible; if
the object (that is, the triangle) were something in itself, without relation
to you the subject; how could you affirm that that which lies necessarily in
your subjective conditions in order to construct a triangle, must also
necessarily belong to the triangle in itself? For to your conceptions of three
lines, you could not add anything new (that is, the figure); which, therefore,
must necessarily be found in the object, because the object is given before
your cognition, and not by means of it. If, therefore, space (and time also)
were not a mere form of your intuition, which contains conditions à priori,
under which alone things can become external objects for you, and without which
subjective conditions the objects are in themselves nothing, you could not
construct any synthetical proposition whatsoever regarding external objects. It
is therefore not merely possible or probable, but indubitably certain, that
space and time, as the necessary conditions of all our external and internal
experience, are merely subjective conditions of all our intuitions, in relation
to which all objects are therefore mere phenomena, and not things in
themselves, presented to us in this particular manner. And for this reason, in
respect to the form of phenomena, much may be said à priori, whilst of the
thing in itself, which may lie at the foundation of these phenomena, it is
impossible to say anything.

II. In confirmation of this theory of the ideality of the external as well as
internal sense, consequently of all objects of sense, as mere phenomena, we may
especially remark that all in our cognition that belongs to intuition contains
nothing more than mere relations. (The feelings of pain and pleasure, and the
will, which are not cognitions, are excepted.) The relations, to wit, of place
in an intuition (extension), change of place (motion), and laws according to
which this change is determined (moving forces). That, however, which is
present in this or that place, or any operation going on, or result taking
place in the things themselves, with the exception of change of place, is not
given to us by intuition. Now by means of mere relations, a thing cannot be
known in itself; and it may therefore be fairly concluded, that, as through the
external sense nothing but mere representations of relations are given us, the
said external sense in its representation can contain only the relation of the
object to the subject, but not the essential nature of the object as a thing in
itself.

The same is the case with the internal intuition, not only because, in the
internal intuition, the representation of the external senses constitutes the
material with which the mind is occupied; but because time, in which we place,
and which itself antecedes the consciousness of, these representations in
experience, and which, as the formal condition of the mode according to which
objects are placed in the mind, lies at the foundation of them, contains
relations of the successive, the coexistent, and of that which always must be
coexistent with succession, the permanent. Now that which, as representation,
can antecede every exercise of thought (of an object), is intuition; and when
it contains nothing but relations, it is the form of the intuition, which, as
it presents us with no representation, except in so far as something is placed
in the mind, can be nothing else than the mode in which the mind is affected by
its own activity, to wit—its presenting to itself representations,
consequently the mode in which the mind is affected by itself; that is, it can
be nothing but an internal sense in respect to its form. Everything that is
represented through the medium of sense is so far phenomenal; consequently, we
must either refuse altogether to admit an internal sense, or the subject, which
is the object of that sense, could only be represented by it as phenomenon, and
not as it would judge of itself, if its intuition were pure spontaneous
activity, that is, were intellectual. The difficulty here lies wholly in the
question: How can the subject have an internal intuition of itself? But this
difficulty is common to every theory. The consciousness of self (apperception)
is the simple representation of the “ego”; and if by means of that
representation alone, all the manifold representations in the subject were
spontaneously given, then our internal intuition would be intellectual. This
consciousness in man requires an internal perception of the manifold
representations which are previously given in the subject; and the manner in
which these representations are given in the mind without spontaneity, must, on
account of this difference (the want of spontaneity), be called sensibility. If
the faculty of self-consciousness is to apprehend what lies in the mind, it
must all act that and can in this way alone produce an intuition of self. But
the form of this intuition, which lies in the original constitution of the
mind, determines, in the representation of time, the manner in which the
manifold representations are to combine themselves in the mind; since the
subject intuites itself, not as it would represent itself immediately and
spontaneously, but according to the manner in which the mind is internally
affected, consequently, as it appears, and not as it is.

III. When we say that the intuition of external objects, and also the
self-intuition of the subject, represent both, objects and subject, in space
and time, as they affect our senses, that is, as they appear—this is by
no means equivalent to asserting that these objects are mere illusory
appearances. For when we speak of things as phenomena, the objects, nay, even
the properties which we ascribe to them, are looked upon as really given; only
that, in so far as this or that property depends upon the mode of intuition of
the subject, in the relation of the given object to the subject, the object as
phenomenon is to be distinguished from the object as a thing in itself. Thus I
do not say that bodies seem or appear to be external to me, or that my soul
seems merely to be given in my self-consciousness, although I maintain that the
properties of space and time, in conformity to which I set both, as the
condition of their existence, abide in my mode of intuition, and not in the
objects in themselves. It would be my own fault, if out of that which I should
reckon as phenomenon, I made mere illusory appearance.^[12] But this will not
happen, because of our principle of the ideality of all sensuous intuitions. On
the contrary, if we ascribe objective reality to these forms of representation,
it becomes impossible to avoid changing everything into mere appearance. For if
we regard space and time as properties, which must be found in objects as
things in themselves, as sine quibus non of the possibility of their existence,
and reflect on the absurdities in which we then find ourselves involved,
inasmuch as we are compelled to admit the existence of two infinite things,
which are nevertheless not substances, nor anything really inhering in
substances, nay, to admit that they are the necessary conditions of the
existence of all things, and moreover, that they must continue to exist,
although all existing things were annihilated—we cannot blame the good
Berkeley for degrading bodies to mere illusory appearances. Nay, even our own
existence, which would in this case depend upon the self-existent reality of
such a mere nonentity as time, would necessarily be changed with it into mere
appearance—an absurdity which no one has as yet been guilty of.

[12]
The predicates of the phenomenon can be affixed to the object itself in
relation to our sensuous faculty; for example, the red colour or the perfume to
the rose. But (illusory) appearance never can be attributed as a predicate to
an object, for this very reason, that it attributes to this object in itself
that which belongs to it only in relation to our sensuous faculty, or to the
subject in general, e.g., the two handles which were formerly ascribed to
Saturn. That which is never to be found in the object itself, but always in the
relation of the object to the subject, and which moreover is inseparable from
our representation of the object, we denominate phenomenon. Thus the predicates
of space and time are rightly attributed to objects of the senses as such, and
in this there is no illusion. On the contrary, if I ascribe redness of the rose
as a thing in itself, or to Saturn his handles, or extension to all external
objects, considered as things in themselves, without regarding the determinate
relation of these objects to the subject, and without limiting my judgement to
that relation—then, and then only, arises illusion.

IV. In natural theology, where we think of an object—God—which
never can be an object of intuition to us, and even to himself can never be an
object of sensuous intuition, we carefully avoid attributing to his intuition
the conditions of space and time—and intuition all his cognition must be,
and not thought, which always includes limitation. But with what right can we
do this if we make them forms of objects as things in themselves, and such,
moreover, as would continue to exist as à priori conditions of the existence of
things, even though the things themselves were annihilated? For as conditions
of all existence in general, space and time must be conditions of the existence
of the Supreme Being also. But if we do not thus make them objective forms of
all things, there is no other way left than to make them subjective forms of
our mode of intuition—external and internal; which is called sensuous,
because it is not primitive, that is, is not such as gives in itself the
existence of the object of the intuition (a mode of intuition which, so far as
we can judge, can belong only to the Creator), but is dependent on the
existence of the object, is possible, therefore, only on condition that the
representative faculty of the subject is affected by the object.

It is, moreover, not necessary that we should limit the mode of intuition in
space and time to the sensuous faculty of man. It may well be that all finite
thinking beings must necessarily in this respect agree with man (though as to
this we cannot decide), but sensibility does not on account of this
universality cease to be sensibility, for this very reason, that it is a
deduced (intuitus derivativus), and not an original (intuitus originarius),
consequently not an intellectual intuition, and this intuition, as such, for
reasons above mentioned, seems to belong solely to the Supreme Being, but never
to a being dependent, quoad its existence, as well as its intuition (which its
existence determines and limits relatively to given objects). This latter
remark, however, must be taken only as an illustration, and not as any proof of
the truth of our æsthetical theory.

§ 10. Conclusion of the Transcendental Æsthetic.

We have now completely before us one part of the solution of the grand general
problem of transcendental philosophy, namely, the question: “How are
synthetical propositions à priori possible?” That is to say, we have
shown that we are in possession of pure à priori intuitions, namely, space and
time, in which we find, when in a judgement à priori we pass out beyond the
given conception, something which is not discoverable in that conception, but
is certainly found à priori in the intuition which corresponds to the
conception, and can be united synthetically with it. But the judgements which
these pure intuitions enable us to make, never reach farther than to objects of
the senses, and are valid only for objects of possible experience.

Second Part—TRANSCENDENTAL LOGIC

INTRODUCTION. Idea of a Transcendental Logic.

I. Of Logic in General.

Our knowledge springs from two main sources in the mind, first of which is the
faculty or power of receiving representations (receptivity for impressions);
the second is the power of cognizing by means of these representations
(spontaneity in the production of conceptions). Through the first an object is
given to us; through the second, it is, in relation to the representation
(which is a mere determination of the mind), thought. Intuition and conceptions
constitute, therefore, the elements of all our knowledge, so that neither
conceptions without an intuition in some way corresponding to them, nor
intuition without conceptions, can afford us a cognition. Both are either pure
or empirical. They are empirical, when sensation (which presupposes the actual
presence of the object) is contained in them; and pure, when no sensation is
mixed with the representation. Sensations we may call the matter of sensuous
cognition. Pure intuition consequently contains merely the form under which
something is intuited, and pure conception only the form of the thought of an
object. Only pure intuitions and pure conceptions are possible à priori; the
empirical only à posteriori.

We apply the term sensibility to the receptivity of the mind for impressions,
in so far as it is in some way affected; and, on the other hand, we call the
faculty of spontaneously producing representations, or the spontaneity of
cognition, understanding. Our nature is so constituted that intuition with us
never can be other than sensuous, that is, it contains only the mode in which
we are affected by objects. On the other hand, the faculty of thinking the
object of sensuous intuition is the understanding. Neither of these faculties
has a preference over the other. Without the sensuous faculty no object would
be given to us, and without the understanding no object would be thought.
Thoughts without content are void; intuitions without conceptions, blind. Hence
it is as necessary for the mind to make its conceptions sensuous (that is, to
join to them the object in intuition), as to make its intuitions intelligible
(that is, to bring them under conceptions). Neither of these faculties can
exchange its proper function. Understanding cannot intuite, and the sensuous
faculty cannot think. In no other way than from the united operation of both,
can knowledge arise. But no one ought, on this account, to overlook the
difference of the elements contributed by each; we have rather great reason
carefully to separate and distinguish them. We therefore distinguish the
science of the laws of sensibility, that is, æsthetic, from the science of the
laws of the understanding, that is, logic.

Now, logic in its turn may be considered as twofold—namely, as logic of
the general, or of the particular use of the understanding. The first contains
the absolutely necessary laws of thought, without which no use whatsoever of
the understanding is possible, and gives laws therefore to the understanding,
without regard to the difference of objects on which it may be employed. The
logic of the particular use of the understanding contains the laws of correct
thinking upon a particular class of objects. The former may be called elemental
logic—the latter, the organon of this or that particular science. The
latter is for the most part employed in the schools, as a propædeutic to the
sciences, although, indeed, according to the course of human reason, it is the
last thing we arrive at, when the science has been already matured, and needs
only the finishing touches towards its correction and completion; for our
knowledge of the objects of our attempted science must be tolerably extensive
and complete before we can indicate the laws by which a science of these
objects can be established.

General logic is again either pure or applied. In the former, we abstract all
the empirical conditions under which the understanding is exercised; for
example, the influence of the senses, the play of the fantasy or imagination,
the laws of the memory, the force of habit, of inclination, etc., consequently
also, the sources of prejudice—in a word, we abstract all causes from
which particular cognitions arise, because these causes regard the
understanding under certain circumstances of its application, and, to the
knowledge of them experience is required. Pure general logic has to do,
therefore, merely with pure à priori principles, and is a canon of
understanding and reason, but only in respect of the formal part of their use,
be the content what it may, empirical or transcendental. General logic is
called applied, when it is directed to the laws of the use of the
understanding, under the subjective empirical conditions which psychology
teaches us. It has therefore empirical principles, although, at the same time,
it is in so far general, that it applies to the exercise of the understanding,
without regard to the difference of objects. On this account, moreover, it is
neither a canon of the understanding in general, nor an organon of a particular
science, but merely a cathartic of the human understanding.

In general logic, therefore, that part which constitutes pure logic must be
carefully distinguished from that which constitutes applied (though still
general) logic. The former alone is properly science, although short and dry,
as the methodical exposition of an elemental doctrine of the understanding
ought to be. In this, therefore, logicians must always bear in mind two rules:

1. As general logic, it makes abstraction of all content of the cognition of
the understanding, and of the difference of objects, and has to do with nothing
but the mere form of thought.

2. As pure logic, it has no empirical principles, and consequently draws
nothing (contrary to the common persuasion) from psychology, which therefore
has no influence on the canon of the understanding. It is a demonstrated
doctrine, and everything in it must be certain completely à priori.

What I called applied logic (contrary to the common acceptation of this term,
according to which it should contain certain exercises for the scholar, for
which pure logic gives the rules), is a representation of the understanding,
and of the rules of its necessary employment in concreto, that is to say, under
the accidental conditions of the subject, which may either hinder or promote
this employment, and which are all given only empirically. Thus applied logic
treats of attention, its impediments and consequences, of the origin of error,
of the state of doubt, hesitation, conviction, etc., and to it is related pure
general logic in the same way that pure morality, which contains only the
necessary moral laws of a free will, is related to practical ethics, which
considers these laws under all the impediments of feelings, inclinations, and
passions to which men are more or less subjected, and which never can furnish
us with a true and demonstrated science, because it, as well as applied logic,
requires empirical and psychological principles.

II. Of Transcendental Logic.

General logic, as we have seen, makes abstraction of all content of cognition,
that is, of all relation of cognition to its object, and regards only the
logical form in the relation of cognitions to each other, that is, the form of
thought in general. But as we have both pure and empirical intuitions (as
transcendental æsthetic proves), in like manner a distinction might be drawn
between pure and empirical thought (of objects). In this case, there would
exist a kind of logic, in which we should not make abstraction of all content
of cognition; for or logic which should comprise merely the laws of pure
thought (of an object), would of course exclude all those cognitions which were
of empirical content. This kind of logic would also examine the origin of our
cognitions of objects, so far as that origin cannot be ascribed to the objects
themselves; while, on the contrary, general logic has nothing to do with the
origin of our cognitions, but contemplates our representations, be they given
primitively à priori in ourselves, or be they only of empirical origin, solely
according to the laws which the understanding observes in employing them in the
process of thought, in relation to each other. Consequently, general logic
treats of the form of the understanding only, which can be applied to
representations, from whatever source they may have arisen.

And here I shall make a remark, which the reader must bear well in mind in the
course of the following considerations, to wit, that not every cognition à
priori, but only those through which we cognize that and how certain
representations (intuitions or conceptions) are applied or are possible only à
priori; that is to say, the à priori possibility of cognition and the à priori
use of it are transcendental. Therefore neither is space, nor any à priori
geometrical determination of space, a transcendental Representation, but only
the knowledge that such a representation is not of empirical origin, and the
possibility of its relating to objects of experience, although itself à priori,
can be called transcendental. So also, the application of space to objects in
general would be transcendental; but if it be limited to objects of sense it is
empirical. Thus, the distinction of the transcendental and empirical belongs
only to the critique of cognitions, and does not concern the relation of these
to their object.

Accordingly, in the expectation that there may perhaps be conceptions which
relate à priori to objects, not as pure or sensuous intuitions, but merely as
acts of pure thought (which are therefore conceptions, but neither of empirical
nor æsthetical origin)—in this expectation, I say, we form to ourselves,
by anticipation, the idea of a science of pure understanding and rational
cognition, by means of which we may cogitate objects entirely à priori. A
science of this kind, which should determine the origin, the extent, and the
objective validity of such cognitions, must be called transcendental logic,
because it has not, like general logic, to do with the laws of understanding
and reason in relation to empirical as well as pure rational cognitions without
distinction, but concerns itself with these only in an à priori relation to
objects.

III. Of the Division of General Logic into Analytic
and Dialectic.

The old question with which people sought to push logicians into a corner, so
that they must either have recourse to pitiful sophisms or confess their
ignorance, and consequently the vanity of their whole art, is this: “What
is truth?” The definition of the word truth, to wit, “the
accordance of the cognition with its object,” is presupposed in the
question; but we desire to be told, in the answer to it, what is the universal
and secure criterion of the truth of every cognition.

To know what questions we may reasonably propose is in itself a strong evidence
of sagacity and intelligence. For if a question be in itself absurd and
unsusceptible of a rational answer, it is attended with the danger—not to
mention the shame that falls upon the person who proposes it—of seducing
the unguarded listener into making absurd answers, and we are presented with
the ridiculous spectacle of one (as the ancients said) “milking the
he-goat, and the other holding a sieve.”

If truth consists in the accordance of a cognition with its object, this object
must be, ipso facto, distinguished from all others; for a cognition is false if
it does not accord with the object to which it relates, although it contains
something which may be affirmed of other objects. Now an universal criterion of
truth would be that which is valid for all cognitions, without distinction of
their objects. But it is evident that since, in the case of such a criterion,
we make abstraction of all the content of a cognition (that is, of all relation
to its object), and truth relates precisely to this content, it must be utterly
absurd to ask for a mark of the truth of this content of cognition; and that,
accordingly, a sufficient, and at the same time universal, test of truth cannot
possibly be found. As we have already termed the content of a cognition its
matter, we shall say: “Of the truth of our cognitions in respect of their
matter, no universal test can be demanded, because such a demand is
self-contradictory.”

On the other hand, with regard to our cognition in respect of its mere form
(excluding all content), it is equally manifest that logic, in so far as it
exhibits the universal and necessary laws of the understanding, must in these
very laws present us with criteria of truth. Whatever contradicts these rules
is false, because thereby the understanding is made to contradict its own
universal laws of thought; that is, to contradict itself. These criteria,
however, apply solely to the form of truth, that is, of thought in general, and
in so far they are perfectly accurate, yet not sufficient. For although a
cognition may be perfectly accurate as to logical form, that is, not
self-contradictory, it is notwithstanding quite possible that it may not stand
in agreement with its object. Consequently, the merely logical criterion of
truth, namely, the accordance of a cognition with the universal and formal laws
of understanding and reason, is nothing more than the conditio sine qua non, or
negative condition of all truth. Farther than this logic cannot go, and the
error which depends not on the form, but on the content of the cognition, it
has no test to discover.

General logic, then, resolves the whole formal business of understanding and
reason into its elements, and exhibits them as principles of all logical
judging of our cognitions. This part of logic may, therefore, be called
analytic, and is at least the negative test of truth, because all cognitions
must first of an be estimated and tried according to these laws before we
proceed to investigate them in respect of their content, in order to discover
whether they contain positive truth in regard to their object. Because,
however, the mere form of a cognition, accurately as it may accord with logical
laws, is insufficient to supply us with material (objective) truth, no one, by
means of logic alone, can venture to predicate anything of or decide concerning
objects, unless he has obtained, independently of logic, well-grounded
information about them, in order afterwards to examine, according to logical
laws, into the use and connection, in a cohering whole, of that information,
or, what is still better, merely to test it by them. Notwithstanding, there
lies so seductive a charm in the possession of a specious art like
this—an art which gives to all our cognitions the form of the
understanding, although with respect to the content thereof we may be sadly
deficient—that general logic, which is merely a canon of judgement, has
been employed as an organon for the actual production, or rather for the
semblance of production, of objective assertions, and has thus been grossly
misapplied. Now general logic, in its assumed character of organon, is called
dialectic.

Different as are the significations in which the ancients used this term for a
science or an art, we may safely infer, from their actual employment of it,
that with them it was nothing else than a logic of illusion—a sophistical
art for giving ignorance, nay, even intentional sophistries, the colouring of
truth, in which the thoroughness of procedure which logic requires was
imitated, and their topic employed to cloak the empty pretensions. Now it may
be taken as a safe and useful warning, that general logic, considered as an
organon, must always be a logic of illusion, that is, be dialectical, for, as
it teaches us nothing whatever respecting the content of our cognitions, but
merely the formal conditions of their accordance with the understanding, which
do not relate to and are quite indifferent in respect of objects, any attempt
to employ it as an instrument (organon) in order to extend and enlarge the
range of our knowledge must end in mere prating; any one being able to maintain
or oppose, with some appearance of truth, any single assertion whatever.

Such instruction is quite unbecoming the dignity of philosophy. For these
reasons we have chosen to denominate this part of logic dialectic, in the sense
of a critique of dialectical illusion, and we wish the term to be so understood
in this place.

IV. Of the Division of Transcendental Logic into
Transcendental Analytic and Dialectic.

In transcendental logic we isolate the understanding (as in transcendental
æsthetic the sensibility) and select from our cognition merely that part of
thought which has its origin in the understanding alone. The exercise of this
pure cognition, however, depends upon this as its condition, that objects to
which it may be applied be given to us in intuition, for without intuition the
whole of our cognition is without objects, and is therefore quite void. That
part of transcendental logic, then, which treats of the elements of pure
cognition of the understanding, and of the principles without which no object
at all can be thought, is transcendental analytic, and at the same time a logic
of truth. For no cognition can contradict it, without losing at the same time
all content, that is, losing all reference to an object, and therefore all
truth. But because we are very easily seduced into employing these pure
cognitions and principles of the understanding by themselves, and that even
beyond the boundaries of experience, which yet is the only source whence we can
obtain matter (objects) on which those pure conceptions may be
employed—understanding runs the risk of making, by means of empty
sophisms, a material and objective use of the mere formal principles of the
pure understanding, and of passing judgements on objects without
distinction—objects which are not given to us, nay, perhaps cannot be
given to us in any way. Now, as it ought properly to be only a canon for
judging of the empirical use of the understanding, this kind of logic is
misused when we seek to employ it as an organon of the universal and unlimited
exercise of the understanding, and attempt with the pure understanding alone to
judge synthetically, affirm, and determine respecting objects in general. In
this case the exercise of the pure understanding becomes dialectical. The
second part of our transcendental logic must therefore be a critique of
dialectical illusion, and this critique we shall term transcendental
dialectic—not meaning it as an art of producing dogmatically such
illusion (an art which is unfortunately too current among the practitioners of
metaphysical juggling), but as a critique of understanding and reason in regard
to their hyperphysical use. This critique will expose the groundless nature of
the pretensions of these two faculties, and invalidate their claims to the
discovery and enlargement of our cognitions merely by means of transcendental
principles, and show that the proper employment of these faculties is to test
the judgements made by the pure understanding, and to guard it from sophistical
delusion.

FIRST DIVISION. TRANSCENDENTAL LOGIC. TRANSCENDENTAL
ANALYTIC. § 1

Transcendental analytic is the dissection of the whole of our à priori
knowledge into the elements of the pure cognition of the understanding. In
order to effect our purpose, it is necessary: (1) That the conceptions be pure
and not empirical; (2) That they belong not to intuition and sensibility, but
to thought and understanding; (3) That they be elementary conceptions, and as
such, quite different from deduced or compound conceptions; (4) That our table
of these elementary conceptions be complete, and fill up the whole sphere of
the pure understanding. Now this completeness of a science cannot be accepted
with confidence on the guarantee of a mere estimate of its existence in an
aggregate formed only by means of repeated experiments and attempts. The
completeness which we require is possible only by means of an idea of the
totality of the à priori cognition of the understanding, and through the
thereby determined division of the conceptions which form the said whole;
consequently, only by means of their connection in a system. Pure understanding
distinguishes itself not merely from everything empirical, but also completely
from all sensibility. It is a unity self-subsistent, self-sufficient, and not
to be enlarged by any additions from without. Hence the sum of its cognition
constitutes a system to be determined by and comprised under an idea; and the
completeness and articulation of this system can at the same time serve as a
test of the correctness and genuineness of all the parts of cognition that
belong to it. The whole of this part of transcendental logic consists of two
books, of which the one contains the conceptions, and the other the principles
of pure understanding.

BOOK I. Analytic of Conceptions. § 2

By the term Analytic of Conceptions, I do not understand the analysis of these,
or the usual process in philosophical investigations of dissecting the
conceptions which present themselves, according to their content, and so making
them clear; but I mean the hitherto little attempted dissection of the faculty
of understanding itself, in order to investigate the possibility of conceptions
à priori, by looking for them in the understanding alone, as their birthplace,
and analysing the pure use of this faculty. For this is the proper duty of a
transcendental philosophy; what remains is the logical treatment of the
conceptions in philosophy in general. We shall therefore follow up the pure
conceptions even to their germs and beginnings in the human understanding, in
which they lie, until they are developed on occasions presented by experience,
and, freed by the same understanding from the empirical conditions attaching to
them, are set forth in their unalloyed purity.

Chapter I. Of the Transcendental Clue to the Discovery
of all Pure Conceptions of the Understanding

Introductory § 3

When we call into play a faculty of cognition, different conceptions manifest
themselves according to the different circumstances, and make known this
faculty, and assemble themselves into a more or less extensive collection,
according to the time or penetration that has been applied to the consideration
of them. Where this process, conducted as it is mechanically, so to speak, will
end, cannot be determined with certainty. Besides, the conceptions which we
discover in this haphazard manner present themselves by no means in order and
systematic unity, but are at last coupled together only according to
resemblances to each other, and arranged in series, according to the quantity
of their content, from the simpler to the more complex—series which are
anything but systematic, though not altogether without a certain kind of method
in their construction.

Transcendental philosophy has the advantage, and moreover the duty, of
searching for its conceptions according to a principle; because these
conceptions spring pure and unmixed out of the understanding as an absolute
unity, and therefore must be connected with each other according to one
conception or idea. A connection of this kind, however, furnishes us with a
ready prepared rule, by which its proper place may be assigned to every pure
conception of the understanding, and the completeness of the system of all be
determined à priori—both which would otherwise have been dependent on
mere choice or chance.

Section I. Of the Logical Use of the Understanding in
General § 4

The understanding was defined above only negatively, as a non-sensuous faculty
of cognition. Now, independently of sensibility, we cannot possibly have any
intuition; consequently, the understanding is no faculty of intuition. But
besides intuition there is no other mode of cognition, except through
conceptions; consequently, the cognition of every, at least of every human,
understanding is a cognition through conceptions—not intuitive, but
discursive. All intuitions, as sensuous, depend on affections; conceptions,
therefore, upon functions. By the word function I understand the unity of the
act of arranging diverse representations under one common representation.
Conceptions, then, are based on the spontaneity of thought, as sensuous
intuitions are on the receptivity of impressions. Now, the understanding cannot
make any other use of these conceptions than to judge by means of them. As no
representation, except an intuition, relates immediately to its object, a
conception never relates immediately to an object, but only to some other
representation thereof, be that an intuition or itself a conception. A
judgement, therefore, is the mediate cognition of an object, consequently the
representation of a representation of it. In every judgement there is a
conception which applies to, and is valid for many other conceptions, and which
among these comprehends also a given representation, this last being
immediately connected with an object. For example, in the
judgement—“All bodies are divisible,” our conception of
divisible applies to various other conceptions; among these, however, it is
here particularly applied to the conception of body, and this conception of
body relates to certain phenomena which occur to us. These objects, therefore,
are mediately represented by the conception of divisibility. All judgements,
accordingly, are functions of unity in our representations, inasmuch as,
instead of an immediate, a higher representation, which comprises this and
various others, is used for our cognition of the object, and thereby many
possible cognitions are collected into one. But we can reduce all acts of the
understanding to judgements, so that understanding may be represented as the
faculty of judging. For it is, according to what has been said above, a faculty
of thought. Now thought is cognition by means of conceptions. But conceptions,
as predicates of possible judgements, relate to some representation of a yet
undetermined object. Thus the conception of body indicates something—for
example, metal—which can be cognized by means of that conception. It is
therefore a conception, for the reason alone that other representations are
contained under it, by means of which it can relate to objects. It is therefore
the predicate to a possible judgement; for example: “Every metal is a
body.” All the functions of the understanding therefore can be
discovered, when we can completely exhibit the functions of unity in
judgements. And that this may be effected very easily, the following section
will show.

Section II. Of the Logical Function of the
Understanding in Judgements § 5

If we abstract all the content of a judgement, and consider only the
intellectual form thereof, we find that the function of thought in a judgement
can be brought under four heads, of which each contains three momenta. These
may be conveniently represented in the following table:

As this division appears to differ in some, though not essential points, from
the usual technique of logicians, the following observations, for the
prevention of otherwise possible misunderstanding, will not be without their
use.

1. Logicians say, with justice, that in the use of judgements in syllogisms,
singular judgements may be treated like universal ones. For, precisely because
a singular judgement has no extent at all, its predicate cannot refer to a part
of that which is contained in the conception of the subject and be excluded
from the rest. The predicate is valid for the whole conception just as if it
were a general conception, and had extent, to the whole of which the predicate
applied. On the other hand, let us compare a singular with a general judgement,
merely as a cognition, in regard to quantity. The singular judgement relates to
the general one, as unity to infinity, and is therefore in itself essentially
different. Thus, if we estimate a singular judgement (judicium
singulare) not merely according to its intrinsic validity as a judgement,
but also as a cognition generally, according to its quantity in comparison with
that of other cognitions, it is then entirely different from a general
judgement (judicium commune), and in a complete table of the momenta of
thought deserves a separate place—though, indeed, this would not be
necessary in a logic limited merely to the consideration of the use of
judgements in reference to each other.

2. In like manner, in transcendental logic, infinite must be distinguished from
affirmative judgements, although in general logic they are rightly enough
classed under affirmative. General logic abstracts all content of the predicate
(though it be negative), and only considers whether the said predicate be
affirmed or denied of the subject. But transcendental logic considers also the
worth or content of this logical affirmation—an affirmation by means of a
merely negative predicate, and inquires how much the sum total of our cognition
gains by this affirmation. For example, if I say of the soul, “It is not
mortal”—by this negative judgement I should at least ward off
error. Now, by the proposition, “The soul is not mortal,” I have,
in respect of the logical form, really affirmed, inasmuch as I thereby place
the soul in the unlimited sphere of immortal beings. Now, because of the whole
sphere of possible existences, the mortal occupies one part, and the immortal
the other, neither more nor less is affirmed by the proposition than that the
soul is one among the infinite multitude of things which remain over, when I
take away the whole mortal part. But by this proceeding we accomplish only this
much, that the infinite sphere of all possible existences is in so far limited
that the mortal is excluded from it, and the soul is placed in the remaining
part of the extent of this sphere. But this part remains, notwithstanding this
exception, infinite, and more and more parts may be taken away from the whole
sphere, without in the slightest degree thereby augmenting or affirmatively
determining our conception of the soul. These judgements, therefore, infinite
in respect of their logical extent, are, in respect of the content of their
cognition, merely limitative; and are consequently entitled to a place in our
transcendental table of all the momenta of thought in judgements, because the
function of the understanding exercised by them may perhaps be of importance in
the field of its pure à priori cognition.

3. All relations of thought in judgements are those (a) of the predicate to the
subject; (b) of the principle to its consequence; (c) of the divided cognition
and all the members of the division to each other. In the first of these three
classes, we consider only two conceptions; in the second, two judgements; in
the third, several judgements in relation to each other. The hypothetical
proposition, “If perfect justice exists, the obstinately wicked are
punished,” contains properly the relation to each other of two
propositions, namely, “Perfect justice exists,” and “The
obstinately wicked are punished.” Whether these propositions are in
themselves true is a question not here decided. Nothing is cogitated by means
of this judgement except a certain consequence. Finally, the disjunctive
judgement contains a relation of two or more propositions to each other—a
relation not of consequence, but of logical opposition, in so far as the sphere
of the one proposition excludes that of the other. But it contains at the same
time a relation of community, in so far as all the propositions taken together
fill up the sphere of the cognition. The disjunctive judgement contains,
therefore, the relation of the parts of the whole sphere of a cognition, since
the sphere of each part is a complemental part of the sphere of the other, each
contributing to form the sum total of the divided cognition. Take, for example,
the proposition, “The world exists either through blind chance, or
through internal necessity, or through an external cause.” Each of these
propositions embraces a part of the sphere of our possible cognition as to the
existence of a world; all of them taken together, the whole sphere. To take the
cognition out of one of these spheres, is equivalent to placing it in one of
the others; and, on the other hand, to place it in one sphere is equivalent to
taking it out of the rest. There is, therefore, in a disjunctive judgement a
certain community of cognitions, which consists in this, that they mutually
exclude each other, yet thereby determine, as a whole, the true cognition,
inasmuch as, taken together, they make up the complete content of a particular
given cognition. And this is all that I find necessary, for the sake of what
follows, to remark in this place.

4. The modality of judgements is a quite peculiar function, with this
distinguishing characteristic, that it contributes nothing to the content of a
judgement (for besides quantity, quality, and relation, there is nothing more
that constitutes the content of a judgement), but concerns itself only with the
value of the copula in relation to thought in general. Problematical judgements
are those in which the affirmation or negation is accepted as merely possible
(ad libitum). In the assertorical, we regard the proposition as real (true); in
the apodeictical, we look on it as necessary.^[13] Thus the two
judgements (antecedens et consequens), the relation of which constitutes a
hypothetical judgement, likewise those (the members of the division) in whose
reciprocity the disjunctive consists, are only problematical. In the example
above given the proposition, “There exists perfect justice,” is not
stated assertorically, but as an ad libitum judgement, which someone may choose
to adopt, and the consequence alone is assertorical. Hence such judgements may
be obviously false, and yet, taken problematically, be conditions of our
cognition of the truth. Thus the proposition, “The world exists only by
blind chance,” is in the disjunctive judgement of problematical import
only: that is to say, one may accept it for the moment, and it helps us (like
the indication of the wrong road among all the roads that one can take) to find
out the true proposition. The problematical proposition is, therefore, that
which expresses only logical possibility (which is not objective); that is, it
expresses a free choice to admit the validity of such a proposition—a
merely arbitrary reception of it into the understanding. The assertorical
speaks of logical reality or truth; as, for example, in a hypothetical
syllogism, the antecedens presents itself in a problematical form in the major,
in an assertorical form in the minor, and it shows that the proposition is in
harmony with the laws of the understanding. The apodeictical proposition
cogitates the assertorical as determined by these very laws of the
understanding, consequently as affirming à priori, and in this manner it
expresses logical necessity. Now because all is here gradually incorporated
with the understanding—inasmuch as in the first place we judge
problematically; then accept assertorically our judgement as true; lastly,
affirm it as inseparably united with the understanding, that is, as necessary
and apodeictical—we may safely reckon these three functions of modality
as so many momenta of thought.

[13]
Just as if thought were in the first instance a function of the understanding;
in the second, of judgement; in the third, of reason. A remark which will be
explained in the sequel.

Section III. Of the Pure Conceptions of the
Understanding, or Categories § 6

General logic, as has been repeatedly said, makes abstraction of all content of
cognition, and expects to receive representations from some other quarter, in
order, by means of analysis, to convert them into conceptions. On the contrary,
transcendental logic has lying before it the manifold content of à priori
sensibility, which transcendental æsthetic presents to it in order to give
matter to the pure conceptions of the understanding, without which
transcendental logic would have no content, and be therefore utterly void. Now
space and time contain an infinite diversity of determinations of pure à priori
intuition, but are nevertheless the condition of the mind’s receptivity,
under which alone it can obtain representations of objects, and which,
consequently, must always affect the conception of these objects. But the
spontaneity of thought requires that this diversity be examined after a certain
manner, received into the mind, and connected, in order afterwards to form a
cognition out of it. This Process I call synthesis.

By the word synthesis, in its most general signification, I understand the
process of joining different representations to each other and of comprehending
their diversity in one cognition. This synthesis is pure when the diversity is
not given empirically but à priori (as that in space and time). Our
representations must be given previously to any analysis of them; and no
conceptions can arise, quoad their content, analytically. But the synthesis of
a diversity (be it given à priori or empirically) is the first requisite for
the production of a cognition, which in its beginning, indeed, may be crude and
confused, and therefore in need of analysis—still, synthesis is that by
which alone the elements of our cognitions are collected and united into a
certain content, consequently it is the first thing on which we must fix our
attention, if we wish to investigate the origin of our knowledge.

Synthesis, generally speaking, is, as we shall afterwards see, the mere
operation of the imagination—a blind but indispensable function of the
soul, without which we should have no cognition whatever, but of the working of
which we are seldom even conscious. But to reduce this synthesis to conceptions
is a function of the understanding, by means of which we attain to cognition,
in the proper meaning of the term.

Pure synthesis, represented generally, gives us the pure conception of the
understanding. But by this pure synthesis, I mean that which rests upon a basis
of à priori synthetical unity. Thus, our numeration (and this is more
observable in large numbers) is a synthesis according to conceptions, because
it takes place according to a common basis of unity (for example, the decade).
By means of this conception, therefore, the unity in the synthesis of the
manifold becomes necessary.

By means of analysis different representations are brought under one
conception—an operation of which general logic treats. On the other hand,
the duty of transcendental logic is to reduce to conceptions, not
representations, but the pure synthesis of representations. The first thing
which must be given to us for the sake of the à priori cognition of all
objects, is the diversity of the pure intuition; the synthesis of this
diversity by means of the imagination is the second; but this gives, as yet, no
cognition. The conceptions which give unity to this pure synthesis, and which
consist solely in the representation of this necessary synthetical unity,
furnish the third requisite for the cognition of an object, and these
conceptions are given by the understanding.

The same function which gives unity to the different representation in a
judgement, gives also unity to the mere synthesis of different representations
in an intuition; and this unity we call the pure conception of the
understanding. Thus, the same understanding, and by the same operations,
whereby in conceptions, by means of analytical unity, it produced the logical
form of a judgement, introduces, by means of the synthetical unity of the
manifold in intuition, a transcendental content into its representations, on
which account they are called pure conceptions of the understanding, and they
apply à priori to objects, a result not within the power of general logic.

In this manner, there arise exactly so many pure conceptions of the
understanding, applying à priori to objects of intuition in general, as there
are logical functions in all possible judgements. For there is no other
function or faculty existing in the understanding besides those enumerated in
that table. These conceptions we shall, with Aristotle, call categories, our
purpose being originally identical with his, notwithstanding the great
difference in the execution.

This, then, is a catalogue of all the originally pure conceptions of the
synthesis which the understanding contains à priori, and these conceptions
alone entitle it to be called a pure understanding; inasmuch as only by them it
can render the manifold of intuition conceivable, in other words, think an
object of intuition. This division is made systematically from a common
principle, namely the faculty of judgement (which is just the same as the power
of thought), and has not arisen rhapsodically from a search at haphazard after
pure conceptions, respecting the full number of which we never could be
certain, inasmuch as we employ induction alone in our search, without
considering that in this way we can never understand wherefore precisely these
conceptions, and none others, abide in the pure understanding. It was a design
worthy of an acute thinker like Aristotle, to search for these fundamental
conceptions. Destitute, however, of any guiding principle, he picked them up
just as they occurred to him, and at first hunted out ten, which he called
categories (predicaments). Afterwards be believed that he had discovered five
others, which were added under the name of post predicaments. But his catalogue
still remained defective. Besides, there are to be found among them some of the
modes of pure sensibility (quando, ubi, situs, also prius, simul), and likewise
an empirical conception (motus)—which can by no means belong to this
genealogical register of the pure understanding. Moreover, there are deduced
conceptions (actio, passio) enumerated among the original conceptions, and, of
the latter, some are entirely wanting.

With regard to these, it is to be remarked, that the categories, as the true
primitive conceptions of the pure understanding, have also their pure deduced
conceptions, which, in a complete system of transcendental philosophy, must by
no means be passed over; though in a merely critical essay we must be contented
with the simple mention of the fact.

Let it be allowed me to call these pure, but deduced conceptions of the
understanding, the predicables of the pure understanding, in contradistinction
to predicaments. If we are in possession of the original and primitive, the
deduced and subsidiary conceptions can easily be added, and the genealogical
tree of the understanding completely delineated. As my present aim is not to
set forth a complete system, but merely the principles of one, I reserve this
task for another time. It may be easily executed by any one who will refer to
the ontological manuals, and subordinate to the category of causality, for
example, the predicables of force, action, passion; to that of community, those
of presence and resistance; to the categories of modality, those of
origination, extinction, change; and so with the rest. The categories combined
with the modes of pure sensibility, or with one another, afford a great number
of deduced à priori conceptions; a complete enumeration of which would be a
useful and not unpleasant, but in this place a perfectly dispensable,
occupation.

I purposely omit the definitions of the categories in this treatise. I shall
analyse these conceptions only so far as is necessary for the doctrine of
method, which is to form a part of this critique. In a system of pure reason,
definitions of them would be with justice demanded of me, but to give them here
would only bide from our view the main aim of our investigation, at the same
time raising doubts and objections, the consideration of which, without
injustice to our main purpose, may be very well postponed till another
opportunity. Meanwhile, it ought to be sufficiently clear, from the little we
have already said on this subject, that the formation of a complete vocabulary
of pure conceptions, accompanied by all the requisite explanations, is not only
a possible, but an easy undertaking. The compartments already exist; it is only
necessary to fill them up; and a systematic topic like the present, indicates
with perfect precision the proper place to which each conception belongs, while
it readily points out any that have not yet been filled up.

§ 7

Our table of the categories suggests considerations of some importance, which
may perhaps have significant results in regard to the scientific form of all
rational cognitions. For, that this table is useful in the theoretical part of
philosophy, nay, indispensable for the sketching of the complete plan of a
science, so far as that science rests upon conceptions à priori, and for
dividing it mathematically, according to fixed principles, is most manifest
from the fact that it contains all the elementary conceptions of the
understanding, nay, even the form of a system of these in the understanding
itself, and consequently indicates all the momenta, and also the internal
arrangement of a projected speculative science, as I have elsewhere shown.^[14] Here follow some of these observations.

[14]
In the “Metaphysical Principles of Natural Science.”

I. This table, which contains four classes of conceptions of the understanding,
may, in the first instance, be divided into two classes, the first of which
relates to objects of intuition—pure as well as empirical; the second, to
the existence of these objects, either in relation to one another, or to the
understanding.

The former of these classes of categories I would entitle the mathematical, and
the latter the dynamical categories. The former, as we see, has no correlates;
these are only to be found in the second class. This difference must have a
ground in the nature of the human understanding.

II. The number of the categories in each class is always the same, namely,
three—a fact which also demands some consideration, because in all other
cases division à priori through conceptions is necessarily dichotomy. It is to
be added, that the third category in each triad always arises from the
combination of the second with the first.

Thus totality is nothing else but plurality contemplated as unity; limitation
is merely reality conjoined with negation; community is the causality of a
substance, reciprocally determining, and determined by other substances; and
finally, necessity is nothing but existence, which is given through the
possibility itself. Let it not be supposed, however, that the third category is
merely a deduced, and not a primitive conception of the pure understanding. For
the conjunction of the first and second, in order to produce the third
conception, requires a particular function of the understanding, which is by no
means identical with those which are exercised in the first and second. Thus,
the conception of a number (which belongs to the category of totality) is not
always possible, where the conceptions of multitude and unity exist (for
example, in the representation of the infinite). Or, if I conjoin the
conception of a cause with that of a substance, it does not follow that the
conception of influence, that is, how one substance can be the cause of
something in another substance, will be understood from that. Thus it is
evident that a particular act of the understanding is here necessary; and so in
the other instances.

III. With respect to one category, namely, that of community, which is found in
the third class, it is not so easy as with the others to detect its accordance
with the form of the disjunctive judgement which corresponds to it in the table
of the logical functions.

In order to assure ourselves of this accordance, we must observe that in every
disjunctive judgement, the sphere of the judgement (that is, the complex of all
that is contained in it) is represented as a whole divided into parts; and,
since one part cannot be contained in the other, they are cogitated as
co-ordinated with, not subordinated to each other, so that they do not
determine each other unilaterally, as in a linear series, but reciprocally, as
in an aggregate—(if one member of the division is posited, all the rest
are excluded; and conversely).

Now a like connection is cogitated in a whole of things; for one thing is not
subordinated, as effect, to another as cause of its existence, but, on the
contrary, is co-ordinated contemporaneously and reciprocally, as a cause in
relation to the determination of the others (for example, in a body—the
parts of which mutually attract and repel each other). And this is an entirely
different kind of connection from that which we find in the mere relation of
the cause to the effect (the principle to the consequence), for in such a
connection the consequence does not in its turn determine the principle, and
therefore does not constitute, with the latter, a whole—just as the
Creator does not with the world make up a whole. The process of understanding
by which it represents to itself the sphere of a divided conception, is
employed also when we think of a thing as divisible; and in the same manner as
the members of the division in the former exclude one another, and yet are
connected in one sphere, so the understanding represents to itself the parts of
the latter, as having—each of them—an existence (as substances),
independently of the others, and yet as united in one whole.

§ 8

In the transcendental philosophy of the ancients there exists one more leading
division, which contains pure conceptions of the understanding, and which,
although not numbered among the categories, ought, according to them, as
conceptions à priori, to be valid of objects. But in this case they would
augment the number of the categories; which cannot be. These are set forth in
the proposition, so renowned among the schoolmen—‘Quodlibet ens
est UNUM, VERUM, BONUM.’ Now, though the inferences from this
principle were mere tautological propositions, and though it is allowed only by
courtesy to retain a place in modern metaphysics, yet a thought which
maintained itself for such a length of time, however empty it seems to be,
deserves an investigation of its origin, and justifies the conjecture that it
must be grounded in some law of the understanding, which, as is often the case,
has only been erroneously interpreted. These pretended transcendental
predicates are, in fact, nothing but logical requisites and criteria of all
cognition of objects, and they employ, as the basis for this cognition, the
categories of quantity, namely, unity, plurality, and totality. But these,
which must be taken as material conditions, that is, as belonging to the
possibility of things themselves, they employed merely in a formal
signification, as belonging to the logical requisites of all cognition, and yet
most unguardedly changed these criteria of thought into properties of objects,
as things in themselves. Now, in every cognition of an object, there is unity
of conception, which may be called qualitative unity, so far as by this term we
understand only the unity in our connection of the manifold; for example, unity
of the theme in a play, an oration, or a story. Secondly, there is truth in
respect of the deductions from it. The more true deductions we have from a
given conception, the more criteria of its objective reality. This we might
call the qualitative plurality of characteristic marks, which belong to a
conception as to a common foundation, but are not cogitated as a quantity in
it. Thirdly, there is perfection—which consists in this, that the
plurality falls back upon the unity of the conception, and accords completely
with that conception and with no other. This we may denominate qualitative
completeness. Hence it is evident that these logical criteria of the
possibility of cognition are merely the three categories of quantity modified
and transformed to suit an unauthorized manner of applying them. That is to
say, the three categories, in which the unity in the production of the quantum
must be homogeneous throughout, are transformed solely with a view to the
connection of heterogeneous parts of cognition in one act of consciousness, by
means of the quality of the cognition, which is the principle of that
connection. Thus the criterion of the possibility of a conception (not of its
object) is the definition of it, in which the unity of the conception, the
truth of all that may be immediately deduced from it, and finally, the
completeness of what has been thus deduced, constitute the requisites for the
reproduction of the whole conception. Thus also, the criterion or test of an
hypothesis is the intelligibility of the received principle of explanation, or
its unity (without help from any subsidiary hypothesis)—the truth of our
deductions from it (consistency with each other and with experience)—and
lastly, the completeness of the principle of the explanation of these
deductions, which refer to neither more nor less than what was admitted in the
hypothesis, restoring analytically and à posteriori, what was cogitated
synthetically and à priori. By the conceptions, therefore, of unity, truth, and
perfection, we have made no addition to the transcendental table of the
categories, which is complete without them. We have, on the contrary, merely
employed the three categories of quantity, setting aside their application to
objects of experience, as general logical laws of the consistency of cognition
with itself.

Chapter II. Of the Deduction of the Pure Conceptions
of the Understanding

Section I. Of the Principles of a Transcendental
Deduction in general § 9

Teachers of jurisprudence, when speaking of rights and claims, distinguish in a
cause the question of right (quid juris) from the question of fact (quid
facti), and while they demand proof of both, they give to the proof of the
former, which goes to establish right or claim in law, the name of deduction.
Now we make use of a great number of empirical conceptions, without opposition
from any one; and consider ourselves, even without any attempt at deduction,
justified in attaching to them a sense, and a supposititious signification,
because we have always experience at hand to demonstrate their objective
reality. There exist also, however, usurped conceptions, such as fortune, fate,
which circulate with almost universal indulgence, and yet are occasionally
challenged by the question, “quid juris?” In such cases, we have
great difficulty in discovering any deduction for these terms, inasmuch as we
cannot produce any manifest ground of right, either from experience or from
reason, on which the claim to employ them can be founded.

Among the many conceptions, which make up the very variegated web of human
cognition, some are destined for pure use à priori, independent of all
experience; and their title to be so employed always requires a deduction,
inasmuch as, to justify such use of them, proofs from experience are not
sufficient; but it is necessary to know how these conceptions can apply to
objects without being derived from experience. I term, therefore, an
examination of the manner in which conceptions can apply à priori to objects,
the transcendental deduction of conceptions, and I distinguish it from the
empirical deduction, which indicates the mode in which conception is obtained
through experience and reflection thereon; consequently, does not concern
itself with the right, but only with the fact of our obtaining conceptions in
such and such a manner. We have already seen that we are in possession of two
perfectly different kinds of conceptions, which nevertheless agree with each
other in this, that they both apply to objects completely à priori. These are
the conceptions of space and time as forms of sensibility, and the categories
as pure conceptions of the understanding. To attempt an empirical deduction of
either of these classes would be labour in vain, because the distinguishing
characteristic of their nature consists in this, that they apply to their
objects, without having borrowed anything from experience towards the
representation of them. Consequently, if a deduction of these conceptions is
necessary, it must always be transcendental.

Meanwhile, with respect to these conceptions, as with respect to all our
cognition, we certainly may discover in experience, if not the principle of
their possibility, yet the occasioning causes of their production. It will be
found that the impressions of sense give the first occasion for bringing into
action the whole faculty of cognition, and for the production of experience,
which contains two very dissimilar elements, namely, a matter for cognition,
given by the senses, and a certain form for the arrangement of this matter,
arising out of the inner fountain of pure intuition and thought; and these, on
occasion given by sensuous impressions, are called into exercise and produce
conceptions. Such an investigation into the first efforts of our faculty of
cognition to mount from particular perceptions to general conceptions is
undoubtedly of great utility; and we have to thank the celebrated Locke for
having first opened the way for this inquiry. But a deduction of the pure à
priori conceptions of course never can be made in this way, seeing that, in
regard to their future employment, which must be entirely independent of
experience, they must have a far different certificate of birth to show from
that of a descent from experience. This attempted physiological derivation,
which cannot properly be called deduction, because it relates merely to a
quaestio facti, I shall entitle an explanation of the possession of a pure
cognition. It is therefore manifest that there can only be a transcendental
deduction of these conceptions and by no means an empirical one; also, that all
attempts at an empirical deduction, in regard to pure à priori conceptions, are
vain, and can only be made by one who does not understand the altogether
peculiar nature of these cognitions.

But although it is admitted that the only possible deduction of pure à priori
cognition is a transcendental deduction, it is not, for that reason, perfectly
manifest that such a deduction is absolutely necessary. We have already traced
to their sources the conceptions of space and time, by means of a
transcendental deduction, and we have explained and determined their objective
validity à priori. Geometry, nevertheless, advances steadily and securely in
the province of pure à priori cognitions, without needing to ask from
philosophy any certificate as to the pure and legitimate origin of its
fundamental conception of space. But the use of the conception in this science
extends only to the external world of sense, the pure form of the intuition of
which is space; and in this world, therefore, all geometrical cognition,
because it is founded upon à priori intuition, possesses immediate evidence,
and the objects of this cognition are given à priori (as regards their form) in
intuition by and through the cognition itself. With the pure conceptions of
understanding, on the contrary, commences the absolute necessity of seeking a
transcendental deduction, not only of these conceptions themselves, but
likewise of space, because, inasmuch as they make affirmations concerning
objects not by means of the predicates of intuition and sensibility, but of
pure thought à priori, they apply to objects without any of the conditions of
sensibility. Besides, not being founded on experience, they are not presented
with any object in à priori intuition upon which, antecedently to experience,
they might base their synthesis. Hence results, not only doubt as to the
objective validity and proper limits of their use, but that even our conception
of space is rendered equivocal; inasmuch as we are very ready with the aid of
the categories, to carry the use of this conception beyond the conditions of
sensuous intuition—and, for this reason, we have already found a
transcendental deduction of it needful. The reader, then, must be quite
convinced of the absolute necessity of a transcendental deduction, before
taking a single step in the field of pure reason; because otherwise he goes to
work blindly, and after he has wondered about in all directions, returns to the
state of utter ignorance from which he started. He ought, moreover, clearly to
recognize beforehand the unavoidable difficulties in his undertaking, so that
he may not afterwards complain of the obscurity in which the subject itself is
deeply involved, or become too soon impatient of the obstacles in his path;
because we have a choice of only two things—either at once to give up all
pretensions to knowledge beyond the limits of possible experience, or to bring
this critical investigation to completion.

We have been able, with very little trouble, to make it comprehensible how the
conceptions of space and time, although à priori cognitions, must necessarily
apply to external objects, and render a synthetical cognition of these
possible, independently of all experience. For inasmuch as only by means of
such pure form of sensibility an object can appear to us, that is, be an object
of empirical intuition, space and time are pure intuitions, which contain à
priori the condition of the possibility of objects as phenomena, and an à
priori synthesis in these intuitions possesses objective validity.

On the other hand, the categories of the understanding do not represent the
conditions under which objects are given to us in intuition; objects can
consequently appear to us without necessarily connecting themselves with these,
and consequently without any necessity binding on the understanding to contain
à priori the conditions of these objects. Thus we find ourselves involved in a
difficulty which did not present itself in the sphere of sensibility, that is
to say, we cannot discover how the subjective conditions of thought can have
objective validity, in other words, can become conditions of the possibility of
all cognition of objects; for phenomena may certainly be given to us in
intuition without any help from the functions of the understanding. Let us
take, for example, the conception of cause, which indicates a peculiar kind of
synthesis, namely, that with something, A, something entirely different, B, is
connected according to a law. It is not à priori manifest why phenomena should
contain anything of this kind (we are of course debarred from appealing for
proof to experience, for the objective validity of this conception must be
demonstrated à priori), and it hence remains doubtful à priori, whether such a
conception be not quite void and without any corresponding object among
phenomena. For that objects of sensuous intuition must correspond to the formal
conditions of sensibility existing à priori in the mind is quite evident, from
the fact that without these they could not be objects for us; but that they
must also correspond to the conditions which understanding requires for the
synthetical unity of thought is an assertion, the grounds for which are not so
easily to be discovered. For phenomena might be so constituted as not to
correspond to the conditions of the unity of thought; and all things might lie
in such confusion that, for example, nothing could be met with in the sphere of
phenomena to suggest a law of synthesis, and so correspond to the conception of
cause and effect; so that this conception would be quite void, null, and
without significance. Phenomena would nevertheless continue to present objects
to our intuition; for mere intuition does not in any respect stand in need of
the functions of thought.

If we thought to free ourselves from the labour of these investigations by
saying: “Experience is constantly offering us examples of the relation of
cause and effect in phenomena, and presents us with abundant opportunity of
abstracting the conception of cause, and so at the same time of corroborating
the objective validity of this conception”; we should in this case be
overlooking the fact, that the conception of cause cannot arise in this way at
all; that, on the contrary, it must either have an à priori basis in the
understanding, or be rejected as a mere chimera. For this conception demands
that something, A, should be of such a nature that something else, B, should
follow from it necessarily, and according to an absolutely universal law. We
may certainly collect from phenomena a law, according to which this or that
usually happens, but the element of necessity is not to be found in it. Hence
it is evident that to the synthesis of cause and effect belongs a dignity,
which is utterly wanting in any empirical synthesis; for it is no mere
mechanical synthesis, by means of addition, but a dynamical one; that is to
say, the effect is not to be cogitated as merely annexed to the cause, but as
posited by and through the cause, and resulting from it. The strict
universality of this law never can be a characteristic of empirical laws, which
obtain through induction only a comparative universality, that is, an extended
range of practical application. But the pure conceptions of the understanding
would entirely lose all their peculiar character, if we treated them merely as
the productions of experience.

Transition to the Transcendental Deduction of the
Categories § 10

There are only two possible ways in which synthetical representation and its
objects can coincide with and relate necessarily to each other, and, as it
were, meet together. Either the object alone makes the representation possible,
or the representation alone makes the object possible. In the former case, the
relation between them is only empirical, and an à priori representation is
impossible. And this is the case with phenomena, as regards that in them which
is referable to mere sensation. In the latter case—although
representation alone (for of its causality, by means of the will, we do not
here speak) does not produce the object as to its existence, it must
nevertheless be à priori determinative in regard to the object, if it is only
by means of the representation that we can cognize anything as an object. Now
there are only two conditions of the possibility of a cognition of objects;
firstly, intuition, by means of which the object, though only as phenomenon, is
given; secondly, conception, by means of which the object which corresponds to
this intuition is thought. But it is evident from what has been said on
æsthetic that the first condition, under which alone objects can be intuited,
must in fact exist, as a formal basis for them, à priori in the mind. With this
formal condition of sensibility, therefore, all phenomena necessarily
correspond, because it is only through it that they can be phenomena at all;
that is, can be empirically intuited and given. Now the question is whether
there do not exist, à priori in the mind, conceptions of understanding also, as
conditions under which alone something, if not intuited, is yet thought as
object. If this question be answered in the affirmative, it follows that all
empirical cognition of objects is necessarily conformable to such conceptions,
since, if they are not presupposed, it is impossible that anything can be an
object of experience. Now all experience contains, besides the intuition of the
senses through which an object is given, a conception also of an object that is
given in intuition. Accordingly, conceptions of objects in general must lie as
à priori conditions at the foundation of all empirical cognition; and
consequently, the objective validity of the categories, as à priori
conceptions, will rest upon this, that experience (as far as regards the form
of thought) is possible only by their means. For in that case they apply
necessarily and à priori to objects of experience, because only through them
can an object of experience be thought.

The whole aim of the transcendental deduction of all à priori conceptions is to
show that these conceptions are à priori conditions of the possibility of all
experience. Conceptions which afford us the objective foundation of the
possibility of experience are for that very reason necessary. But the analysis
of the experiences in which they are met with is not deduction, but only an
illustration of them, because from experience they could never derive the
attribute of necessity. Without their original applicability and relation to
all possible experience, in which all objects of cognition present themselves,
the relation of the categories to objects, of whatever nature, would be quite
incomprehensible.

The celebrated Locke, for want of due reflection on these points, and because
he met with pure conceptions of the understanding in experience, sought also to
deduce them from experience, and yet proceeded so inconsequently as to attempt,
with their aid, to arrive it cognitions which lie far beyond the limits of all
experience. David Hume perceived that, to render this possible, it was
necessary that the conceptions should have an à priori origin. But as he could
not explain how it was possible that conceptions which are not connected with
each other in the understanding must nevertheless be thought as necessarily
connected in the object—and it never occurred to him that the
understanding itself might, perhaps, by means of these conceptions, be the
author of the experience in which its objects were presented to it—he was
forced to drive these conceptions from experience, that is, from a subjective
necessity arising from repeated association of experiences erroneously
considered to be objective—in one word, from habit. But he proceeded with
perfect consequence and declared it to be impossible, with such conceptions and
the principles arising from them, to overstep the limits of experience. The
empirical derivation, however, which both of these philosophers attributed to
these conceptions, cannot possibly be reconciled with the fact that we do
possess scientific à priori cognitions, namely, those of pure mathematics and
general physics.

The former of these two celebrated men opened a wide door to
extravagance—(for if reason has once undoubted right on its side, it will
not allow itself to be confined to set limits, by vague recommendations of
moderation); the latter gave himself up entirely to scepticism—a natural
consequence, after having discovered, as he thought, that the faculty of
cognition was not trustworthy. We now intend to make a trial whether it be not
possible safely to conduct reason between these two rocks, to assign her
determinate limits, and yet leave open for her the entire sphere of her
legitimate activity.

I shall merely premise an explanation of what the categories are. They are
conceptions of an object in general, by means of which its intuition is
contemplated as determined in relation to one of the logical functions of
judgement. The following will make this plain. The function of the categorical
judgement is that of the relation of subject to predicate; for example, in the
proposition: “All bodies are divisible.” But in regard to the
merely logical use of the understanding, it still remains undetermined to which
Of these two conceptions belongs the function Of subject and to which that of
predicate. For we could also say: “Some divisible is a body.” But
the category of substance, when the conception of a body is brought under it,
determines that; and its empirical intuition in experience must be contemplated
always as subject and never as mere predicate. And so with all the other
categories.

Section II Transcendental Deduction of the pure
Conceptions of the Understanding

Of the Possibility of a Conjunction of the manifold
representations given by Sense § 11.

The manifold content in our representations can be given in an intuition which
is merely sensuous—in other words, is nothing but susceptibility; and the
form of this intuition can exist à priori in our faculty of representation,
without being anything else but the mode in which the subject is affected. But
the conjunction (conjunctio) of a manifold in intuition never can be given us
by the senses; it cannot therefore be contained in the pure form of sensuous
intuition, for it is a spontaneous act of the faculty of representation. And as
we must, to distinguish it from sensibility, entitle this faculty
understanding; so all conjunction whether conscious or unconscious, be it of
the manifold in intuition, sensuous or non-sensuous, or of several
conceptions—is an act of the understanding. To this act we shall give the
general appellation of synthesis, thereby to indicate, at the same time, that
we cannot represent anything as conjoined in the object without having
previously conjoined it ourselves. Of all mental notions, that of conjunction
is the only one which cannot be given through objects, but can be originated
only by the subject itself, because it is an act of its purely spontaneous
activity. The reader will easily enough perceive that the possibility of
conjunction must be grounded in the very nature of this act, and that it must
be equally valid for all conjunction, and that analysis, which appears to be
its contrary, must, nevertheless, always presuppose it; for where the
understanding has not previously conjoined, it cannot dissect or analyse,
because only as conjoined by it, must that which is to be analysed have been
given to our faculty of representation.

But the conception of conjunction includes, besides the conception of the
manifold and of the synthesis of it, that of the unity of it also. Conjunction
is the representation of the synthetical unity of the manifold.^[15] This idea of unity, therefore, cannot
arise out of that of conjunction; much rather does that idea, by combining
itself with the representation of the manifold, render the conception of
conjunction possible. This unity, which à priori precedes all conceptions of
conjunction, is not the category of unity (§ 6); for all the categories are
based upon logical functions of judgement, and in these functions we already
have conjunction, and consequently unity of given conceptions. It is therefore
evident that the category of unity presupposes conjunction. We must therefore
look still higher for this unity (as qualitative, § 8), in that, namely, which
contains the ground of the unity of diverse conceptions in judgements, the
ground, consequently, of the possibility of the existence of the understanding,
even in regard to its logical use.

[15]
Whether the representations are in themselves identical, and consequently
whether one can be thought analytically by means of and through the other, is a
question which we need not at present consider. Our Consciousness of the one,
when we speak of the manifold, is always distinguishable from our consciousness
of the other; and it is only respecting the synthesis of this (possible)
consciousness that we here treat.

Of the Originally Synthetical Unity of Apperception §
12

The “I think” must accompany all my representations, for otherwise
something would be represented in me which could not be thought; in other
words, the representation would either be impossible, or at least be, in
relation to me, nothing. That representation which can be given previously to
all thought is called intuition. All the diversity or manifold content of
intuition, has, therefore, a necessary relation to the “I think,”
in the subject in which this diversity is found. But this representation,
“I think,” is an act of spontaneity; that is to say, it cannot be
regarded as belonging to mere sensibility. I call it pure apperception, in
order to distinguish it from empirical; or primitive apperception, because it
is self-consciousness which, whilst it gives birth to the representation
“I think,” must necessarily be capable of accompanying all our
representations. It is in all acts of consciousness one and the same, and
unaccompanied by it, no representation can exist for me. The unity of this
apperception I call the transcendental unity of self-consciousness, in order to
indicate the possibility of à priori cognition arising from it. For the
manifold representations which are given in an intuition would not all of them
be my representations, if they did not all belong to one self-consciousness,
that is, as my representations (even although I am not conscious of them as
such), they must conform to the condition under which alone they can exist
together in a common self-consciousness, because otherwise they would not all
without exception belong to me. From this primitive conjunction follow many
important results.

For example, this universal identity of the apperception of the manifold given
in intuition contains a synthesis of representations and is possible only by
means of the consciousness of this synthesis. For the empirical consciousness
which accompanies different representations is in itself fragmentary and
disunited, and without relation to the identity of the subject. This relation,
then, does not exist because I accompany every representation with
consciousness, but because I join one representation to another, and am
conscious of the synthesis of them. Consequently, only because I can connect a
variety of given representations in one consciousness, is it possible that I
can represent to myself the identity of consciousness in these representations;
in other words, the analytical unity of apperception is possible only under the
presupposition of a synthetical unity.^[16] The thought,
“These representations given in intuition belong all of them to
me,” is accordingly just the same as, “I unite them in one
self-consciousness, or can at least so unite them”; and although this
thought is not itself the consciousness of the synthesis of representations, it
presupposes the possibility of it; that is to say, for the reason alone that I
can comprehend the variety of my representations in one consciousness, do I
call them my representations, for otherwise I must have as many-coloured and
various a self as are the representations of which I am conscious. Synthetical
unity of the manifold in intuitions, as given à priori, is therefore the
foundation of the identity of apperception itself, which antecedes à priori all
determinate thought. But the conjunction of representations into a conception
is not to be found in objects themselves, nor can it be, as it were, borrowed
from them and taken up into the understanding by perception, but it is on the
contrary an operation of the understanding itself, which is nothing more than
the faculty of conjoining à priori and of bringing the variety of given
representations under the unity of apperception. This principle is the highest
in all human cognition.

[16]
All general conceptions—as such—depend, for their existence, on the
analytical unity of consciousness. For example, when I think of red in general,
I thereby think to myself a property which (as a characteristic mark) can be
discovered somewhere, or can be united with other representations;
consequently, it is only by means of a forethought possible synthetical unity
that I can think to myself the analytical. A representation which is cogitated
as common to different representations, is regarded as belonging to such as,
besides this common representation, contain something different; consequently
it must be previously thought in synthetical unity with other although only
possible representations, before I can think in it the analytical unity of
consciousness which makes it a conceptas communis. And thus the synthetical
unity of apperception is the highest point with which we must connect every
operation of the understanding, even the whole of logic, and after it our
transcendental philosophy; indeed, this faculty is the understanding itself.

This fundamental principle of the necessary unity of apperception is indeed an
identical, and therefore analytical, proposition; but it nevertheless explains
the necessity for a synthesis of the manifold given in an intuition, without
which the identity of self-consciousness would be incogitable. For the ego, as
a simple representation, presents us with no manifold content; only in
intuition, which is quite different from the representation ego, can it be
given us, and by means of conjunction it is cogitated in one
self-consciousness. An understanding, in which all the manifold should be given
by means of consciousness itself, would be intuitive; our understanding can
only think and must look for its intuition to sense. I am, therefore, conscious
of my identical self, in relation to all the variety of representations given
to me in an intuition, because I call all of them my representations. In other
words, I am conscious myself of a necessary à priori synthesis of my
representations, which is called the original synthetical unity of
apperception, under which rank all the representations presented to me, but
that only by means of a synthesis.

The Principle of the Synthetical Unity of Apperception
is the highest Principle of all exercise of the Understanding § 13

The supreme principle of the possibility of all intuition in relation to
sensibility was, according to our transcendental æsthetic, that all the
manifold in intuition be subject to the formal conditions of space and time.
The supreme principle of the possibility of it in relation to the understanding
is that all the manifold in it be subject to conditions of the originally
synthetical unity or apperception.^[17] To the former of these two principles
are subject all the various representations of intuition, in so far as they are
given to us; to the latter, in so far as they must be capable of conjunction in
one consciousness; for without this nothing can be thought or cognized, because
the given representations would not have in common the act Of the apperception
“I think” and therefore could not be connected in one
self-consciousness.

[17]
Space and time, and all portions thereof, are intuitions; consequently are,
with a manifold for their content, single representations. (See the
Transcendental Æsthetic.) Consequently, they are not pure conceptions, by means
of which the same consciousness is found in a great number of representations;
but, on the contrary, they are many representations contained in one, the
consciousness of which is, so to speak, compounded. The unity of consciousness
is nevertheless synthetical and, therefore, primitive. From this peculiar
character of consciousness follow many important consequences. (See § 21.)

Understanding is, to speak generally, the faculty Of cognitions. These consist
in the determined relation of given representation to an object. But an object
is that, in the conception of which the manifold in a given intuition is
united. Now all union of representations requires unity of consciousness in the
synthesis of them. Consequently, it is the unity of consciousness alone that
constitutes the possibility of representations relating to an object, and
therefore of their objective validity, and of their becoming cognitions, and
consequently, the possibility of the existence of the understanding itself.

The first pure cognition of understanding, then, upon which is founded all its
other exercise, and which is at the same time perfectly independent of all
conditions of mere sensuous intuition, is the principle of the original
synthetical unity of apperception. Thus the mere form of external sensuous
intuition, namely, space, affords us, per se, no cognition; it merely
contributes the manifold in à priori intuition to a possible cognition. But, in
order to cognize something in space (for example, a line), I must draw it, and
thus produce synthetically a determined conjunction of the given manifold, so
that the unity of this act is at the same time the unity of consciousness (in
the conception of a line), and by this means alone is an object (a determinate
space) cognized. The synthetical unity of consciousness is, therefore, an
objective condition of all cognition, which I do not merely require in order to
cognize an object, but to which every intuition must necessarily be subject, in
order to become an object for me; because in any other way, and without this
synthesis, the manifold in intuition could not be united in one consciousness.

This proposition is, as already said, itself analytical, although it
constitutes the synthetical unity, the condition of all thought; for it states
nothing more than that all my representations in any given intuition must be
subject to the condition which alone enables me to connect them, as my
representation with the identical self, and so to unite them synthetically in
one apperception, by means of the general expression, “I think.”

But this principle is not to be regarded as a principle for every possible
understanding, but only for the understanding by means of whose pure
apperception in the thought I am, no manifold content is given. The
understanding or mind which contained the manifold in intuition, in and through
the act itself of its own self-consciousness, in other words, an understanding
by and in the representation of which the objects of the representation should
at the same time exist, would not require a special act of synthesis of the
manifold as the condition of the unity of its consciousness, an act of which
the human understanding, which thinks only and cannot intuite, has absolute
need. But this principle is the first principle of all the operations of our
understanding, so that we cannot form the least conception of any other
possible understanding, either of one such as should be itself intuition, or
possess a sensuous intuition, but with forms different from those of space and
time.

What Objective Unity of Self-consciousness is §
14

It is by means of the transcendental unity of apperception that all the
manifold, given in an intuition is united into a conception of the object. On
this account it is called objective, and must be distinguished from the
subjective unity of consciousness, which is a determination of the internal
sense, by means of which the said manifold in intuition is given empirically to
be so united. Whether I can be empirically conscious of the manifold as
coexistent or as successive, depends upon circumstances, or empirical
conditions. Hence the empirical unity of consciousness by means of association
of representations, itself relates to a phenomenal world and is wholly
contingent. On the contrary, the pure form of intuition in time, merely as an
intuition, which contains a given manifold, is subject to the original unity of
consciousness, and that solely by means of the necessary relation of the
manifold in intuition to the “I think,” consequently by means of
the pure synthesis of the understanding, which lies à priori at the foundation
of all empirical synthesis. The transcendental unity of apperception is alone
objectively valid; the empirical which we do not consider in this essay, and
which is merely a unity deduced from the former under given conditions in
concreto, possesses only subjective validity. One person connects the notion
conveyed in a word with one thing, another with another thing; and the unity of
consciousness in that which is empirical, is, in relation to that which is
given by experience, not necessarily and universally valid.

The Logical Form of all Judgements consists in the
Objective Unity of Apperception of the Conceptions contained therein § 15

I could never satisfy myself with the definition which logicians give of a
judgement. It is, according to them, the representation of a relation between
two conceptions. I shall not dwell here on the faultiness of this definition,
in that it suits only for categorical and not for hypothetical or disjunctive
judgements, these latter containing a relation not of conceptions but of
judgements themselves—a blunder from which many evil results have
followed.^[18] It is more important for our present
purpose to observe, that this definition does not determine in what the said
relation consists.

[18]
The tedious doctrine of the four syllogistic figures concerns only categorical
syllogisms; and although it is nothing more than an artifice by surreptitiously
introducing immediate conclusions (consequentiae immediatae) among the premises
of a pure syllogism, to give ism give rise to an appearance of more modes of
drawing a conclusion than that in the first figure, the artifice would not have
had much success, had not its authors succeeded in bringing categorical
judgements into exclusive respect, as those to which all others must be
referred—a doctrine, however, which, according to § 5, is utterly false.

But if I investigate more closely the relation of given cognitions in every
judgement, and distinguish it, as belonging to the understanding, from the
relation which is produced according to laws of the reproductive imagination
(which has only subjective validity), I find that judgement is nothing but the
mode of bringing given cognitions under the objective unit of apperception.
This is plain from our use of the term of relation is in judgements, in order
to distinguish the objective unity of given representations from the subjective
unity. For this term indicates the relation of these representations to the
original apperception, and also their necessary unity, even although the
judgement is empirical, therefore contingent, as in the judgement: “All
bodies are heavy.” I do not mean by this, that these representations do
necessarily belong to each other in empirical intuition, but that by means of
the necessary unity of appreciation they belong to each other in the synthesis
of intuitions, that is to say, they belong to each other according to
principles of the objective determination of all our representations, in so far
as cognition can arise from them, these principles being all deduced from the
main principle of the transcendental unity of apperception. In this way alone
can there arise from this relation a judgement, that is, a relation which has
objective validity, and is perfectly distinct from that relation of the very
same representations which has only subjective validity—a relation, to
wit, which is produced according to laws of association. According to these
laws, I could only say: “When I hold in my hand or carry a body, I feel
an impression of weight”; but I could not say: “It, the body, is
heavy”; for this is tantamount to saying both these representations are
conjoined in the object, that is, without distinction as to the condition of
the subject, and do not merely stand together in my perception, however
frequently the perceptive act may be repeated.

All Sensuous Intuitions are subject to the Categories,
as Conditions under which alone the manifold Content of them can be united in
one Consciousness § 16

The manifold content given in a sensuous intuition comes necessarily under the
original synthetical unity of apperception, because thereby alone is the unity
of intuition possible (§ 13). But that act of the understanding, by which the
manifold content of given representations (whether intuitions or conceptions)
is brought under one apperception, is the logical function of judgements (§
15). All the manifold, therefore, in so far as it is given in one empirical
intuition, is determined in relation to one of the logical functions of
judgement, by means of which it is brought into union in one consciousness. Now
the categories are nothing else than these functions of judgement so far as the
manifold in a given intuition is determined in relation to them (§ 9).
Consequently, the manifold in a given intuition is necessarily subject to the
categories of the understanding.

Observation § 17

The manifold in an intuition, which I call mine, is represented by means of the
synthesis of the understanding, as belonging to the necessary unity of
self-consciousness, and this takes place by means of the category.^[19] The category indicates accordingly that
the empirical consciousness of a given manifold in an intuition is subject to a
pure self-consciousness à priori, in the same manner as an empirical intuition
is subject to a pure sensuous intuition, which is also à priori. In the above
proposition, then, lies the beginning of a deduction of the pure conceptions of
the understanding. Now, as the categories have their origin in the
understanding alone, independently of sensibility, I must in my deduction make
abstraction of the mode in which the manifold of an empirical intuition is
given, in order to fix my attention exclusively on the unity which is brought
by the understanding into the intuition by means of the category. In what
follows (§ 22), it will be shown, from the mode in which the empirical
intuition is given in the faculty of sensibility, that the unity which belongs
to it is no other than that which the category (according to § 16) imposes on
the manifold in a given intuition, and thus, its à priori validity in regard to
all objects of sense being established, the purpose of our deduction will be
fully attained.

[19]
The proof of this rests on the represented unity of intuition, by means of
which an object is given, and which always includes in itself a synthesis of
the manifold to be intuited, and also the relation of this latter to unity of
apperception.

But there is one thing in the above demonstration of which I could not make
abstraction, namely, that the manifold to be intuited must be given previously
to the synthesis of the understanding, and independently of it. How this takes
place remains here undetermined. For if I cogitate an understanding which was
itself intuitive (as, for example, a divine understanding which should not
represent given objects, but by whose representation the objects themselves
should be given or produced), the categories would possess no significance in
relation to such a faculty of cognition. They are merely rules for an
understanding, whose whole power consists in thought, that is, in the act of
submitting the synthesis of the manifold which is presented to it in intuition
from a very different quarter, to the unity of apperception; a faculty,
therefore, which cognizes nothing per se, but only connects and arranges the
material of cognition, the intuition, namely, which must be presented to it by
means of the object. But to show reasons for this peculiar character of our
understandings, that it produces unity of apperception à priori only by means
of categories, and a certain kind and number thereof, is as impossible as to
explain why we are endowed with precisely so many functions of judgement and no
more, or why time and space are the only forms of our intuition.

In Cognition, its Application to Objects of Experience
is the only legitimate use of the Category § 18

To think an object and to cognize an object are by no means the same thing. In
cognition there are two elements: firstly, the conception, whereby an object is
cogitated (the category); and, secondly, the intuition, whereby the object is
given. For supposing that to the conception a corresponding intuition could not
be given, it would still be a thought as regards its form, but without any
object, and no cognition of anything would be possible by means of it, inasmuch
as, so far as I knew, there existed and could exist nothing to which my thought
could be applied. Now all intuition possible to us is sensuous; consequently,
our thought of an object by means of a pure conception of the understanding,
can become cognition for us only in so far as this conception is applied to
objects of the senses. Sensuous intuition is either pure intuition (space and
time) or empirical intuition—of that which is immediately represented in
space and time by means of sensation as real. Through the determination of pure
intuition we obtain à priori cognitions of objects, as in mathematics, but only
as regards their form as phenomena; whether there can exist things which must
be intuited in this form is not thereby established. All mathematical
conceptions, therefore, are not per se cognition, except in so far as we
presuppose that there exist things which can only be represented conformably to
the form of our pure sensuous intuition. But things in space and time are given
only in so far as they are perceptions (representations accompanied with
sensation), therefore only by empirical representation. Consequently the pure
conceptions of the understanding, even when they are applied to intuitions à
priori (as in mathematics), produce cognition only in so far as these (and
therefore the conceptions of the understanding by means of them) can be applied
to empirical intuitions. Consequently the categories do not, even by means of
pure intuition afford us any cognition of things; they can only do so in so far
as they can be applied to empirical intuition. That is to say, the categories
serve only to render empirical cognition possible. But this is what we call
experience. Consequently, in cognition, their application to objects of
experience is the only legitimate use of the categories.

§ 19

The foregoing proposition is of the utmost importance, for it determines the
limits of the exercise of the pure conceptions of the understanding in regard
to objects, just as transcendental æsthetic determined the limits of the
exercise of the pure form of our sensuous intuition. Space and time, as
conditions of the possibility of the presentation of objects to us, are valid
no further than for objects of sense, consequently, only for experience. Beyond
these limits they represent to us nothing, for they belong only to sense, and
have no reality apart from it. The pure conceptions of the understanding are
free from this limitation, and extend to objects of intuition in general, be
the intuition like or unlike to ours, provided only it be sensuous, and not
intellectual. But this extension of conceptions beyond the range of our
intuition is of no advantage; for they are then mere empty conceptions of
objects, as to the possibility or impossibility of the existence of which they
furnish us with no means of discovery. They are mere forms of thought, without
objective reality, because we have no intuition to which the synthetical unity
of apperception, which alone the categories contain, could be applied, for the
purpose of determining an object. Our sensuous and empirical intuition can
alone give them significance and meaning.

If, then, we suppose an object of a non-sensuous intuition to be given we can
in that case represent it by all those predicates which are implied in the
presupposition that nothing appertaining to sensuous intuition belongs to it;
for example, that it is not extended, or in space; that its duration is not
time; that in it no change (the effect of the determinations in time) is to be
met with, and so on. But it is no proper knowledge if I merely indicate what
the intuition of the object is not, without being able to say what is contained
in it, for I have not shown the possibility of an object to which my pure
conception of understanding could be applicable, because I have not been able
to furnish any intuition corresponding to it, but am only able to say that our
intuition is not valid for it. But the most important point is this, that to a
something of this kind not one category can be found applicable. Take, for
example, the conception of substance, that is, something that can exist as
subject, but never as mere predicate; in regard to this conception I am quite
ignorant whether there can really be anything to correspond to such a
determination of thought, if empirical intuition did not afford me the occasion
for its application. But of this more in the sequel.

Of the Application of the Categories to Objects of the
Senses in general § 20

The pure conceptions of the understanding apply to objects of intuition in
general, through the understanding alone, whether the intuition be our own or
some other, provided only it be sensuous, but are, for this very reason, mere
forms of thought, by means of which alone no determined object can be cognized.
The synthesis or conjunction of the manifold in these conceptions relates, we
have said, only to the unity of apperception, and is for this reason the ground
of the possibility of à priori cognition, in so far as this cognition is
dependent on the understanding. This synthesis is, therefore, not merely
transcendental, but also purely intellectual. But because a certain form of
sensuous intuition exists in the mind à priori which rests on the receptivity
of the representative faculty (sensibility), the understanding, as a
spontaneity, is able to determine the internal sense by means of the diversity
of given representations, conformably to the synthetical unity of apperception,
and thus to cogitate the synthetical unity of the apperception of the manifold
of sensuous intuition à priori, as the condition to which must necessarily be
submitted all objects of human intuition. And in this manner the categories as
mere forms of thought receive objective reality, that is, application to
objects which are given to us in intuition, but that only as phenomena, for it
is only of phenomena that we are capable of à priori intuition.

This synthesis of the manifold of sensuous intuition, which is possible and
necessary à priori, may be called figurative (synthesis speciosa), in
contradistinction to that which is cogitated in the mere category in regard to
the manifold of an intuition in general, and is called connection or
conjunction of the understanding (synthesis intellectualis). Both are
transcendental, not merely because they themselves precede à priori all
experience, but also because they form the basis for the possibility of other
cognition à priori.

But the figurative synthesis, when it has relation only to the originally
synthetical unity of apperception, that is to the transcendental unity
cogitated in the categories, must, to be distinguished from the purely
intellectual conjunction, be entitled the transcendental synthesis of
imagination. Imagination is the faculty of representing an object even without
its presence in intuition. Now, as all our intuition is sensuous, imagination,
by reason of the subjective condition under which alone it can give a
corresponding intuition to the conceptions of the understanding, belongs to
sensibility. But in so far as the synthesis of the imagination is an act of
spontaneity, which is determinative, and not, like sense, merely determinable,
and which is consequently able to determine sense à priori, according to its
form, conformably to the unity of apperception, in so far is the imagination a
faculty of determining sensibility à priori, and its synthesis of intuitions
according to the categories must be the transcendental synthesis of the
imagination. It is an operation of the understanding on sensibility, and the
first application of the understanding to objects of possible intuition, and at
the same time the basis for the exercise of the other functions of that
faculty. As figurative, it is distinguished from the merely intellectual
synthesis, which is produced by the understanding alone, without the aid of
imagination. Now, in so far as imagination is spontaneity, I sometimes call it
also the productive imagination, and distinguish it from the reproductive, the
synthesis of which is subject entirely to empirical laws, those of association,
namely, and which, therefore, contributes nothing to the explanation of the
possibility of à priori cognition, and for this reason belongs not to
transcendental philosophy, but to psychology.

We have now arrived at the proper place for explaining the paradox which must
have struck every one in our exposition of the internal sense (§ 6),
namely—how this sense represents us to our own consciousness, only as we
appear to ourselves, not as we are in ourselves, because, to wit, we intuite
ourselves only as we are inwardly affected. Now this appears to be
contradictory, inasmuch as we thus stand in a passive relation to ourselves;
and therefore in the systems of psychology, the internal sense is commonly held
to be one with the faculty of apperception, while we, on the contrary,
carefully distinguish them.

That which determines the internal sense is the understanding, and its original
power of conjoining the manifold of intuition, that is, of bringing this under
an apperception (upon which rests the possibility of the understanding itself).
Now, as the human understanding is not in itself a faculty of intuition, and is
unable to exercise such a power, in order to conjoin, as it were, the manifold
of its own intuition, the synthesis of understanding is, considered per se,
nothing but the unity of action, of which, as such, it is self-conscious, even
apart from sensibility, by which, moreover, it is able to determine our
internal sense in respect of the manifold which may be presented to it
according to the form of sensuous intuition. Thus, under the name of a
transcendental synthesis of imagination, the understanding exercises an
activity upon the passive subject, whose faculty it is; and so we are right in
saying that the internal sense is affected thereby. Apperception and its
synthetical unity are by no means one and the same with the internal sense. The
former, as the source of all our synthetical conjunction, applies, under the
name of the categories, to the manifold of intuition in general, prior to all
sensuous intuition of objects. The internal sense, on the contrary, contains
merely the form of intuition, but without any synthetical conjunction of the
manifold therein, and consequently does not contain any determined intuition,
which is possible only through consciousness of the determination of the
manifold by the transcendental act of the imagination (synthetical influence of
the understanding on the internal sense), which I have named figurative
synthesis.

This we can indeed always perceive in ourselves. We cannot cogitate a
geometrical line without drawing it in thought, nor a circle without describing
it, nor represent the three dimensions of space without drawing three lines
from the same point perpendicular to one another. We cannot even cogitate time,
unless, in drawing a straight line (which is to serve as the external
figurative representation of time), we fix our attention on the act of the
synthesis of the manifold, whereby we determine successively the internal
sense, and thus attend also to the succession of this determination. Motion as
an act of the subject (not as a determination of an object),^[20] consequently the synthesis of the
manifold in space, if we make abstraction of space and attend merely to the act
by which we determine the internal sense according to its form, is that which
produces the conception of succession. The understanding, therefore, does by no
means find in the internal sense any such synthesis of the manifold, but
produces it, in that it affects this sense. At the same time, how “I who
think” is distinct from the “i” which intuites itself (other
modes of intuition being cogitable as at least possible), and yet one and the
same with this latter as the same subject; how, therefore, I am able to say:
“I, as an intelligence and thinking subject, cognize myself as an object
thought, so far as I am, moreover, given to myself in intuition—only,
like other phenomena, not as I am in myself, and as considered by the
understanding, but merely as I appear”—is a question that has in it
neither more nor less difficulty than the question—“How can I be an
object to myself?” or this—“How I can be an object of my own
intuition and internal perceptions?” But that such must be the fact, if
we admit that space is merely a pure form of the phenomena of external sense,
can be clearly proved by the consideration that we cannot represent time, which
is not an object of external intuition, in any other way than under the image
of a line, which we draw in thought, a mode of representation without which we
could not cognize the unity of its dimension, and also that we are necessitated
to take our determination of periods of time, or of points of time, for all our
internal perceptions from the changes which we perceive in outward things. It
follows that we must arrange the determinations of the internal sense, as
phenomena in time, exactly in the same manner as we arrange those of the
external senses in space. And consequently, if we grant, respecting this
latter, that by means of them we know objects only in so far as we are affected
externally, we must also confess, with regard to the internal sense, that by
means of it we intuite ourselves only as we are internally affected by
ourselves; in other words, as regards internal intuition, we cognize our own
subject only as phenomenon, and not as it is in itself.^[21]

[20]
Motion of an object in space does not belong to a pure science, consequently
not to geometry; because, that a thing is movable cannot be known à priori, but
only from experience. But motion, considered as the description of a space, is
a pure act of the successive synthesis of the manifold in external intuition by
means of productive imagination, and belongs not only to geometry, but even to
transcendental philosophy.

[21]
I do not see why so much difficulty should be found in admitting that our
internal sense is affected by ourselves. Every act of attention exemplifies it.
In such an act the understanding determines the internal sense by the
synthetical conjunction which it cogitates, conformably to the internal
intuition which corresponds to the manifold in the synthesis of the
understanding. How much the mind is usually affected thereby every one will be
able to perceive in himself.

§ 21

On the other hand, in the transcendental synthesis of the manifold content of
representations, consequently in the synthetical unity of apperception, I am
conscious of myself, not as I appear to myself, nor as I am in myself, but only
that “I am.” This representation is a thought, not an intuition.
Now, as in order to cognize ourselves, in addition to the act of thinking,
which subjects the manifold of every possible intuition to the unity of
apperception, there is necessary a determinate mode of intuition, whereby this
manifold is given; although my own existence is certainly not mere phenomenon
(much less mere illusion), the determination of my existence^[22] Can only take place conformably to the
form of the internal sense, according to the particular mode in which the
manifold which I conjoin is given in internal intuition, and I have therefore
no knowledge of myself as I am, but merely as I appear to myself. The
consciousness of self is thus very far from a knowledge of self, in which I do
not use the categories, whereby I cogitate an object, by means of the
conjunction of the manifold in one apperception. In the same way as I require,
for the sake of the cognition of an object distinct from myself, not only the
thought of an object in general (in the category), but also an intuition by
which to determine that general conception, in the same way do I require, in
order to the cognition of myself, not only the consciousness of myself or the
thought that I think myself, but in addition an intuition of the manifold in
myself, by which to determine this thought. It is true that I exist as an
intelligence which is conscious only of its faculty of conjunction or
synthesis, but subjected in relation to the manifold which this intelligence
has to conjoin to a limitative conjunction called the internal sense. My
intelligence (that is, I) can render that conjunction or synthesis perceptible
only according to the relations of time, which are quite beyond the proper
sphere of the conceptions of the understanding and consequently cognize itself
in respect to an intuition (which cannot possibly be intellectual, nor given by
the understanding), only as it appears to itself, and not as it would cognize
itself, if its intuition were intellectual.

[22]
The “I think” expresses the act of determining my own existence. My
existence is thus already given by the act of consciousness; but the mode in
which I must determine my existence, that is, the mode in which I must place
the manifold belonging to my existence, is not thereby given. For this purpose
intuition of self is required, and this intuition possesses a form given à
priori, namely, time, which is sensuous, and belongs to our receptivity of the
determinable. Now, as I do not possess another intuition of self which gives
the determining in me (of the spontaneity of which I am conscious), prior to
the act of determination, in the same manner as time gives the determinable, it
is clear that I am unable to determine my own existence as that of a
spontaneous being, but I am only able to represent to myself the spontaneity of
my thought, that is, of my determination, and my existence remains ever
determinable in a purely sensuous manner, that is to say, like the existence of
a phenomenon. But it is because of this spontaneity that I call myself an
intelligence.

Transcendental Deduction of the universally possible
employment in experience of the Pure Conceptions of the Understanding § 22

In the metaphysical deduction, the à priori origin of categories was proved by
their complete accordance with the general logical of thought; in the
transcendental deduction was exhibited the possibility of the categories as à
priori cognitions of objects of an intuition in general (§ 16 and 17).At
present we are about to explain the possibility of cognizing, à priori, by
means of the categories, all objects which can possibly be presented to our
senses, not, indeed, according to the form of their intuition, but according to
the laws of their conjunction or synthesis, and thus, as it were, of
prescribing laws to nature and even of rendering nature possible. For if the
categories were inadequate to this task, it would not be evident to us why
everything that is presented to our senses must be subject to those laws which
have an à priori origin in the understanding itself.

I premise that by the term synthesis of apprehension I understand the
combination of the manifold in an empirical intuition, whereby perception, that
is, empirical consciousness of the intuition (as phenomenon), is possible.

We have à priori forms of the external and internal sensuous intuition in the
representations of space and time, and to these must the synthesis of
apprehension of the manifold in a phenomenon be always comformable, because the
synthesis itself can only take place according to these forms. But space and
time are not merely forms of sensuous intuition, but intuitions themselves
(which contain a manifold), and therefore contain à priori the determination of
the unity of this manifold.^[23] (See the Transcendent Æsthetic.)
Therefore is unity of the synthesis of the manifold without or within us,
consequently also a conjunction to which all that is to be represented as
determined in space or time must correspond, given à priori along with (not in)
these intuitions, as the condition of the synthesis of all apprehension of
them. But this synthetical unity can be no other than that of the conjunction
of the manifold of a given intuition in general, in a primitive act of
consciousness, according to the categories, but applied to our sensuous
intuition. Consequently all synthesis, whereby alone is even perception
possible, is subject to the categories. And, as experience is cognition by
means of conjoined perceptions, the categories are conditions of the
possibility of experience and are therefore valid à priori for all objects of
experience.

[23]
Space represented as an object (as geometry really requires it to be) contains
more than the mere form of the intuition; namely, a combination of the manifold
given according to the form of sensibility into a representation that can be
intuited; so that the form of the intuition gives us merely the manifold, but
the formal intuition gives unity of representation. In the æsthetic, I regarded
this unity as belonging entirely to sensibility, for the purpose of indicating
that it antecedes all conceptions, although it presupposes a synthesis which
does not belong to sense, through which alone, however, all our conceptions of
space and time are possible. For as by means of this unity alone (the
understanding determining the sensibility) space and time are given as
intuitions, it follows that the unity of this intuition à priori belongs to
space and time, and not to the conception of the understanding (§ 20).

When, then, for example, I make the empirical intuition of a house by
apprehension of the manifold contained therein into a perception, the necessary
unity of space and of my external sensuous intuition lies at the foundation of
this act, and I, as it were, draw the form of the house conformably to this
synthetical unity of the manifold in space. But this very synthetical unity
remains, even when I abstract the form of space, and has its seat in the
understanding, and is in fact the category of the synthesis of the homogeneous
in an intuition; that is to say, the category of quantity, to which the
aforesaid synthesis of apprehension, that is, the perception, must be
completely conformable.^[24]

[24]
In this manner it is proved, that the synthesis of apprehension, which is
empirical, must necessarily be conformable to the synthesis of apperception,
which is intellectual, and contained à priori in the category. It is one and
the same spontaneity which at one time, under the name of imagination, at
another under that of understanding, produces conjunction in the manifold of
intuition.

To take another example, when I perceive the freezing of water, I apprehend two
states (fluidity and solidity), which, as such, stand toward each other
mutually in a relation of time. But in the time, which I place as an internal
intuition, at the foundation of this phenomenon, I represent to myself
synthetical unity of the manifold, without which the aforesaid relation could
not be given in an intuition as determined (in regard to the succession of
time). Now this synthetical unity, as the à priori condition under which I
conjoin the manifold of an intuition, is, if I make abstraction of the
permanent form of my internal intuition (that is to say, of time), the category
of cause, by means of which, when applied to my sensibility, I determine
everything that occurs according to relations of time. Consequently
apprehension in such an event, and the event itself, as far as regards the
possibility of its perception, stands under the conception of the relation of
cause and effect: and so in all other cases.

Categories are conceptions which prescribe laws à priori to phenomena,
consequently to nature as the complex of all phenomena (natura materialiter
spectata). And now the question arises—inasmuch as these categories are
not derived from nature, and do not regulate themselves according to her as
their model (for in that case they would be empirical)—how it is
conceivable that nature must regulate herself according to them, in other
words, how the categories can determine à priori the synthesis of the manifold
of nature, and yet not derive their origin from her. The following is the
solution of this enigma.

It is not in the least more difficult to conceive how the laws of the phenomena
of nature must harmonize with the understanding and with its à priori
form—that is, its faculty of conjoining the manifold—than it is to
understand how the phenomena themselves must correspond with the à priori form
of our sensuous intuition. For laws do not exist in the phenomena any more than
the phenomena exist as things in themselves. Laws do not exist except by
relation to the subject in which the phenomena inhere, in so far as it
possesses understanding, just as phenomena have no existence except by relation
to the same existing subject in so far as it has senses. To things as things in
themselves, conformability to law must necessarily belong independently of an
understanding to cognize them. But phenomena are only representations of things
which are utterly unknown in respect to what they are in themselves. But as
mere representations, they stand under no law of conjunction except that which
the conjoining faculty prescribes. Now that which conjoins the manifold of
sensuous intuition is imagination, a mental act to which understanding
contributes unity of intellectual synthesis, and sensibility, manifoldness of
apprehension. Now as all possible perception depends on the synthesis of
apprehension, and this empirical synthesis itself on the transcendental,
consequently on the categories, it is evident that all possible perceptions,
and therefore everything that can attain to empirical consciousness, that is,
all phenomena of nature, must, as regards their conjunction, be subject to the
categories. And nature (considered merely as nature in general) is dependent on
them, as the original ground of her necessary conformability to law (as natura
formaliter spectata). But the pure faculty (of the understanding) of
prescribing laws à priori to phenomena by means of mere categories, is not
competent to enounce other or more laws than those on which a nature in
general, as a conformability to law of phenomena of space and time, depends.
Particular laws, inasmuch as they concern empirically determined phenomena,
cannot be entirely deduced from pure laws, although they all stand under them.
Experience must be superadded in order to know these particular laws; but in
regard to experience in general, and everything that can be cognized as an
object thereof, these à priori laws are our only rule and guide.

Result of this Deduction of the Conceptions of the
Understanding § 23

We cannot think any object except by means of the categories; we cannot cognize
any thought except by means of intuitions corresponding to these conceptions.
Now all our intuitions are sensuous, and our cognition, in so far as the object
of it is given, is empirical. But empirical cognition is experience;
consequently no à priori cognition is possible for us, except of objects of
possible experience.^[25]

[25]
Lest my readers should stumble at this assertion, and the conclusions that may
be too rashly drawn from it, I must remind them that the categories in the act
of thought are by no means limited by the conditions of our sensuous intuition,
but have an unbounded sphere of action. It is only the cognition of the object
of thought, the determining of the object, which requires intuition. In the
absence of intuition, our thought of an object may still have true and useful
consequences in regard to the exercise of reason by the subject. But as this
exercise of reason is not always directed on the determination of the object,
in other words, on cognition thereof, but also on the determination of the
subject and its volition, I do not intend to treat of it in this place.

But this cognition, which is limited to objects of experience, is not for that
reason derived entirely, from, experience, but—and this is asserted of
the pure intuitions and the pure conceptions of the understanding—there
are, unquestionably, elements of cognition, which exist in the mind à priori.
Now there are only two ways in which a necessary harmony of experience with the
conceptions of its objects can be cogitated. Either experience makes these
conceptions possible, or the conceptions make experience possible. The former
of these statements will not hold good with respect to the categories (nor in
regard to pure sensuous intuition), for they are à priori conceptions, and
therefore independent of experience. The assertion of an empirical origin would
attribute to them a sort of generatio aequivoca. Consequently, nothing remains
but to adopt the second alternative (which presents us with a system, as it
were, of the epigenesis of pure reason), namely, that on the part of the
understanding the categories do contain the grounds of the possibility of all
experience. But with respect to the questions how they make experience
possible, and what are the principles of the possibility thereof with which
they present us in their application to phenomena, the following section on the
transcendental exercise of the faculty of judgement will inform the reader.

It is quite possible that someone may propose a species of preformation-system
of pure reason—a middle way between the two—to wit, that the
categories are neither innate and first à priori principles of cognition, nor
derived from experience, but are merely subjective aptitudes for thought
implanted in us contemporaneously with our existence, which were so ordered and
disposed by our Creator, that their exercise perfectly harmonizes with the laws
of nature which regulate experience. Now, not to mention that with such an
hypothesis it is impossible to say at what point we must stop in the employment
of predetermined aptitudes, the fact that the categories would in this case
entirely lose that character of necessity which is essentially involved in the
very conception of them, is a conclusive objection to it. The conception of
cause, for example, which expresses the necessity of an effect under a
presupposed condition, would be false, if it rested only upon such an arbitrary
subjective necessity of uniting certain empirical representations according to
such a rule of relation. I could not then say—“The effect is
connected with its cause in the object (that is, necessarily),” but only,
“I am so constituted that I can think this representation as so
connected, and not otherwise.” Now this is just what the sceptic wants.
For in this case, all our knowledge, depending on the supposed objective
validity of our judgement, is nothing but mere illusion; nor would there be
wanting people who would deny any such subjective necessity in respect to
themselves, though they must feel it. At all events, we could not dispute with
any one on that which merely depends on the manner in which his subject is
organized.

Short view of the above Deduction.

The foregoing deduction is an exposition of the pure conceptions of the
understanding (and with them of all theoretical à priori cognition), as
principles of the possibility of experience, but of experience as the
determination of all phenomena in space and time in general—of
experience, finally, from the principle of the original synthetical unity of
apperception, as the form of the understanding in relation to time and space as
original forms of sensibility.

I consider the division by paragraphs to be necessary only up to this point,
because we had to treat of the elementary conceptions. As we now proceed to the
exposition of the employment of these, I shall not designate the chapters in
this manner any further.

BOOK II. Analytic of Principles

General logic is constructed upon a plan which coincides exactly with the
division of the higher faculties of cognition. These are, understanding,
judgement, and reason. This science, accordingly, treats in its analytic of
conceptions, judgements, and conclusions in exact correspondence with the
functions and order of those mental powers which we include generally under the
generic denomination of understanding.

As this merely formal logic makes abstraction of all content of cognition,
whether pure or empirical, and occupies itself with the mere form of thought
(discursive cognition), it must contain in its analytic a canon for reason. For
the form of reason has its law, which, without taking into consideration the
particular nature of the cognition about which it is employed, can be
discovered à priori, by the simple analysis of the action of reason into its
momenta.

Transcendental logic, limited as it is to a determinate content, that of pure à
priori cognitions, to wit, cannot imitate general logic in this division. For
it is evident that the transcendental employment of reason is not objectively
valid, and therefore does not belong to the logic of truth (that is, to
analytic), but as a logic of illusion, occupies a particular department in the
scholastic system under the name of transcendental dialectic.

Understanding and judgement accordingly possess in transcendental logic a canon
of objectively valid, and therefore true exercise, and are comprehended in the
analytical department of that logic. But reason, in her endeavours to arrive by
à priori means at some true statement concerning objects and to extend
cognition beyond the bounds of possible experience, is altogether dialectic,
and her illusory assertions cannot be constructed into a canon such as an
analytic ought to contain.

Accordingly, the analytic of principles will be merely a canon for the faculty
of judgement, for the instruction of this faculty in its application to
phenomena of the pure conceptions of the understanding, which contain the
necessary condition for the establishment of à priori laws. On this account,
although the subject of the following chapters is the especial principles of
understanding, I shall make use of the term Doctrine of the faculty of
judgement, in order to define more particularly my present purpose.

INTRODUCTION. Of the Transcendental Faculty of
judgement in General

If understanding in general be defined as the faculty of laws or rules, the
faculty of judgement may be termed the faculty of subsumption under these
rules; that is, of distinguishing whether this or that does or does not stand
under a given rule (casus datae legis). General logic contains no directions or
precepts for the faculty of judgement, nor can it contain any such. For as it
makes abstraction of all content of cognition, no duty is left for it, except
that of exposing analytically the mere form of cognition in conceptions,
judgements, and conclusions, and of thereby establishing formal rules for all
exercise of the understanding. Now if this logic wished to give some general
direction how we should subsume under these rules, that is, how we should
distinguish whether this or that did or did not stand under them, this again
could not be done otherwise than by means of a rule. But this rule, precisely
because it is a rule, requires for itself direction from the faculty of
judgement. Thus, it is evident that the understanding is capable of being
instructed by rules, but that the judgement is a peculiar talent, which does
not, and cannot require tuition, but only exercise. This faculty is therefore
the specific quality of the so-called mother wit, the want of which no
scholastic discipline can compensate.

For although education may furnish, and, as it were, engraft upon a limited
understanding rules borrowed from other minds, yet the power of employing these
rules correctly must belong to the pupil himself; and no rule which we can
prescribe to him with this purpose is, in the absence or deficiency of this
gift of nature, secure from misuse.^[26] A physician therefore, a judge or a
statesman, may have in his head many admirable pathological, juridical, or
political rules, in a degree that may enable him to be a profound teacher in
his particular science, and yet in the application of these rules he may very
possibly blunder—either because he is wanting in natural judgement
(though not in understanding) and, whilst he can comprehend the general in
abstracto, cannot distinguish whether a particular case in concreto ought to
rank under the former; or because his faculty of judgement has not been
sufficiently exercised by examples and real practice. Indeed, the grand and
only use of examples, is to sharpen the judgement. For as regards the
correctness and precision of the insight of the understanding, examples are
commonly injurious rather than otherwise, because, as casus in terminis they
seldom adequately fulfil the conditions of the rule. Besides, they often weaken
the power of our understanding to apprehend rules or laws in their
universality, independently of particular circumstances of experience; and
hence, accustom us to employ them more as formulae than as principles. Examples
are thus the go-cart of the judgement, which he who is naturally deficient in
that faculty cannot afford to dispense with.

[26]
Deficiency in judgement is properly that which is called stupidity; and for
such a failing we know no remedy. A dull or narrow-minded person, to whom
nothing is wanting but a proper degree of understanding, may be improved by
tuition, even so far as to deserve the epithet of learned. But as such persons
frequently labour under a deficiency in the faculty of judgement, it is not
uncommon to find men extremely learned who in the application of their science
betray a lamentable degree this irremediable want.

But although general logic cannot give directions to the faculty of judgement,
the case is very different as regards transcendental logic, insomuch that it
appears to be the especial duty of the latter to secure and direct, by means of
determinate rules, the faculty of judgement in the employment of the pure
understanding. For, as a doctrine, that is, as an endeavour to enlarge the
sphere of the understanding in regard to pure à priori cognitions, philosophy
is worse than useless, since from all the attempts hitherto made, little or no
ground has been gained. But, as a critique, in order to guard against the
mistakes of the faculty of judgement (lapsus judicii) in the employment of the
few pure conceptions of the understanding which we possess, although its use is
in this case purely negative, philosophy is called upon to apply all its
acuteness and penetration.

But transcendental philosophy has this peculiarity, that besides indicating the
rule, or rather the general condition for rules, which is given in the pure
conception of the understanding, it can, at the same time, indicate à priori
the case to which the rule must be applied. The cause of the superiority which,
in this respect, transcendental philosophy possesses above all other sciences
except mathematics, lies in this: it treats of conceptions which must relate à
priori to their objects, whose objective validity consequently cannot be
demonstrated à posteriori, and is, at the same time, under the obligation of
presenting in general but sufficient tests, the conditions under which objects
can be given in harmony with those conceptions; otherwise they would be mere
logical forms, without content, and not pure conceptions of the understanding.

Our transcendental doctrine of the faculty of judgement will contain two
chapters. The first will treat of the sensuous condition under which alone pure
conceptions of the understanding can be employed—that is, of the
schematism of the pure understanding. The second will treat of those
synthetical judgements which are derived à priori from pure conceptions of the
understanding under those conditions, and which lie à priori at the foundation
of all other cognitions, that is to say, it will treat of the principles of the
pure understanding.

TRANSCENDENTAL DOCTRINE OF THE FACULTY OF JUDGEMENT
OR, ANALYTIC OF PRINCIPLES

Chapter I. Of the Schematism at of the Pure
Conceptions of the Understanding

In all subsumptions of an object under a conception, the representation of the
object must be homogeneous with the conception; in other words, the conception
must contain that which is represented in the object to be subsumed under it.
For this is the meaning of the expression: “An object is contained under
a conception.” Thus the empirical conception of a plate is homogeneous
with the pure geometrical conception of a circle, inasmuch as the roundness
which is cogitated in the former is intuited in the latter.

But pure conceptions of the understanding, when compared with empirical
intuitions, or even with sensuous intuitions in general, are quite
heterogeneous, and never can be discovered in any intuition. How then is the
subsumption of the latter under the former, and consequently the application of
the categories to phenomena, possible?—For it is impossible to say, for
example: “Causality can be intuited through the senses and is contained
in the phenomenon.”—This natural and important question forms the
real cause of the necessity of a transcendental doctrine of the faculty of
judgement, with the purpose, to wit, of showing how pure conceptions of the
understanding can be applied to phenomena. In all other sciences, where the
conceptions by which the object is thought in the general are not so different
and heterogeneous from those which represent the object in concreto—as it
is given, it is quite unnecessary to institute any special inquiries concerning
the application of the former to the latter.

Now it is quite clear that there must be some third thing, which on the one
side is homogeneous with the category, and with the phenomenon on the other,
and so makes the application of the former to the latter possible. This
mediating representation must be pure (without any empirical content), and yet
must on the one side be intellectual, on the other sensuous. Such a
representation is the transcendental schema.

The conception of the understanding contains pure synthetical unity of the
manifold in general. Time, as the formal condition of the manifold of the
internal sense, consequently of the conjunction of all representations,
contains à priori a manifold in the pure intuition. Now a transcendental
determination of time is so far homogeneous with the category, which
constitutes the unity thereof, that it is universal and rests upon a rule à
priori. On the other hand, it is so far homogeneous with the phenomenon,
inasmuch as time is contained in every empirical representation of the
manifold. Thus an application of the category to phenomena becomes possible, by
means of the transcendental determination of time, which, as the schema of the
conceptions of the understanding, mediates the subsumption of the latter under
the former.

After what has been proved in our deduction of the categories, no one, it is to
be hoped, can hesitate as to the proper decision of the question, whether the
employment of these pure conceptions of the understanding ought to be merely
empirical or also transcendental; in other words, whether the categories, as
conditions of a possible experience, relate à priori solely to phenomena, or
whether, as conditions of the possibility of things in general, their
application can be extended to objects as things in themselves. For we have
there seen that conceptions are quite impossible, and utterly without
signification, unless either to them, or at least to the elements of which they
consist, an object be given; and that, consequently, they cannot possibly apply
to objects as things in themselves without regard to the question whether and
how these may be given to us; and, further, that the only manner in which
objects can be given to us is by means of the modification of our sensibility;
and, finally, that pure à priori conceptions, in addition to the function of
the understanding in the category, must contain à priori formal conditions of
sensibility (of the internal sense, namely), which again contain the general
condition under which alone the category can be applied to any object. This
formal and pure condition of sensibility, to which the conception of the
understanding is restricted in its employment, we shall name the schema of the
conception of the understanding, and the procedure of the understanding with
these schemata we shall call the schematism of the pure understanding.

The schema is, in itself, always a mere product of the imagination. But, as the
synthesis of imagination has for its aim no single intuition, but merely unity
in the determination of sensibility, the schema is clearly distinguishable from
the image. Thus, if I place five points one after another…. this is an image
of the number five. On the other hand, if I only think a number in general,
which may be either five or a hundred, this thought is rather the
representation of a method of representing in an image a sum (e.g., a thousand)
in conformity with a conception, than the image itself, an image which I should
find some little difficulty in reviewing, and comparing with the conception.
Now this representation of a general procedure of the imagination to present
its image to a conception, I call the schema of this conception.

In truth, it is not images of objects, but schemata, which lie at the
foundation of our pure sensuous conceptions. No image could ever be adequate to
our conception of a triangle in general. For the generalness of the conception
it never could attain to, as this includes under itself all triangles, whether
right-angled, acute-angled, etc., whilst the image would always be limited to a
single part of this sphere. The schema of the triangle can exist nowhere else
than in thought, and it indicates a rule of the synthesis of the imagination in
regard to pure figures in space. Still less is an object of experience, or an
image of the object, ever to the empirical conception. On the contrary, the
conception always relates immediately to the schema of the imagination, as a
rule for the determination of our intuition, in conformity with a certain
general conception. The conception of a dog indicates a rule, according to
which my imagination can delineate the figure of a four-footed animal in
general, without being limited to any particular individual form which
experience presents to me, or indeed to any possible image that I can represent
to myself in concreto. This schematism of our understanding in regard to
phenomena and their mere form, is an art, hidden in the depths of the human
soul, whose true modes of action we shall only with difficulty discover and
unveil. Thus much only can we say: “The image is a product of the
empirical faculty of the productive imagination—the schema of sensuous
conceptions (of figures in space, for example) is a product, and, as it were, a
monogram of the pure imagination à priori, whereby and according to which
images first become possible, which, however, can be connected with the
conception only mediately by means of the schema which they indicate, and are
in themselves never fully adequate to it.” On the other hand, the schema
of a pure conception of the understanding is something that cannot be reduced
into any image—it is nothing else than the pure synthesis expressed by
the category, conformably, to a rule of unity according to conceptions. It is a
transcendental product of the imagination, a product which concerns the
determination of the internal sense, according to conditions of its form (time)
in respect to all representations, in so far as these representations must be
conjoined à 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 à 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 à 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 à 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 à 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 à 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
æsthetic, 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 à 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 à 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 à priori or à
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 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 à 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 à 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 à 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 à 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 à 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,
à 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, à 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 à 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 à 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.”

À priori synthetical judgements are possible when we apply the formal
conditions of the à 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 à 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 à 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
à 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 à 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 à
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 à 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 à 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:

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 à 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.^[27] 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.

[27]
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 à priori. This combination—not an arbitrary
one—I entitle dynamical because it concerns the connection of the
existence of the manifold. This, again, may be divided into the physical
synthesis, of the phenomena divided among each other, and the metaphysical
synthesis, or the connection of phenomena à priori in the faculty of cognition.

1. AXIOMS OF INTUITION.

The principle of these is: All Intuitions are Extensive Quantities.

PROOF.

All phenomena contain, as regards their form, an intuition in space and time,
which lies à priori at the foundation of all without exception. Phenomena,
therefore, cannot be apprehended, that is, received into empirical
consciousness otherwise than through the synthesis of a manifold, through which
the representations of a determinate space or time are generated; that is to
say, through the composition of the homogeneous and the consciousness of the
synthetical unity of this manifold (homogeneous). Now the consciousness of a
homogeneous manifold in intuition, in so far as thereby the representation of
an object is rendered possible, is the conception of a quantity (quanti).
Consequently, even the perception of an object as phenomenon is possible only
through the same synthetical unity of the manifold of the given sensuous
intuition, through which the unity of the composition of the homogeneous
manifold in the conception of a quantity is cogitated; that is to say, all
phenomena are quantities, and extensive quantities, because as intuitions in
space or time they must be represented by means of the same synthesis through
which space and time themselves are determined.

An extensive quantity I call that wherein the representation of the parts
renders possible (and therefore necessarily antecedes) the representation of
the whole. I cannot represent to myself any line, however small, without
drawing it in thought, that is, without generating from a point all its parts
one after another, and in this way alone producing this intuition. Precisely
the same is the case with every, even the smallest, portion of time. I cogitate
therein only the successive progress from one moment to another, and hence, by
means of the different portions of time and the addition of them, a determinate
quantity of time is produced. As the pure intuition in all phenomena is either
time or space, so is every phenomenon in its character of intuition an
extensive quantity, inasmuch as it can only be cognized in our apprehension by
successive synthesis (from part to part). All phenomena are, accordingly, to be
considered as aggregates, that is, as a collection of previously given parts;
which is not the case with every sort of quantities, but only with those which
are represented and apprehended by us as extensive.

On this successive synthesis of the productive imagination, in the generation
of figures, is founded the mathematics of extension, or geometry, with its
axioms, which express the conditions of sensuous intuition à priori, under
which alone the schema of a pure conception of external intuition can exist;
for example, “be tween two points only one straight line is
possible,” “two straight lines cannot enclose a space,” etc.
These are the axioms which properly relate only to quantities (quanta) as such.

But, as regards the quantity of a thing (quantitas), that is to say, the answer
to the question: “How large is this or that object?” although, in
respect to this question, we have various propositions synthetical and
immediately certain (indemonstrabilia); we have, in the proper sense of the
term, no axioms. For example, the propositions: “If equals be added to
equals, the wholes are equal”; “If equals be taken from equals, the
remainders are equal”; are analytical, because I am immediately conscious
of the identity of the production of the one quantity with the production of
the other; whereas axioms must be à priori synthetical propositions. On the
other hand, the self-evident propositions as to the relation of numbers, are
certainly synthetical but not universal, like those of geometry, and for this
reason cannot be called axioms, but numerical formulae. That 7 + 5 = 12 is not
an analytical proposition. For neither in the representation of seven, nor of
five, nor of the composition of the two numbers, do I cogitate the number
twelve. (Whether I cogitate the number in the addition of both, is not at
present the question; for in the case of an analytical proposition, the only
point is whether I really cogitate the predicate in the representation of the
subject.) But although the proposition is synthetical, it is nevertheless only
a singular proposition. In so far as regard is here had merely to the synthesis
of the homogeneous (the units), it cannot take place except in one manner,
although our use of these numbers is afterwards general. If I say: “A
triangle can be constructed with three lines, any two of which taken together
are greater than the third,” I exercise merely the pure function of the
productive imagination, which may draw the lines longer or shorter and
construct the angles at its pleasure. On the contrary, the number seven is
possible only in one manner, and so is likewise the number twelve, which
results from the synthesis of seven and five. Such propositions, then, cannot
be termed axioms (for in that case we should have an infinity of these), but
numerical formulae.

This transcendental principle of the mathematics of phenomena greatly enlarges
our à priori cognition. For it is by this principle alone that pure mathematics
is rendered applicable in all its precision to objects of experience, and
without it the validity of this application would not be so self-evident; on
the contrary, contradictions and confusions have often arisen on this very
point. Phenomena are not things in themselves. Empirical intuition is possible
only through pure intuition (of space and time); consequently, what geometry
affirms of the latter, is indisputably valid of the former. All evasions, such
as the statement that objects of sense do not conform to the rules of
construction in space (for example, to the rule of the infinite divisibility of
lines or angles), must fall to the ground. For, if these objections hold good,
we deny to space, and with it to all mathematics, objective validity, and no
longer know wherefore, and how far, mathematics can be applied to phenomena.
The synthesis of spaces and times as the essential form of all intuition, is
that which renders possible the apprehension of a phenomenon, and therefore
every external experience, consequently all cognition of the objects of
experience; and whatever mathematics in its pure use proves of the former, must
necessarily hold good of the latter. All objections are but the chicaneries of
an ill-instructed reason, which erroneously thinks to liberate the objects of
sense from the formal conditions of our sensibility, and represents these,
although mere phenomena, as things in themselves, presented as such to our
understanding. But in this case, no à priori synthetical cognition of them
could be possible, consequently not through pure conceptions of space and the
science which determines these conceptions, that is to say, geometry, would
itself be impossible.

2. ANTICIPATIONS OF PERCEPTION.

The principle of these is: In all phenomena the Real, that which is an object
of sensation, has Intensive Quantity, that is, has a Degree.

PROOF.

Perception is empirical consciousness, that is to say, a consciousness which
contains an element of sensation. Phenomena as objects of perception are not
pure, that is, merely formal intuitions, like space and time, for they cannot
be perceived in themselves.^[28] They contain, then, over and above the
intuition, the materials for an object (through which is represented something
existing in space or time), that is to say, they contain the real of sensation,
as a representation merely subjective, which gives us merely the consciousness
that the subject is affected, and which we refer to some external object. Now,
a gradual transition from empirical consciousness to pure consciousness is
possible, inasmuch as the real in this consciousness entirely vanishes, and
there remains a merely formal consciousness (à priori) of the manifold in time
and space; consequently there is possible a synthesis also of the production of
the quantity of a sensation from its commencement, that is, from the pure
intuition = 0 onwards up to a certain quantity of the sensation. Now as
sensation in itself is not an objective representation, and in it is to be
found neither the intuition of space nor of time, it cannot possess any
extensive quantity, and yet there does belong to it a quantity (and that by
means of its apprehension, in which empirical consciousness can within a
certain time rise from nothing = 0 up to its given amount), consequently an
intensive quantity. And thus we must ascribe intensive quantity, that is, a
degree of influence on sense to all objects of perception, in so far as this
perception contains sensation.

[28]
They can be perceived only as phenomena, and some part of them must always
belong to the non-ego; whereas pure intuitions are entirely the products of the
mind itself, and as such are cognized in themselves.—Tr

All cognition, by means of which I am enabled to cognize and determine à priori
what belongs to empirical cognition, may be called an anticipation; and without
doubt this is the sense in which Epicurus employed his expression prholepsis.
But as there is in phenomena something which is never cognized à priori, which
on this account constitutes the proper difference between pure and empirical
cognition, that is to say, sensation (as the matter of perception), it follows,
that sensation is just that element in cognition which cannot be at all
anticipated. On the other hand, we might very well term the pure determinations
in space and time, as well in regard to figure as to quantity, anticipations of
phenomena, because they represent à priori that which may always be given à
posteriori in experience. But suppose that in every sensation, as sensation in
general, without any particular sensation being thought of, there existed
something which could be cognized à priori, this would deserve to be called
anticipation in a special sense—special, because it may seem surprising
to forestall experience, in that which concerns the matter of experience, and
which we can only derive from itself. Yet such really is the case here.

Apprehension^[29], by means of sensation alone, fills
only one moment, that is, if I do not take into consideration a succession of
many sensations. As that in the phenomenon, the apprehension of which is not a
successive synthesis advancing from parts to an entire representation,
sensation has therefore no extensive quantity; the want of sensation in a
moment of time would represent it as empty, consequently = 0. That which in the
empirical intuition corresponds to sensation is reality (realitas phaenomenon);
that which corresponds to the absence of it, negation = 0. Now every sensation
is capable of a diminution, so that it can decrease, and thus gradually
disappear. Therefore, between reality in a phenomenon and negation, there
exists a continuous concatenation of many possible intermediate sensations, the
difference of which from each other is always smaller than that between the
given sensation and zero, or complete negation. That is to say, the real in a
phenomenon has always a quantity, which however is not discoverable in
apprehension, inasmuch as apprehension take place by means of mere sensation in
one instant, and not by the successive synthesis of many sensations, and
therefore does not progress from parts to the whole. Consequently, it has a
quantity, but not an extensive quantity.

[29]
Apprehension is the Kantian word for preception, in the largest sense in which
we employ that term. It is the genus which includes under i, as species,
perception proper and sensation proper—Tr

Now that quantity which is apprehended only as unity, and in which plurality
can be represented only by approximation to negation = O, I term intensive
quantity. Consequently, reality in a phenomenon has intensive quantity, that
is, a degree. If we consider this reality as cause (be it of sensation or of
another reality in the phenomenon, for example, a change), we call the degree
of reality in its character of cause a momentum, for example, the momentum of
weight; and for this reason, that the degree only indicates that quantity the
apprehension of which is not successive, but instantaneous. This, however, I
touch upon only in passing, for with causality I have at present nothing to do.

Accordingly, every sensation, consequently every reality in phenomena, however
small it may be, has a degree, that is, an intensive quantity, which may always
be lessened, and between reality and negation there exists a continuous
connection of possible realities, and possible smaller perceptions. Every
colour—for example, red—has a degree, which, be it ever so small,
is never the smallest, and so is it always with heat, the momentum of weight,
etc.

This property of quantities, according to which no part of them is the smallest
possible (no part simple), is called their continuity. Space and time are
quanta continua, because no part of them can be given, without enclosing it
within boundaries (points and moments), consequently, this given part is itself
a space or a time. Space, therefore, consists only of spaces, and time of
times. Points and moments are only boundaries, that is, the mere places or
positions of their limitation. But places always presuppose intuitions which
are to limit or determine them; and we cannot conceive either space or time
composed of constituent parts which are given before space or time. Such
quantities may also be called flowing, because synthesis (of the productive
imagination) in the production of these quantities is a progression in time,
the continuity of which we are accustomed to indicate by the expression
flowing.

All phenomena, then, are continuous quantities, in respect both to intuition
and mere perception (sensation, and with it reality). In the former case they
are extensive quantities; in the latter, intensive. When the synthesis of the
manifold of a phenomenon is interrupted, there results merely an aggregate of
several phenomena, and not properly a phenomenon as a quantity, which is not
produced by the mere continuation of the productive synthesis of a certain
kind, but by the repetition of a synthesis always ceasing. For example, if I
call thirteen dollars a sum or quantity of money, I employ the term quite
correctly, inasmuch as I understand by thirteen dollars the value of a mark in
standard silver, which is, to be sure, a continuous quantity, in which no part
is the smallest, but every part might constitute a piece of money, which would
contain material for still smaller pieces. If, however, by the words thirteen
dollars I understand so many coins (be their value in silver what it may), it
would be quite erroneous to use the expression a quantity of dollars; on the
contrary, I must call them aggregate, that is, a number of coins. And as in
every number we must have unity as the foundation, so a phenomenon taken as
unity is a quantity, and as such always a continuous quantity (quantum
continuum).

Now, seeing all phenomena, whether considered as extensive or intensive, are
continuous quantities, the proposition: “All change (transition of a
thing from one state into another) is continuous,” might be proved here
easily, and with mathematical evidence, were it not that the causality of a
change lies, entirely beyond the bounds of a transcendental philosophy, and
presupposes empirical principles. For of the possibility of a cause which
changes the condition of things, that is, which determines them to the contrary
to a certain given state, the understanding gives us à priori no knowledge; not
merely because it has no insight into the possibility of it (for such insight
is absent in several à priori cognitions), but because the notion of change
concerns only certain determinations of phenomena, which experience alone can
acquaint us with, while their cause lies in the unchangeable. But seeing that
we have nothing which we could here employ but the pure fundamental conceptions
of all possible experience, among which of course nothing empirical can be
admitted, we dare not, without injuring the unity of our system, anticipate
general physical science, which is built upon certain fundamental experiences.

Nevertheless, we are in no want of proofs of the great influence which the
principle above developed exercises in the anticipation of perceptions, and
even in supplying the want of them, so far as to shield us against the false
conclusions which otherwise we might rashly draw.

If all reality in perception has a degree, between which and negation there is
an endless sequence of ever smaller degrees, and if, nevertheless, every sense
must have a determinate degree of receptivity for sensations; no perception,
and consequently no experience is possible, which can prove, either immediately
or mediately, an entire absence of all reality in a phenomenon; in other words,
it is impossible ever to draw from experience a proof of the existence of empty
space or of empty time. For in the first place, an entire absence of reality in
a sensuous intuition cannot of course be an object of perception; secondly,
such absence cannot be deduced from the contemplation of any single phenomenon,
and the difference of the degrees in its reality; nor ought it ever to be
admitted in explanation of any phenomenon. For if even the complete intuition
of a determinate space or time is thoroughly real, that is, if no part thereof
is empty, yet because every reality has its degree, which, with the extensive
quantity of the phenomenon unchanged, can diminish through endless gradations
down to nothing (the void), there must be infinitely graduated degrees, with
which space or time is filled, and the intensive quantity in different
phenomena may be smaller or greater, although the extensive quantity of the
intuition remains equal and unaltered.

We shall give an example of this. Almost all natural philosophers, remarking a
great difference in the quantity of the matter of different kinds in bodies
with the same volume (partly on account of the momentum of gravity or weight,
partly on account of the momentum of resistance to other bodies in motion),
conclude unanimously that this volume (extensive quantity of the phenomenon)
must be void in all bodies, although in different proportion. But who would
suspect that these for the most part mathematical and mechanical inquirers into
nature should ground this conclusion solely on a metaphysical
hypothesis—a sort of hypothesis which they profess to disparage and
avoid? Yet this they do, in assuming that the real in space (I must not here
call it impenetrability or weight, because these are empirical conceptions) is
always identical, and can only be distinguished according to its extensive
quantity, that is, multiplicity. Now to this presupposition, for which they can
have no ground in experience, and which consequently is merely metaphysical, I
oppose a transcendental demonstration, which it is true will not explain the
difference in the filling up of spaces, but which nevertheless completely does
away with the supposed necessity of the above-mentioned presupposition that we
cannot explain the said difference otherwise than by the hypothesis of empty
spaces. This demonstration, moreover, has the merit of setting the
understanding at liberty to conceive this distinction in a different manner, if
the explanation of the fact requires any such hypothesis. For we perceive that
although two equal spaces may be completely filled by matters altogether
different, so that in neither of them is there left a single point wherein
matter is not present, nevertheless, every reality has its degree (of
resistance or of weight), which, without diminution of the extensive quantity,
can become less and less ad infinitum, before it passes into nothingness and
disappears. Thus an expansion which fills a space—for example, caloric,
or any other reality in the phenomenal world—can decrease in its degrees
to infinity, yet without leaving the smallest part of the space empty; on the
contrary, filling it with those lesser degrees as completely as another
phenomenon could with greater. My intention here is by no means to maintain
that this is really the case with the difference of matters, in regard to their
specific gravity; I wish only to prove, from a principle of the pure
understanding, that the nature of our perceptions makes such a mode of
explanation possible, and that it is erroneous to regard the real in a
phenomenon as equal quoad its degree, and different only quoad its aggregation
and extensive quantity, and this, too, on the pretended authority of an à
priori principle of the understanding.

Nevertheless, this principle of the anticipation of perception must somewhat
startle an inquirer whom initiation into transcendental philosophy has rendered
cautious. We must naturally entertain some doubt whether or not the
understanding can enounce any such synthetical proposition as that respecting
the degree of all reality in phenomena, and consequently the possibility of the
internal difference of sensation itself—abstraction being made of its
empirical quality. Thus it is a question not unworthy of solution: “How
the understanding can pronounce synthetically and à priori respecting
phenomena, and thus anticipate these, even in that which is peculiarly and
merely empirical, that, namely, which concerns sensation itself?”

The quality of sensation is in all cases merely empirical, and cannot be
represented à priori (for example, colours, taste, etc.). But the
real—that which corresponds to sensation—in opposition to negation
= 0, only represents something the conception of which in itself contains a
being (ein seyn), and signifies nothing but the synthesis in an empirical
consciousness. That is to say, the empirical consciousness in the internal
sense can be raised from 0 to every higher degree, so that the very same
extensive quantity of intuition, an illuminated surface, for example, excites
as great a sensation as an aggregate of many other surfaces less illuminated.
We can therefore make complete abstraction of the extensive quantity of a
phenomenon, and represent to ourselves in the mere sensation in a certain
momentum, a synthesis of homogeneous ascension from 0 up to the given empirical
consciousness, All sensations therefore as such are given only à posteriori,
but this property thereof, namely, that they have a degree, can be known à
priori. It is worthy of remark, that in respect to quantities in general, we
can cognize à priori only a single quality, namely, continuity; but in respect
to all quality (the real in phenomena), we cannot cognize à priori anything
more than the intensive quantity thereof, namely, that they have a degree. All
else is left to experience.

3. ANALOGIES OF EXPERIENCE.

The principle of these is: Experience is possible only through the
representation of a necessary connection of Perceptions.

PROOF.

Experience is an empirical cognition; that is to say, a cognition which
determines an object by means of perceptions. It is therefore a synthesis of
perceptions, a synthesis which is not itself contained in perception, but which
contains the synthetical unity of the manifold of perception in a
consciousness; and this unity constitutes the essential of our cognition of
objects of the senses, that is, of experience (not merely of intuition or
sensation). Now in experience our perceptions come together contingently, so
that no character of necessity in their connection appears, or can appear from
the perceptions themselves, because apprehension is only a placing together of
the manifold of empirical intuition, and no representation of a necessity in
the connected existence of the phenomena which apprehension brings together, is
to be discovered therein. But as experience is a cognition of objects by means
of perceptions, it follows that the relation of the existence of the existence
of the manifold must be represented in experience not as it is put together in
time, but as it is objectively in time. And as time itself cannot be perceived,
the determination of the existence of objects in time can only take place by
means of their connection in time in general, consequently only by means of à
priori connecting conceptions. Now as these conceptions always possess the
character of necessity, experience is possible only by means of a
representation of the necessary connection of perception.

The three modi of time are permanence, succession, and coexistence.
Accordingly, there are three rules of all relations of time in phenomena,
according to which the existence of every phenomenon is determined in respect
of the unity of all time, and these antecede all experience and render it
possible.

The general principle of all three analogies rests on the necessary unity of
apperception in relation to all possible empirical consciousness (perception)
at every time, consequently, as this unity lies à priori at the foundation of
all mental operations, the principle rests on the synthetical unity of all
phenomena according to their relation in time. For the original apperception
relates to our internal sense (the complex of all representations), and indeed
relates à priori to its form, that is to say, the relation of the manifold
empirical consciousness in time. Now this manifold must be combined in original
apperception according to relations of time—a necessity imposed by the à
priori transcendental unity of apperception, to which is subjected all that can
belong to my (i.e., my own) cognition, and therefore all that can become an
object for me. This synthetical and à priori determined unity in relation of
perceptions in time is therefore the rule: “All empirical determinations
of time must be subject to rules of the general determination of time”;
and the analogies of experience, of which we are now about to treat, must be
rules of this nature.

These principles have this peculiarity, that they do not concern phenomena, and
the synthesis of the empirical intuition thereof, but merely the existence of
phenomena and their relation to each other in regard to this existence. Now the
mode in which we apprehend a thing in a phenomenon can be determined à priori
in such a manner that the rule of its synthesis can give, that is to say, can
produce this à priori intuition in every empirical example. But the existence
of phenomena cannot be known à priori, and although we could arrive by this
path at a conclusion of the fact of some existence, we could not cognize that
existence determinately, that is to say, we should be incapable of anticipating
in what respect the empirical intuition of it would be distinguishable from
that of others.

The two principles above mentioned, which I called mathematical, in
consideration of the fact of their authorizing the application of mathematic
phenomena, relate to these phenomena only in regard to their possibility, and
instruct us how phenomena, as far as regards their intuition or the real in
their perception, can be generated according to the rules of a mathematical
synthesis. Consequently, numerical quantities, and with them the determination
of a phenomenon as a quantity, can be employed in the one case as well as in
the other. Thus, for example, out of 200,000 illuminations by the moon, I might
compose and give à priori, that is construct, the degree of our sensations of
the sun-light.^[30] We may therefore entitle these two
principles constitutive.

[30]
Kant’s meaning is: The two principles enunciated under the heads of
“Axioms of Intuition,” and “Anticipations of
Perception,” authorize the application to phenomena of determinations of
size and number, that is of mathematic. For example, I may compute the light of
the sun, and say that its quantity is a certain number of times greater than
that of the moon. In the same way, heat is measured by the comparison of its
different effects on water, &c., and on mercury in a thermometer.—Tr

The case is very different with those principles whose province it is to
subject the existence of phenomena to rules à priori. For as existence does not
admit of being constructed, it is clear that they must only concern the
relations of existence and be merely regulative principles. In this case,
therefore, neither axioms nor anticipations are to be thought of. Thus, if a
perception is given us, in a certain relation of time to other (although
undetermined) perceptions, we cannot then say à priori, what and how great (in
quantity) the other perception necessarily connected with the former is, but
only how it is connected, quoad its existence, in this given modus of time.
Analogies in philosophy mean something very different from that which they
represent in mathematics. In the latter they are formulae, which enounce the
equality of two relations of quantity, and are always constitutive, so that if
two terms of the proportion are given, the third is also given, that is, can be
constructed by the aid of these formulae. But in philosophy, analogy is not the
equality of two quantitative but of two qualitative relations. In this case,
from three given terms, I can give à priori and cognize the relation to a
fourth member, but not this fourth term itself, although I certainly possess a
rule to guide me in the search for this fourth term in experience, and a mark
to assist me in discovering it. An analogy of experience is therefore only a
rule according to which unity of experience must arise out of perceptions in
respect to objects (phenomena) not as a constitutive, but merely as a
regulative principle. The same holds good also of the postulates of empirical
thought in general, which relate to the synthesis of mere intuition (which
concerns the form of phenomena), the synthesis of perception (which concerns
the matter of phenomena), and the synthesis of experience (which concerns the
relation of these perceptions). For they are only regulative principles, and
clearly distinguishable from the mathematical, which are constitutive, not
indeed in regard to the certainty which both possess à priori, but in the mode
of evidence thereof, consequently also in the manner of demonstration.

But what has been observed of all synthetical propositions, and must be
particularly remarked in this place, is this, that these analogies possess
significance and validity, not as principles of the transcendental, but only as
principles of the empirical use of the understanding, and their truth can
therefore be proved only as such, and that consequently the phenomena must not
be subjoined directly under the categories, but only under their schemata. For
if the objects to which those principles must be applied were things in
themselves, it would be quite impossible to cognize aught concerning them
synthetically à priori. But they are nothing but phenomena; a complete
knowledge of which—a knowledge to which all principles à priori must at
last relate—is the only possible experience. It follows that these
principles can have nothing else for their aim than the conditions of the
empirical cognition in the unity of synthesis of phenomena. But this synthesis
is cogitated only in the schema of the pure conception of the understanding, of
whose unity, as that of a synthesis in general, the category contains the
function unrestricted by any sensuous condition. These principles will
therefore authorize us to connect phenomena according to an analogy, with the
logical and universal unity of conceptions, and consequently to employ the
categories in the principles themselves; but in the application of them to
experience, we shall use only their schemata, as the key to their proper
application, instead of the categories, or rather the latter as restricting
conditions, under the title of “formulae” of the former.

A. FIRST ANALOGY.

Principle of the Permanence of Substance.

In all changes of phenomena, substance is permanent, and the quantum thereof in
nature is neither increased nor diminished.

PROOF.

All phenomena exist in time, wherein alone as substratum, that is, as the
permanent form of the internal intuition, coexistence and succession can be
represented. Consequently time, in which all changes of phenomena must be
cogitated, remains and changes not, because it is that in which succession and
coexistence can be represented only as determinations thereof. Now, time in
itself cannot be an object of perception. It follows that in objects of
perception, that is, in phenomena, there must be found a substratum which
represents time in general, and in which all change or coexistence can be
perceived by means of the relation of phenomena to it. But the substratum of
all reality, that is, of all that pertains to the existence of things, is
substance; all that pertains to existence can be cogitated only as a
determination of substance. Consequently, the permanent, in relation to which
alone can all relations of time in phenomena be determined, is substance in the
world of phenomena, that is, the real in phenomena, that which, as the
substratum of all change, remains ever the same. Accordingly, as this cannot
change in existence, its quantity in nature can neither be increased nor
diminished.

Our apprehension of the manifold in a phenomenon is always successive, is
Consequently always changing. By it alone we could, therefore, never determine
whether this manifold, as an object of experience, is coexistent or successive,
unless it had for a foundation something fixed and permanent, of the existence
of which all succession and coexistence are nothing but so many modes (modi of
time). Only in the permanent, then, are relations of time possible (for
simultaneity and succession are the only relations in time); that is to say,
the permanent is the substratum of our empirical representation of time itself,
in which alone all determination of time is possible. Permanence is, in fact,
just another expression for time, as the abiding correlate of all existence of
phenomena, and of all change, and of all coexistence. For change does not
affect time itself, but only the phenomena in time (just as coexistence cannot
be regarded as a modus of time itself, seeing that in time no parts are
coexistent, but all successive). If we were to attribute succession to time
itself, we should be obliged to cogitate another time, in which this succession
would be possible. It is only by means of the permanent that existence in
different parts of the successive series of time receives a quantity, which we
entitle duration. For in mere succession, existence is perpetually vanishing
and recommencing, and therefore never has even the least quantity. Without the
permanent, then, no relation in time is possible. Now, time in itself is not an
object of perception; consequently the permanent in phenomena must be regarded
as the substratum of all determination of time, and consequently also as the
condition of the possibility of all synthetical unity of perceptions, that is,
of experience; and all existence and all change in time can only be regarded as
a mode in the existence of that which abides unchangeably. Therefore, in all
phenomena, the permanent is the object in itself, that is, the substance
(phenomenon); but all that changes or can change belongs only to the mode of
the existence of this substance or substances, consequently to its
determinations.

I find that in all ages not only the philosopher, but even the common
understanding, has preposited this permanence as a substratum of all change in
phenomena; indeed, I am compelled to believe that they will always accept this
as an indubitable fact. Only the philosopher expresses himself in a more
precise and definite manner, when he says: “In all changes in the world,
the substance remains, and the accidents alone are changeable.” But of
this decidedly synthetical proposition, I nowhere meet with even an attempt at
proof; nay, it very rarely has the good fortune to stand, as it deserves to do,
at the head of the pure and entirely à priori laws of nature. In truth, the
statement that substance is permanent, is tautological. For this very
permanence is the ground on which we apply the category of substance to the
phenomenon; and we should have been obliged to prove that in all phenomena
there is something permanent, of the existence of which the changeable is
nothing but a determination. But because a proof of this nature cannot be
dogmatical, that is, cannot be drawn from conceptions, inasmuch as it concerns
a synthetical proposition à priori, and as philosophers never reflected that
such propositions are valid only in relation to possible experience, and
therefore cannot be proved except by means of a deduction of the possibility of
experience, it is no wonder that while it has served as the foundation of all
experience (for we feel the need of it in empirical cognition), it has never
been supported by proof.

A philosopher was asked: “What is the weight of smoke?” He
answered: “Subtract from the weight of the burnt wood the weight of the
remaining ashes, and you will have the weight of the smoke.” Thus he
presumed it to be incontrovertible that even in fire the matter (substance)
does not perish, but that only the form of it undergoes a change. In like
manner was the saying: “From nothing comes nothing,” only another
inference from the principle or permanence, or rather of the ever-abiding
existence of the true subject in phenomena. For if that in the phenomenon which
we call substance is to be the proper substratum of all determination of time,
it follows that all existence in past as well as in future time, must be
determinable by means of it alone. Hence we are entitled to apply the term
substance to a phenomenon, only because we suppose its existence in all time, a
notion which the word permanence does not fully express, as it seems rather to
be referable to future time. However, the internal necessity perpetually to be,
is inseparably connected with the necessity always to have been, and so the
expression may stand as it is. “Gigni de nihilo nihil; in nihilum nil
posse reverti,”^[31] are two propositions which the ancients
never parted, and which people nowadays sometimes mistakenly disjoin, because
they imagine that the propositions apply to objects as things in themselves,
and that the former might be inimical to the dependence (even in respect of its
substance also) of the world upon a supreme cause. But this apprehension is
entirely needless, for the question in this case is only of phenomena in the
sphere of experience, the unity of which never could be possible, if we
admitted the possibility that new things (in respect of their substance) should
arise. For in that case, we should lose altogether that which alone can
represent the unity of time, to wit, the identity of the substratum, as that
through which alone all change possesses complete and thorough unity. This
permanence is, however, nothing but the manner in which we represent to
ourselves the existence of things in the phenomenal world.

[31]
Persius, Satirae, iii.83-84.

The determinations of a substance, which are only particular modes of its
existence, are called accidents. They are always real, because they concern the
existence of substance (negations are only determinations, which express the
non-existence of something in the substance). Now, if to this real in the
substance we ascribe a particular existence (for example, to motion as an
accident of matter), this existence is called inherence, in contradistinction
to the existence of substance, which we call subsistence. But hence arise many
misconceptions, and it would be a more accurate and just mode of expression to
designate the accident only as the mode in which the existence of a substance
is positively determined. Meanwhile, by reason of the conditions of the logical
exercise of our understanding, it is impossible to avoid separating, as it
were, that which in the existence of a substance is subject to change, whilst
the substance remains, and regarding it in relation to that which is properly
permanent and radical. On this account, this category of substance stands under
the title of relation, rather because it is the condition thereof than because
it contains in itself any relation.

Now, upon this notion of permanence rests the proper notion of the conception
change. Origin and extinction are not changes of that which originates or
becomes extinct. Change is but a mode of existence, which follows on another
mode of existence of the same object; hence all that changes is permanent, and
only the condition thereof changes. Now since this mutation affects only
determinations, which can have a beginning or an end, we may say, employing an
expression which seems somewhat paradoxical: “Only the permanent
(substance) is subject to change; the mutable suffers no change, but rather
alternation, that is, when certain determinations cease, others begin.”

Change, when, cannot be perceived by us except in substances, and origin or
extinction in an absolute sense, that does not concern merely a determination
of the permanent, cannot be a possible perception, for it is this very notion
of the permanent which renders possible the representation of a transition from
one state into another, and from non-being to being, which, consequently, can
be empirically cognized only as alternating determinations of that which is
permanent. Grant that a thing absolutely begins to be; we must then have a
point of time in which it was not. But how and by what can we fix and determine
this point of time, unless by that which already exists? For a void
time—preceding—is not an object of perception; but if we connect
this beginning with objects which existed previously, and which continue to
exist till the object in question in question begins to be, then the latter can
only be a determination of the former as the permanent. The same holds good of
the notion of extinction, for this presupposes the empirical representation of
a time, in which a phenomenon no longer exists.

Substances (in the world of phenomena) are the substratum of all determinations
of time. The beginning of some, and the ceasing to be of other substances,
would utterly do away with the only condition of the empirical unity of time;
and in that case phenomena would relate to two different times, in which, side
by side, existence would pass; which is absurd. For there is only one time in
which all different times must be placed, not as coexistent, but as successive.

Accordingly, permanence is a necessary condition under which alone phenomena,
as things or objects, are determinable in a possible experience. But as regards
the empirical criterion of this necessary permanence, and with it of the
substantiality of phenomena, we shall find sufficient opportunity to speak in
the sequel.

B. SECOND ANALOGY.

Principle of the Succession of Time According to the Law of Causality. All
changes take place according to the law of the connection of Cause and Effect.

PROOF.

(That all phenomena in the succession of time are only changes, that is, a
successive being and non-being of the determinations of substance, which is
permanent; consequently that a being of substance itself which follows on the
non-being thereof, or a non-being of substance which follows on the being
thereof, in other words, that the origin or extinction of substance itself, is
impossible—all this has been fully established in treating of the
foregoing principle. This principle might have been expressed as follows:
“All alteration (succession) of phenomena is merely change”; for
the changes of substance are not origin or extinction, because the conception
of change presupposes the same subject as existing with two opposite
determinations, and consequently as permanent. After this premonition, we shall
proceed to the proof.)

I perceive that phenomena succeed one another, that is to say, a state of
things exists at one time, the opposite of which existed in a former state. In
this case, then, I really connect together two perceptions in time. Now
connection is not an operation of mere sense and intuition, but is the product
of a synthetical faculty of imagination, which determines the internal sense in
respect of a relation of time. But imagination can connect these two states in
two ways, so that either the one or the other may antecede in time; for time in
itself cannot be an object of perception, and what in an object precedes and
what follows cannot be empirically determined in relation to it. I am only
conscious, then, that my imagination places one state before and the other
after; not that the one state antecedes the other in the object. In other
words, the objective relation of the successive phenomena remains quite
undetermined by means of mere perception. Now in order that this relation may
be cognized as determined, the relation between the two states must be so
cogitated that it is thereby determined as necessary, which of them must be
placed before and which after, and not conversely. But the conception which
carries with it a necessity of synthetical unity, can be none other than a pure
conception of the understanding which does not lie in mere perception; and in
this case it is the conception of “the relation of cause and
effect,” the former of which determines the latter in time, as its
necessary consequence, and not as something which might possibly antecede (or
which might in some cases not be perceived to follow). It follows that it is
only because we subject the sequence of phenomena, and consequently all change,
to the law of causality, that experience itself, that is, empirical cognition
of phenomena, becomes possible; and consequently, that phenomena themselves, as
objects of experience, are possible only by virtue of this law.

Our apprehension of the manifold of phenomena is always successive. The
representations of parts succeed one another. Whether they succeed one another
in the object also, is a second point for reflection, which was not contained
in the former. Now we may certainly give the name of object to everything, even
to every representation, so far as we are conscious thereof; but what this word
may mean in the case of phenomena, not merely in so far as they (as
representations) are objects, but only in so far as they indicate an object, is
a question requiring deeper consideration. In so far as they, regarded merely
as representations, are at the same time objects of consciousness, they are not
to be distinguished from apprehension, that is, reception into the synthesis of
imagination, and we must therefore say: “The manifold of phenomena is
always produced successively in the mind.” If phenomena were things in
themselves, no man would be able to conjecture from the succession of our
representations how this manifold is connected in the object; for we have to do
only with our representations. How things may be in themselves, without regard
to the representations through which they affect us, is utterly beyond the
sphere of our cognition. Now although phenomena are not things in themselves,
and are nevertheless the only thing given to us to be cognized, it is my duty
to show what sort of connection in time belongs to the manifold in phenomena
themselves, while the representation of this manifold in apprehension is always
successive. For example, the apprehension of the manifold in the phenomenon of
a house which stands before me, is successive. Now comes the question whether
the manifold of this house is in itself successive—which no one will be
at all willing to grant. But, so soon as I raise my conception of an object to
the transcendental signification thereof, I find that the house is not a thing
in itself, but only a phenomenon, that is, a representation, the transcendental
object of which remains utterly unknown. What then am I to understand by the
question: “How can the manifold be connected in the phenomenon
itself—not considered as a thing in itself, but merely as a
phenomenon?” Here that which lies in my successive apprehension is
regarded as representation, whilst the phenomenon which is given me,
notwithstanding that it is nothing more than a complex of these
representations, is regarded as the object thereof, with which my conception,
drawn from the representations of apprehension, must harmonize. It is very soon
seen that, as accordance of the cognition with its object constitutes truth,
the question now before us can only relate to the formal conditions of
empirical truth; and that the phenomenon, in opposition to the representations
of apprehension, can only be distinguished therefrom as the object of them, if
it is subject to a rule which distinguishes it from every other apprehension,
and which renders necessary a mode of connection of the manifold. That in the
phenomenon which contains the condition of this necessary rule of apprehension,
is the object.

Let us now proceed to our task. That something happens, that is to say, that
something or some state exists which before was not, cannot be empirically
perceived, unless a phenomenon precedes, which does not contain in itself this
state. For a reality which should follow upon a void time, in other words, a
beginning, which no state of things precedes, can just as little be apprehended
as the void time itself. Every apprehension of an event is therefore a
perception which follows upon another perception. But as this is the case with
all synthesis of apprehension, as I have shown above in the example of a house,
my apprehension of an event is not yet sufficiently distinguished from other
apprehensions. But I remark also that if in a phenomenon which contains an
occurrence, I call the antecedent state of my perception, A, and the following
state, B, the perception B can only follow A in apprehension, and the
perception A cannot follow B, but only precede it. For example, I see a ship
float down the stream of a river. My perception of its place lower down follows
upon my perception of its place higher up the course of the river, and it is
impossible that, in the apprehension of this phenomenon, the vessel should be
perceived first below and afterwards higher up the stream. Here, therefore, the
order in the sequence of perceptions in apprehension is determined; and by this
order apprehension is regulated. In the former example, my perceptions in the
apprehension of a house might begin at the roof and end at the foundation, or
vice versa; or I might apprehend the manifold in this empirical intuition, by
going from left to right, and from right to left. Accordingly, in the series of
these perceptions, there was no determined order, which necessitated my
beginning at a certain point, in order empirically to connect the manifold. But
this rule is always to be met with in the perception of that which happens, and
it makes the order of the successive perceptions in the apprehension of such a
phenomenon necessary.

I must, therefore, in the present case, deduce the subjective sequence of
apprehension from the objective sequence of phenomena, for otherwise the former
is quite undetermined, and one phenomenon is not distinguishable from another.
The former alone proves nothing as to the connection of the manifold in an
object, for it is quite arbitrary. The latter must consist in the order of the
manifold in a phenomenon, according to which order the apprehension of one
thing (that which happens) follows that of another thing (which precedes), in
conformity with a rule. In this way alone can I be authorized to say of the
phenomenon itself, and not merely of my own apprehension, that a certain order
or sequence is to be found therein. That is, in other words, I cannot arrange
my apprehension otherwise than in this order.

In conformity with this rule, then, it is necessary that in that which
antecedes an event there be found the condition of a rule, according to which
in this event follows always and necessarily; but I cannot reverse this and go
back from the event, and determine (by apprehension) that which antecedes it.
For no phenomenon goes back from the succeeding point of time to the preceding
point, although it does certainly relate to a preceding point of time; from a
given time, on the other hand, there is always a necessary progression to the
determined succeeding time. Therefore, because there certainly is something
that follows, I must of necessity connect it with something else, which
antecedes, and upon which it follows, in conformity with a rule, that is
necessarily, so that the event, as conditioned, affords certain indication of a
condition, and this condition determines the event.

Let us suppose that nothing precedes an event, upon which this event must
follow in conformity with a rule. All sequence of perception would then exist
only in apprehension, that is to say, would be merely subjective, and it could
not thereby be objectively determined what thing ought to precede, and what
ought to follow in perception. In such a case, we should have nothing but a
play of representations, which would possess no application to any object. That
is to say, it would not be possible through perception to distinguish one
phenomenon from another, as regards relations of time; because the succession
in the act of apprehension would always be of the same sort, and therefore
there would be nothing in the phenomenon to determine the succession, and to
render a certain sequence objectively necessary. And, in this case, I cannot
say that two states in a phenomenon follow one upon the other, but only that
one apprehension follows upon another. But this is merely subjective, and does
not determine an object, and consequently cannot be held to be cognition of an
object—not even in the phenomenal world.

Accordingly, when we know in experience that something happens, we always
presuppose that something precedes, whereupon it follows in conformity with a
rule. For otherwise I could not say of the object that it follows; because the
mere succession in my apprehension, if it be not determined by a rule in
relation to something preceding, does not authorize succession in the object.
Only, therefore, in reference to a rule, according to which phenomena are
determined in their sequence, that is, as they happen, by the preceding state,
can I make my subjective synthesis (of apprehension) objective, and it is only
under this presupposition that even the experience of an event is possible.

No doubt it appears as if this were in thorough contradiction to all the
notions which people have hitherto entertained in regard to the procedure of
the human understanding. According to these opinions, it is by means of the
perception and comparison of similar consequences following upon certain
antecedent phenomena that the understanding is led to the discovery of a rule,
according to which certain events always follow certain phenomena, and it is
only by this process that we attain to the conception of cause. Upon such a
basis, it is clear that this conception must be merely empirical, and the rule
which it furnishes us with—“Everything that happens must have a
cause”—would be just as contingent as experience itself. The
universality and necessity of the rule or law would be perfectly spurious
attributes of it. Indeed, it could not possess universal validity, inasmuch as
it would not in this case be à priori, but founded on deduction. But the same
is the case with this law as with other pure à priori representations (e.g.,
space and time), which we can draw in perfect clearness and completeness from
experience, only because we had already placed them therein, and by that means,
and by that alone, had rendered experience possible. Indeed, the logical
clearness of this representation of a rule, determining the series of events,
is possible only when we have made use thereof in experience. Nevertheless, the
recognition of this rule, as a condition of the synthetical unity of phenomena
in time, was the ground of experience itself and consequently preceded it à
priori.

It is now our duty to show by an example that we never, even in experience,
attribute to an object the notion of succession or effect (of an
event—that is, the happening of something that did not exist before), and
distinguish it from the subjective succession of apprehension, unless when a
rule lies at the foundation, which compels us to observe this order of
perception in preference to any other, and that, indeed, it is this necessity
which first renders possible the representation of a succession in the object.

We have representations within us, of which also we can be conscious. But,
however widely extended, however accurate and thoroughgoing this consciousness
may be, these representations are still nothing more than representations, that
is, internal determinations of the mind in this or that relation of time. Now
how happens it that to these representations we should set an object, or that,
in addition to their subjective reality, as modifications, we should still
further attribute to them a certain unknown objective reality? It is clear that
objective significancy cannot consist in a relation to another representation
(of that which we desire to term object), for in that case the question again
arises: “How does this other representation go out of itself, and obtain
objective significancy over and above the subjective, which is proper to it, as
a determination of a state of mind?” If we try to discover what sort of
new property the relation to an object gives to our subjective representations,
and what new importance they thereby receive, we shall find that this relation
has no other effect than that of rendering necessary the connection of our
representations in a certain manner, and of subjecting them to a rule; and that
conversely, it is only because a certain order is necessary in the relations of
time of our representations, that objective significancy is ascribed to them.

In the synthesis of phenomena, the manifold of our representations is always
successive. Now hereby is not represented an object, for by means of this
succession, which is common to all apprehension, no one thing is distinguished
from another. But so soon as I perceive or assume that in this succession there
is a relation to a state antecedent, from which the representation follows in
accordance with a rule, so soon do I represent something as an event, or as a
thing that happens; in other words, I cognize an object to which I must assign
a certain determinate position in time, which cannot be altered, because of the
preceding state in the object. When, therefore, I perceive that something
happens, there is contained in this representation, in the first place, the
fact, that something antecedes; because, it is only in relation to this that
the phenomenon obtains its proper relation of time, in other words, exists
after an antecedent time, in which it did not exist. But it can receive its
determined place in time only by the presupposition that something existed in
the foregoing state, upon which it follows inevitably and always, that is, in
conformity with a rule. From all this it is evident that, in the first place, I
cannot reverse the order of succession, and make that which happens precede
that upon which it follows; and that, in the second place, if the antecedent
state be posited, a certain determinate event inevitably and necessarily
follows. Hence it follows that there exists a certain order in our
representations, whereby the present gives a sure indication of some previously
existing state, as a correlate, though still undetermined, of the existing
event which is given—a correlate which itself relates to the event as its
consequence, conditions it, and connects it necessarily with itself in the
series of time.

If then it be admitted as a necessary law of sensibility, and consequently a
formal condition of all perception, that the preceding necessarily determines
the succeeding time (inasmuch as I cannot arrive at the succeeding except
through the preceding), it must likewise be an indispensable law of empirical
representation of the series of time that the phenomena of the past determine
all phenomena in the succeeding time, and that the latter, as events, cannot
take place, except in so far as the former determine their existence in time,
that is to say, establish it according to a rule. For it is of course only in
phenomena that we can empirically cognize this continuity in the connection of
times.

For all experience and for the possibility of experience, understanding is
indispensable, and the first step which it takes in this sphere is not to
render the representation of objects clear, but to render the representation of
an object in general, possible. It does this by applying the order of time to
phenomena, and their existence. In other words, it assigns to each phenomenon,
as a consequence, a place in relation to preceding phenomena, determined à
priori in time, without which it could not harmonize with time itself, which
determines a place à priori to all its parts. This determination of place
cannot be derived from the relation of phenomena to absolute time (for it is
not an object of perception); but, on the contrary, phenomena must reciprocally
determine the places in time of one another, and render these necessary in the
order of time. In other words, whatever follows or happens, must follow in
conformity with a universal rule upon that which was contained in the foregoing
state. Hence arises a series of phenomena, which, by means of the
understanding, produces and renders necessary exactly the same order and
continuous connection in the series of our possible perceptions, as is found à
priori in the form of internal intuition (time), in which all our perceptions
must have place.

That something happens, then, is a perception which belongs to a possible
experience, which becomes real only because I look upon the phenomenon as
determined in regard to its place in time, consequently as an object, which can
always be found by means of a rule in the connected series of my perceptions.
But this rule of the determination of a thing according to succession in time
is as follows: “In what precedes may be found the condition, under which
an event always (that is, necessarily) follows.” From all this it is
obvious that the principle of cause and effect is the principle of possible
experience, that is, of objective cognition of phenomena, in regard to their
relations in the succession of time.

The proof of this fundamental proposition rests entirely on the following
momenta of argument. To all empirical cognition belongs the synthesis of the
manifold by the imagination, a synthesis which is always successive, that is,
in which the representations therein always follow one another. But the order
of succession in imagination is not determined, and the series of successive
representations may be taken retrogressively as well as progressively. But if
this synthesis is a synthesis of apprehension (of the manifold of a given
phenomenon), then the order is determined in the object, or to speak more
accurately, there is therein an order of successive synthesis which determines
an object, and according to which something necessarily precedes, and when this
is posited, something else necessarily follows. If, then, my perception is to
contain the cognition of an event, that is, of something which really happens,
it must be an empirical judgement, wherein we think that the succession is
determined; that is, it presupposes another phenomenon, upon which this event
follows necessarily, or in conformity with a rule. If, on the contrary, when I
posited the antecedent, the event did not necessarily follow, I should be
obliged to consider it merely as a subjective play of my imagination, and if in
this I represented to myself anything as objective, I must look upon it as a
mere dream. Thus, the relation of phenomena (as possible perceptions),
according to which that which happens is, as to its existence, necessarily
determined in time by something which antecedes, in conformity with a
rule—in other words, the relation of cause and effect—is the
condition of the objective validity of our empirical judgements in regard to
the sequence of perceptions, consequently of their empirical truth, and
therefore of experience. The principle of the relation of causality in the
succession of phenomena is therefore valid for all objects of experience,
because it is itself the ground of the possibility of experience.

Here, however, a difficulty arises, which must be resolved. The principle of
the connection of causality among phenomena is limited in our formula to the
succession thereof, although in practice we find that the principle applies
also when the phenomena exist together in the same time, and that cause and
effect may be simultaneous. For example, there is heat in a room, which does
not exist in the open air. I look about for the cause, and find it to be the
fire, Now the fire as the cause is simultaneous with its effect, the heat of
the room. In this case, then, there is no succession as regards time, between
cause and effect, but they are simultaneous; and still the law holds good. The
greater part of operating causes in nature are simultaneous with their effects,
and the succession in time of the latter is produced only because the cause
cannot achieve the total of its effect in one moment. But at the moment when
the effect first arises, it is always simultaneous with the causality of its
cause, because, if the cause had but a moment before ceased to be, the effect
could not have arisen. Here it must be specially remembered that we must
consider the order of time and not the lapse thereof. The relation remains,
even though no time has elapsed. The time between the causality of the cause
and its immediate effect may entirely vanish, and the cause and effect be thus
simultaneous, but the relation of the one to the other remains always
determinable according to time. If, for example, I consider a leaden ball,
which lies upon a cushion and makes a hollow in it, as a cause, then it is
simultaneous with the effect. But I distinguish the two through the relation of
time of the dynamical connection of both. For if I lay the ball upon the
cushion, then the hollow follows upon the before smooth surface; but supposing
the cushion has, from some cause or another, a hollow, there does not thereupon
follow a leaden ball.

Thus, the law of succession of time is in all instances the only empirical
criterion of effect in relation to the causality of the antecedent cause. The
glass is the cause of the rising of the water above its horizontal surface,
although the two phenomena are contemporaneous. For, as soon as I draw some
water with the glass from a larger vessel, an effect follows thereupon, namely,
the change of the horizontal state which the water had in the large vessel into
a concave, which it assumes in the glass.

This conception of causality leads us to the conception of action; that of
action, to the conception of force; and through it, to the conception of
substance. As I do not wish this critical essay, the sole purpose of which is
to treat of the sources of our synthetical cognition à priori, to be crowded
with analyses which merely explain, but do not enlarge the sphere of our
conceptions, I reserve the detailed explanation of the above conceptions for a
future system of pure reason. Such an analysis, indeed, executed with great
particularity, may already be found in well-known works on this subject. But I
cannot at present refrain from making a few remarks on the empirical criterion
of a substance, in so far as it seems to be more evident and more easily
recognized through the conception of action than through that of the permanence
of a phenomenon.

Where action (consequently activity and force) exists, substance also must
exist, and in it alone must be sought the seat of that fruitful source of
phenomena. Very well. But if we are called upon to explain what we mean by
substance, and wish to avoid the vice of reasoning in a circle, the answer is
by no means so easy. How shall we conclude immediately from the action to the
permanence of that which acts, this being nevertheless an essential and
peculiar criterion of substance (phenomenon)? But after what has been said
above, the solution of this question becomes easy enough, although by the
common mode of procedure—merely analysing our conceptions—it would
be quite impossible. The conception of action indicates the relation of the
subject of causality to the effect. Now because all effect consists in that
which happens, therefore in the changeable, the last subject thereof is the
permanent, as the substratum of all that changes, that is, substance. For
according to the principle of causality, actions are always the first ground of
all change in phenomena and, consequently, cannot be a property of a subject
which itself changes, because if this were the case, other actions and another
subject would be necessary to determine this change. From all this it results
that action alone, as an empirical criterion, is a sufficient proof of the
presence of substantiality, without any necessity on my part of endeavouring to
discover the permanence of substance by a comparison. Besides, by this mode of
induction we could not attain to the completeness which the magnitude and
strict universality of the conception requires. For that the primary subject of
the causality of all arising and passing away, all origin and extinction,
cannot itself (in the sphere of phenomena) arise and pass away, is a sound and
safe conclusion, a conclusion which leads us to the conception of empirical
necessity and permanence in existence, and consequently to the conception of a
substance as phenomenon.

When something happens, the mere fact of the occurrence, without regard to that
which occurs, is an object requiring investigation. The transition from the
non-being of a state into the existence of it, supposing that this state
contains no quality which previously existed in the phenomenon, is a fact of
itself demanding inquiry. Such an event, as has been shown in No. A, does not
concern substance (for substance does not thus originate), but its condition or
state. It is therefore only change, and not origin from nothing. If this origin
be regarded as the effect of a foreign cause, it is termed creation, which
cannot be admitted as an event among phenomena, because the very possibility of
it would annihilate the unity of experience. If, however, I regard all things
not as phenomena, but as things in themselves and objects of understanding
alone, they, although substances, may be considered as dependent, in respect of
their existence, on a foreign cause. But this would require a very different
meaning in the words, a meaning which could not apply to phenomena as objects
of possible experience.

How a thing can be changed, how it is possible that upon one state existing in
one point of time, an opposite state should follow in another point of
time—of this we have not the smallest conception à priori. There is
requisite for this the knowledge of real powers, which can only be given
empirically; for example, knowledge of moving forces, or, in other words, of
certain successive phenomena (as movements) which indicate the presence of such
forces. But the form of every change, the condition under which alone it can
take place as the coming into existence of another state (be the content of the
change, that is, the state which is changed, what it may), and consequently the
succession of the states themselves can very well be considered à priori, in
relation to the law of causality and the conditions of time.^[32]

[32]
It must be remarked that I do not speak of the change of certain relations, but
of the change of the state. Thus, when a body moves in a uniform manner, it
does not change its state (of motion); but only when all motion increases or
decreases.

When a substance passes from one state, a, into another state, b, the point of
time in which the latter exists is different from, and subsequent to that in
which the former existed. In like manner, the second state, as reality (in the
phenomenon), differs from the first, in which the reality of the second did not
exist, as b from zero. That is to say, if the state, b, differs from the state,
a, only in respect to quantity, the change is a coming into existence of b -a,
which in the former state did not exist, and in relation to which that state is
= O.

Now the question arises how a thing passes from one state = a, into another
state = b. Between two moments there is always a certain time, and between two
states existing in these moments there is always a difference having a certain
quantity (for all parts of phenomena are in their turn quantities).
Consequently, every transition from one state into another is always effected
in a time contained between two moments, of which the first determines the
state which leaves, and the second determines the state into the thing passes.
The thing leaves, and the second determines the state into which the thing Both
moments, then, are limitations of the time of a change, consequently of the
intermediate state between both, and as such they belong to the total of the
change. Now every change has a cause, which evidences its causality in the
whole time during which the charge takes place. The cause, therefore, does not
produce the change all at once or in one moment, but in a time, so that, as the
time gradually increases from the commencing instant, a, to its completion at
b, in like manner also, the quantity of the reality (b – a) is generated
through the lesser degrees which are contained between the first and last. All
change is therefore possible only through a continuous action of the causality,
which, in so far as it is uniform, we call a momentum. The change does not
consist of these momenta, but is generated or produced by them as their effect.

Such is the law of the continuity of all change, the ground of which is that
neither time itself nor any phenomenon in time consists of parts which are the
smallest possible, but that, notwithstanding, the state of a thing passes in
the process of a change through all these parts, as elements, to its second
state. There is no smallest degree of reality in a phenomenon, just as there is
no smallest degree in the quantity of time; and so the new state of reality
grows up out of the former state, through all the infinite degrees thereof, the
differences of which one from another, taken all together, are less than the
difference between o and a.

It is not our business to inquire here into the utility of this principle in
the investigation of nature. But how such a proposition, which appears so
greatly to extend our knowledge of nature, is possible completely à priori, is
indeed a question which deserves investigation, although the first view seems
to demonstrate the truth and reality of the principle, and the question, how it
is possible, may be considered superfluous. For there are so many groundless
pretensions to the enlargement of our knowledge by pure reason that we must
take it as a general rule to be mistrustful of all such, and without a
thoroughgoing and radical deduction, to believe nothing of the sort even on the
clearest dogmatical evidence.

Every addition to our empirical knowledge, and every advance made in the
exercise of our perception, is nothing more than an extension of the
determination of the internal sense, that is to say, a progression in time, be
objects themselves what they may, phenomena, or pure intuitions. This
progression in time determines everything, and is itself determined by nothing
else. That is to say, the parts of the progression exist only in time, and by
means of the synthesis thereof, and are not given antecedently to it. For this
reason, every transition in perception to anything which follows upon another
in time, is a determination of time by means of the production of this
perception. And as this determination of time is, always and in all its parts,
a quantity, the perception produced is to be considered as a quantity which
proceeds through all its degrees—no one of which is the smallest
possible—from zero up to its determined degree. From this we perceive the
possibility of cognizing à priori a law of changes—a law, however, which
concerns their form merely. We merely anticipate our own apprehension, the
formal condition of which, inasmuch as it is itself to be found in the mind
antecedently to all given phenomena, must certainly be capable of being
cognized à priori.

Thus, as time contains the sensuous condition à priori of the possibility of a
continuous progression of that which exists to that which follows it, the
understanding, by virtue of the unity of apperception, contains the condition à
priori of the possibility of a continuous determination of the position in time
of all phenomena, and this by means of the series of causes and effects, the
former of which necessitate the sequence of the latter, and thereby render
universally and for all time, and by consequence, objectively, valid the
empirical cognition of the relations of time.

C. THIRD ANALOGY.

Principle of Coexistence, According to the Law of Reciprocity or Community.

All substances, in so far as they can be perceived in space at the same time,
exist in a state of complete reciprocity of action.

PROOF.

Things are coexistent, when in empirical intuition the perception of the one
can follow upon the perception of the other, and vice versa—which cannot
occur in the succession of phenomena, as we have shown in the explanation of
the second principle. Thus I can perceive the moon and then the earth, or
conversely, first the earth and then the moon; and for the reason that my
perceptions of these objects can reciprocally follow each other, I say, they
exist contemporaneously. Now coexistence is the existence of the manifold in
the same time. But time itself is not an object of perception; and therefore we
cannot conclude from the fact that things are placed in the same time, the
other fact, that the perception of these things can follow each other
reciprocally. The synthesis of the imagination in apprehension would only
present to us each of these perceptions as present in the subject when the
other is not present, and contrariwise; but would not show that the objects are
coexistent, that is to say, that, if the one exists, the other also exists in
the same time, and that this is necessarily so, in order that the perceptions
may be capable of following each other reciprocally. It follows that a
conception of the understanding or category of the reciprocal sequence of the
determinations of phenomena (existing, as they do, apart from each other, and
yet contemporaneously), is requisite to justify us in saying that the
reciprocal succession of perceptions has its foundation in the object, and to
enable us to represent coexistence as objective. But that relation of
substances in which the one contains determinations the ground of which is in
the other substance, is the relation of influence. And, when this influence is
reciprocal, it is the relation of community or reciprocity. Consequently the
coexistence of substances in space cannot be cognized in experience otherwise
than under the precondition of their reciprocal action. This is therefore the
condition of the possibility of things themselves as objects of experience.

Things are coexistent, in so far as they exist in one and the same time. But
how can we know that they exist in one and the same time? Only by observing
that the order in the synthesis of apprehension of the manifold is arbitrary
and a matter of indifference, that is to say, that it can proceed from A,
through B, C, D, to E, or contrariwise from E to A. For if they were successive
in time (and in the order, let us suppose, which begins with A), it is quite
impossible for the apprehension in perception to begin with E and go backwards
to A, inasmuch as A belongs to past time and, therefore, cannot be an object of
apprehension.

Let us assume that in a number of substances considered as phenomena each is
completely isolated, that is, that no one acts upon another. Then I say that
the coexistence of these cannot be an object of possible perception and that
the existence of one cannot, by any mode of empirical synthesis, lead us to the
existence of another. For we imagine them in this case to be separated by a
completely void space, and thus perception, which proceeds from the one to the
other in time, would indeed determine their existence by means of a following
perception, but would be quite unable to distinguish whether the one phenomenon
follows objectively upon the first, or is coexistent with it.

Besides the mere fact of existence, then, there must be something by means of
which A determines the position of B in time and, conversely, B the position of
A; because only under this condition can substances be empirically represented
as existing contemporaneously. Now that alone determines the position of
another thing in time which is the cause of it or of its determinations.
Consequently every substance (inasmuch as it can have succession predicated of
it only in respect of its determinations) must contain the causality of certain
determinations in another substance, and at the same time the effects of the
causality of the other in itself. That is to say, substances must stand
(mediately or immediately) in dynamical community with each other, if
coexistence is to be cognized in any possible experience. But, in regard to
objects of experience, that is absolutely necessary without which the
experience of these objects would itself be impossible. Consequently it is
absolutely necessary that all substances in the world of phenomena, in so far
as they are coexistent, stand in a relation of complete community of reciprocal
action to each other.

The word community has in our language^[33] two meanings, and
contains the two notions conveyed in the Latin communio and commercium. We
employ it in this place in the latter sense—that of a dynamical
community, without which even the community of place (communio spatii) could
not be empirically cognized. In our experiences it is easy to observe that it
is only the continuous influences in all parts of space that can conduct our
senses from one object to another; that the light which plays between our eyes
and the heavenly bodies produces a mediating community between them and us, and
thereby evidences their coexistence with us; that we cannot empirically change
our position (perceive this change), unless the existence of matter throughout
the whole of space rendered possible the perception of the positions we occupy;
and that this perception can prove the contemporaneous existence of these
places only through their reciprocal influence, and thereby also the
coexistence of even the most remote objects—although in this case the
proof is only mediate. Without community, every perception (of a phenomenon in
space) is separated from every other and isolated, and the chain of empirical
representations, that is, of experience, must, with the appearance of a new
object, begin entirely de novo, without the least connection with preceding
representations, and without standing towards these even in the relation of
time. My intention here is by no means to combat the notion of empty space; for
it may exist where our perceptions cannot exist, inasmuch as they cannot reach
thereto, and where, therefore, no empirical perception of coexistence takes
place. But in this case it is not an object of possible experience.

[33]
German

The following remarks may be useful in the way of explanation. In the mind, all
phenomena, as contents of a possible experience, must exist in community
(communio) of apperception or consciousness, and in so far as it is requisite
that objects be represented as coexistent and connected, in so far must they
reciprocally determine the position in time of each other and thereby
constitute a whole. If this subjective community is to rest upon an objective
basis, or to be applied to substances as phenomena, the perception of one
substance must render possible the perception of another, and conversely. For
otherwise succession, which is always found in perceptions as apprehensions,
would be predicated of external objects, and their representation of their
coexistence be thus impossible. But this is a reciprocal influence, that is to
say, a real community (commercium) of substances, without which therefore the
empirical relation of coexistence would be a notion beyond the reach of our
minds. By virtue of this commercium, phenomena, in so far as they are apart
from, and nevertheless in connection with each other, constitute a compositum
reale. Such composita are possible in many different ways. The three dynamical
relations then, from which all others spring, are those of inherence,
consequence, and composition.

These, then, are the three analogies of experience. They are nothing more than
principles of the determination of the existence of phenomena in time,
according to the three modi of this determination; to wit, the relation to time
itself as a quantity (the quantity of existence, that is, duration), the
relation in time as a series or succession, finally, the relation in time as
the complex of all existence (simultaneity). This unity of determination in
regard to time is thoroughly dynamical; that is to say, time is not considered
as that in which experience determines immediately to every existence its
position; for this is impossible, inasmuch as absolute time is not an object of
perception, by means of which phenomena can be connected with each other. On
the contrary, the rule of the understanding, through which alone the existence
of phenomena can receive synthetical unity as regards relations of time,
determines for every phenomenon its position in time, and consequently à
priori, and with validity for all and every time.

By nature, in the empirical sense of the word, we understand the totality of
phenomena connected, in respect of their existence, according to necessary
rules, that is, laws. There are therefore certain laws (which are moreover à
priori) which make nature possible; and all empirical laws can exist only by
means of experience, and by virtue of those primitive laws through which
experience itself becomes possible. The purpose of the analogies is therefore
to represent to us the unity of nature in the connection of all phenomena under
certain exponents, the only business of which is to express the relation of
time (in so far as it contains all existence in itself) to the unity of
apperception, which can exist in synthesis only according to rules. The
combined expression of all is this: “All phenomena exist in one nature,
and must so exist, inasmuch as without this à priori unity, no unity of
experience, and consequently no determination of objects in experience, is
possible.”

As regards the mode of proof which we have employed in treating of these
transcendental laws of nature, and the peculiar character of we must make one
remark, which will at the same time be important as a guide in every other
attempt to demonstrate the truth of intellectual and likewise synthetical
propositions à priori. Had we endeavoured to prove these analogies
dogmatically, that is, from conceptions; that is to say, had we employed this
method in attempting to show that everything which exists, exists only in that
which is permanent—that every thing or event presupposes the existence of
something in a preceding state, upon which it follows in conformity with a
rule—lastly, that in the manifold, which is coexistent, the states
coexist in connection with each other according to a rule, all our labour would
have been utterly in vain. For more conceptions of things, analyse them as we
may, cannot enable us to conclude from the existence of one object to the
existence of another. What other course was left for us to pursue? This only,
to demonstrate the possibility of experience as a cognition in which at last
all objects must be capable of being presented to us, if the representation of
them is to possess any objective reality. Now in this third, this mediating
term, the essential form of which consists in the synthetical unity of the
apperception of all phenomena, we found à priori conditions of the universal
and necessary determination as to time of all existences in the world of
phenomena, without which the empirical determination thereof as to time would
itself be impossible, and we also discovered rules of synthetical unity à
priori, by means of which we could anticipate experience. For want of this
method, and from the fancy that it was possible to discover a dogmatical proof
of the synthetical propositions which are requisite in the empirical employment
of the understanding, has it happened that a proof of the principle of
sufficient reason has been so often attempted, and always in vain. The other
two analogies nobody has ever thought of, although they have always been
silently employed by the mind,^[34] because the guiding thread furnished by
the categories was wanting, the guide which alone can enable us to discover
every hiatus, both in the system of conceptions and of principles.

[34]
The unity of the universe, in which all phenomena to be connected, is evidently
a mere consequence of the admitted principle of the community of all substances
which are coexistent. For were substances isolated, they could not as parts
constitute a whole, and were their connection (reciprocal action of the
manifold) not necessary from the very fact of coexistence, we could not
conclude from the fact of the latter as a merely ideal relation to the former
as a real one. We have, however, shown in its place that community is the
proper ground of the possibility of an empirical cognition of coexistence, and
that we may therefore properly reason from the latter to the former as its
condition.

4. THE POSTULATES OF EMPIRICAL THOUGHT.

1. That which agrees with the formal conditions (intuition and conception) of
experience, is possible.

2. That which coheres with the material conditions of experience (sensation),
is real.

3. That whose coherence with the real is determined according to universal
conditions of experience is (exists) necessary.

Explanation.

The categories of modality possess this peculiarity, that they do not in the
least determine the object, or enlarge the conception to which they are annexed
as predicates, but only express its relation to the faculty of cognition.
Though my conception of a thing is in itself complete, I am still entitled to
ask whether the object of it is merely possible, or whether it is also real,
or, if the latter, whether it is also necessary. But hereby the object itself
is not more definitely determined in thought, but the question is only in what
relation it, including all its determinations, stands to the understanding and
its employment in experience, to the empirical faculty of judgement, and to the
reason of its application to experience.

For this very reason, too, the categories of modality are nothing more than
explanations of the conceptions of possibility, reality, and necessity, as
employed in experience, and at the same time, restrictions of all the
categories to empirical use alone, not authorizing the transcendental
employment of them. For if they are to have something more than a merely
logical significance, and to be something more than a mere analytical
expression of the form of thought, and to have a relation to things and their
possibility, reality, or necessity, they must concern possible experience and
its synthetical unity, in which alone objects of cognition can be given.

The postulate of the possibility of things requires also, that the conception
of the things agree with the formal conditions of our experience in general.
But this, that is to say, the objective form of experience, contains all the
kinds of synthesis which are requisite for the cognition of objects. A
conception which contains a synthesis must be regarded as empty and, without
reference to an object, if its synthesis does not belong to
experience—either as borrowed from it, and in this case it is called an
empirical conception, or such as is the ground and à priori condition of
experience (its form), and in this case it is a pure conception, a conception
which nevertheless belongs to experience, inasmuch as its object can be found
in this alone. For where shall we find the criterion or character of the
possibility of an object which is cogitated by means of an à priori synthetical
conception, if not in the synthesis which constitutes the form of empirical
cognition of objects? That in such a conception no contradiction exists is
indeed a necessary logical condition, but very far from being sufficient to
establish the objective reality of the conception, that is, the possibility of
such an object as is thought in the conception. Thus, in the conception of a
figure which is contained within two straight lines, there is no contradiction,
for the conceptions of two straight lines and of their junction contain no
negation of a figure. The impossibility in such a case does not rest upon the
conception in itself, but upon the construction of it in space, that is to say,
upon the conditions of space and its determinations. But these have themselves
objective reality, that is, they apply to possible things, because they contain
à priori the form of experience in general.

And now we shall proceed to point out the extensive utility and influence of
this postulate of possibility. When I represent to myself a thing that is
permanent, so that everything in it which changes belongs merely to its state
or condition, from such a conception alone I never can cognize that such a
thing is possible. Or, if I represent to myself something which is so
constituted that, when it is posited, something else follows always and
infallibly, my thought contains no self-contradiction; but whether such a
property as causality is to be found in any possible thing, my thought alone
affords no means of judging. Finally, I can represent to myself different
things (substances) which are so constituted that the state or condition of one
causes a change in the state of the other, and reciprocally; but whether such a
relation is a property of things cannot be perceived from these conceptions,
which contain a merely arbitrary synthesis. Only from the fact, therefore, that
these conceptions express à priori the relations of perceptions in every
experience, do we know that they possess objective reality, that is,
transcendental truth; and that independent of experience, though not
independent of all relation to form of an experience in general and its
synthetical unity, in which alone objects can be empirically cognized.

But when we fashion to ourselves new conceptions of substances, forces, action,
and reaction, from the material presented to us by perception, without
following the example of experience in their connection, we create mere
chimeras, of the possibility of which we cannot discover any criterion, because
we have not taken experience for our instructress, though we have borrowed the
conceptions from her. Such fictitious conceptions derive their character of
possibility not, like the categories, à priori, as conceptions on which all
experience depends, but only, à posteriori, as conceptions given by means of
experience itself, and their possibility must either be cognized à posteriori
and empirically, or it cannot be cognized at all. A substance which is
permanently present in space, yet without filling it (like that tertium quid
between matter and the thinking subject which some have tried to introduce into
metaphysics), or a peculiar fundamental power of the mind of intuiting the
future by anticipation (instead of merely inferring from past and present
events), or, finally, a power of the mind to place itself in community of
thought with other men, however distant they may be—these are conceptions
the possibility of which has no ground to rest upon. For they are not based
upon experience and its known laws; and, without experience, they are a merely
arbitrary conjunction of thoughts, which, though containing no internal
contradiction, has no claim to objective reality, neither, consequently, to the
possibility of such an object as is thought in these conceptions. As far as
concerns reality, it is self-evident that we cannot cogitate such a possibility
in concreto without the aid of experience; because reality is concerned only
with sensation, as the matter of experience, and not with the form of thought,
with which we can no doubt indulge in shaping fancies.

But I pass by everything which derives its possibility from reality in
experience, and I purpose treating here merely of the possibility of things by
means of à priori conceptions. I maintain, then, that the possibility of things
is not derived from such conceptions per se, but only when considered as formal
and objective conditions of an experience in general.

It seems, indeed, as if the possibility of a triangle could be cognized from
the conception of it alone (which is certainly independent of experience); for
we can certainly give to the conception a corresponding object completely à
priori, that is to say, we can construct it. But as a triangle is only the form
of an object, it must remain a mere product of the imagination, and the
possibility of the existence of an object corresponding to it must remain
doubtful, unless we can discover some other ground, unless we know that the
figure can be cogitated under the conditions upon which all objects of
experience rest. Now, the facts that space is a formal condition à priori of
external experience, that the formative synthesis, by which we construct a
triangle in imagination, is the very same as that we employ in the apprehension
of a phenomenon for the purpose of making an empirical conception of it, are
what alone connect the notion of the possibility of such a thing, with the
conception of it. In the same manner, the possibility of continuous quantities,
indeed of quantities in general, for the conceptions of them are without
exception synthetical, is never evident from the conceptions in themselves, but
only when they are considered as the formal conditions of the determination of
objects in experience. And where, indeed, should we look for objects to
correspond to our conceptions, if not in experience, by which alone objects are
presented to us? It is, however, true that without antecedent experience we can
cognize and characterize the possibility of things, relatively to the formal
conditions, under which something is determined in experience as an object,
consequently, completely à priori. But still this is possible only in relation
to experience and within its limits.

The postulate concerning the cognition of the reality of things requires
perception, consequently conscious sensation, not indeed immediately, that is,
of the object itself, whose existence is to be cognized, but still that the
object have some connection with a real perception, in accordance with the
analogies of experience, which exhibit all kinds of real connection in
experience.

From the mere conception of a thing it is impossible to conclude its existence.
For, let the conception be ever so complete, and containing a statement of all
the determinations of the thing, the existence of it has nothing to do with all
this, but only with thew question whether such a thing is given, so that the
perception of it can in every case precede the conception. For the fact that
the conception of it precedes the perception, merely indicates the possibility
of its existence; it is perception which presents matter to the conception,
that is the sole criterion of reality. Prior to the perception of the thing,
however, and therefore comparatively à priori, we are able to cognize its
existence, provided it stands in connection with some perceptions according to
the principles of the empirical conjunction of these, that is, in conformity
with the analogies of perception. For, in this case, the existence of the
supposed thing is connected with our perception in a possible experience, and
we are able, with the guidance of these analogies, to reason in the series of
possible perceptions from a thing which we do really perceive to the thing we
do not perceive. Thus, we cognize the existence of a magnetic matter
penetrating all bodies from the perception of the attraction of the
steel-filings by the magnet, although the constitution of our organs renders an
immediate perception of this matter impossible for us. For, according to the
laws of sensibility and the connected context of our perceptions, we should in
an experience come also on an immediate empirical intuition of this matter, if
our senses were more acute—but this obtuseness has no influence upon and
cannot alter the form of possible experience in general. Our knowledge of the
existence of things reaches as far as our perceptions, and what may be inferred
from them according to empirical laws, extend. If we do not set out from
experience, or do not proceed according to the laws of the empirical connection
of phenomena, our pretensions to discover the existence of a thing which we do
not immediately perceive are vain. Idealism, however, brings forward powerful
objections to these rules for proving existence mediately. This is, therefore,
the proper place for its refutation.

REFUTATION OF IDEALISM.

Idealism—I mean material idealism—is the theory which declares the
existence of objects in space without us to be either () doubtful and
indemonstrable, or (2) false and impossible. The first is the problematical
idealism of Descartes, who admits the undoubted certainty of only one empirical
assertion (assertio), to wit, “I am.” The second is the dogmatical
idealism of Berkeley, who maintains that space, together with all the objects
of which it is the inseparable condition, is a thing which is in itself
impossible, and that consequently the objects in space are mere products of the
imagination. The dogmatical theory of idealism is unavoidable, if we regard
space as a property of things in themselves; for in that case it is, with all
to which it serves as condition, a nonentity. But the foundation for this kind
of idealism we have already destroyed in the transcendental æsthetic.
Problematical idealism, which makes no such assertion, but only alleges our
incapacity to prove the existence of anything besides ourselves by means of
immediate experience, is a theory rational and evidencing a thorough and
philosophical mode of thinking, for it observes the rule not to form a decisive
judgement before sufficient proof be shown. The desired proof must therefore
demonstrate that we have experience of external things, and not mere fancies.
For this purpose, we must prove, that our internal and, to Descartes,
indubitable experience is itself possible only under the previous assumption of
external experience.

THEOREM.

The simple but empirically determined consciousness of my own existence proves
the existence of external objects in space.

PROOF

I am conscious of my own existence as determined in time. All determination in
regard to time presupposes the existence of something permanent in perception.
But this permanent something cannot be something in me, for the very reason
that my existence in time is itself determined by this permanent something. It
follows that the perception of this permanent existence is possible only
through a thing without me and not through the mere representation of a thing
without me. Consequently, the determination of my existence in time is possible
only through the existence of real things external to me. Now, consciousness in
time is necessarily connected with the consciousness of the possibility of this
determination in time. Hence it follows that consciousness in time is
necessarily connected also with the existence of things without me, inasmuch as
the existence of these things is the condition of determination in time. That
is to say, the consciousness of my own existence is at the same time an
immediate consciousness of the existence of other things without me.

Remark I. The reader will observe, that in the foregoing proof the game which
idealism plays is retorted upon itself, and with more justice. It assumed that
the only immediate experience is internal and that from this we can only infer
the existence of external things. But, as always happens, when we reason from
given effects to determined causes, idealism has reasoned with too much haste
and uncertainty, for it is quite possible that the cause of our representations
may lie in ourselves, and that we ascribe it falsely to external things. But
our proof shows that external experience is properly immediate,^[35] that only by virtue of it—not,
indeed, the consciousness of our own existence, but certainly the determination
of our existence in time, that is, internal experience—is possible. It is
true, that the representation “I am,” which is the expression of
the consciousness which can accompany all my thoughts, is that which
immediately includes the existence of a subject. But in this representation we
cannot find any knowledge of the subject, and therefore also no empirical
knowledge, that is, experience. For experience contains, in addition to the
thought of something existing, intuition, and in this case it must be internal
intuition, that is, time, in relation to which the subject must be determined.
But the existence of external things is absolutely requisite for this purpose,
so that it follows that internal experience is itself possible only mediately
and through external experience.

[35]
The immediate consciousness of the existence of external things is, in the
preceding theorem, not presupposed, but proved, by the possibility of this
consciousness understood by us or not. The question as to the possibility of it
would stand thus: “Have we an internal sense, but no external sense, and
is our belief in external perception a mere delusion?” But it is evident
that, in order merely to fancy to ourselves anything as external, that is, to
present it to the sense in intuition we must already possess an external sense,
and must thereby distinguish immediately the mere receptivity of an external
intuition from the spontaneity which characterizes every act of imagination.
For merely to imagine also an external sense, would annihilate the faculty of
intuition itself which is to be determined by the imagination.

Remark II. Now with this view all empirical use of our faculty of cognition in
the determination of time is in perfect accordance. Its truth is supported by
the fact that it is possible to perceive a determination of time only by means
of a change in external relations (motion) to the permanent in space (for
example, we become aware of the sun’s motion by observing the changes of
his relation to the objects of this earth). But this is not all. We find that
we possess nothing permanent that can correspond and be submitted to the
conception of a substance as intuition, except matter. This idea of permanence
is not itself derived from external experience, but is an à priori necessary
condition of all determination of time, consequently also of the internal sense
in reference to our own existence, and that through the existence of external
things. In the representation “I,” the consciousness of myself is
not an intuition, but a merely intellectual representation produced by the
spontaneous activity of a thinking subject. It follows, that this
“i” has not any predicate of intuition, which, in its character of
permanence, could serve as correlate to the determination of time in the
internal sense—in the same way as impenetrability is the correlate of
matter as an empirical intuition.

Remark III. From the fact that the existence of external things is a necessary
condition of the possibility of a determined consciousness of ourselves, it
does not follow that every intuitive representation of external things involves
the existence of these things, for their representations may very well be the
mere products of the imagination (in dreams as well as in madness); though,
indeed, these are themselves created by the reproduction of previous external
perceptions, which, as has been shown, are possible only through the reality of
external objects. The sole aim of our remarks has, however, been to prove that
internal experience in general is possible only through external experience in
general. Whether this or that supposed experience be purely imaginary must be
discovered from its particular determinations and by comparing these with the
criteria of all real experience.

Finally, as regards the third postulate, it applies to material necessity in
existence, and not to merely formal and logical necessity in the connection of
conceptions. Now as we cannot cognize completely à priori the existence of any
object of sense, though we can do so comparatively à priori, that is,
relatively to some other previously given existence—a cognition, however,
which can only be of such an existence as must be contained in the complex of
experience, of which the previously given perception is a part—the
necessity of existence can never be cognized from conceptions, but always, on
the contrary, from its connection with that which is an object of perception.
But the only existence cognized, under the condition of other given phenomena,
as necessary, is the existence of effects from given causes in conformity with
the laws of causality. It is consequently not the necessity of the existence of
things (as substances), but the necessity of the state of things that we
cognize, and that not immediately, but by means of the existence of other
states given in perception, according to empirical laws of causality. Hence it
follows that the criterion of necessity is to be found only in the law of
possible experience—that everything which happens is determined à priori
in the phenomenon by its cause. Thus we cognize only the necessity of effects
in nature, the causes of which are given us. Moreover, the criterion of
necessity in existence possesses no application beyond the field of possible
experience, and even in this it is not valid of the existence of things as
substances, because these can never be considered as empirical effects, or as
something that happens and has a beginning. Necessity, therefore, regards only
the relations of phenomena according to the dynamical law of causality, and the
possibility grounded thereon, of reasoning from some given existence (of a
cause) à priori to another existence (of an effect). “Everything that
happens is hypothetically necessary,” is a principle which subjects the
changes that take place in the world to a law, that is, to a rule of necessary
existence, without which nature herself could not possibly exist. Hence the
proposition, “Nothing happens by blind chance (in mundo non datur
casus),” is an à priori law of nature. The case is the same with the
proposition, “Necessity in nature is not blind,” that is, it is
conditioned, consequently intelligible necessity (non datur fatum). Both laws
subject the play of change to “a nature of things (as phenomena),”
or, which is the same thing, to the unity of the understanding, and through the
understanding alone can changes belong to an experience, as the synthetical
unity of phenomena. Both belong to the class of dynamical principles. The
former is properly a consequence of the principle of causality—one of the
analogies of experience. The latter belongs to the principles of modality,
which to the determination of causality adds the conception of necessity, which
is itself, however, subject to a rule of the understanding. The principle of
continuity forbids any leap in the series of phenomena regarded as changes (in
mundo non datur saltus); and likewise, in the complex of all empirical
intuitions in space, any break or hiatus between two phenomena (non datur
hiatus)—for we can so express the principle, that experience can admit
nothing which proves the existence of a vacuum, or which even admits it as a
part of an empirical synthesis. For, as regards a vacuum or void, which we may
cogitate as out and beyond the field of possible experience (the world), such a
question cannot come before the tribunal of mere understanding, which decides
only upon questions that concern the employment of given phenomena for the
construction of empirical cognition. It is rather a problem for ideal reason,
which passes beyond the sphere of a possible experience and aims at forming a
judgement of that which surrounds and circumscribes it, and the proper place
for the consideration of it is the transcendental dialectic. These four
propositions, “In mundo non datur hiatus, non datur saltus, non datur
casus, non datur fatum,” as well as all principles of transcendental
origin, we could very easily exhibit in their proper order, that is, in
conformity with the order of the categories, and assign to each its proper
place. But the already practised reader will do this for himself, or discover
the clue to such an arrangement. But the combined result of all is simply this,
to admit into the empirical synthesis nothing which might cause a break in or
be foreign to the understanding and the continuous connection of all phenomena,
that is, the unity of the conceptions of the understanding. For in the
understanding alone is the unity of experience, in which all perceptions must
have their assigned place, possible.

Whether the field of possibility be greater than that of reality, and whether
the field of the latter be itself greater than that of necessity, are
interesting enough questions, and quite capable of synthetic solution,
questions, however, which come under the jurisdiction of reason alone. For they
are tantamount to asking whether all things as phenomena do without exception
belong to the complex and connected whole of a single experience, of which
every given perception is a part which therefore cannot be conjoined with any
other phenomena—or, whether my perceptions can belong to more than one
possible experience? The understanding gives to experience, according to the
subjective and formal conditions, of sensibility as well as of apperception,
the rules which alone make this experience possible. Other forms of intuition
besides those of space and time, other forms of understanding besides the
discursive forms of thought, or of cognition by means of conceptions, we can
neither imagine nor make intelligible to ourselves; and even if we could, they
would still not belong to experience, which is the only mode of cognition by
which objects are presented to us. Whether other perceptions besides those
which belong to the total of our possible experience, and consequently whether
some other sphere of matter exists, the understanding has no power to decide,
its proper occupation being with the synthesis of that which is given.
Moreover, the poverty of the usual arguments which go to prove the existence of
a vast sphere of possibility, of which all that is real (every object of
experience) is but a small part, is very remarkable. “All real is
possible”; from this follows naturally, according to the logical laws of
conversion, the particular proposition: “Some possible is real.”
Now this seems to be equivalent to: “Much is possible that is not
real.” No doubt it does seem as if we ought to consider the sum of the
possible to be greater than that of the real, from the fact that something must
be added to the former to constitute the latter. But this notion of adding to
the possible is absurd. For that which is not in the sum of the possible, and
consequently requires to be added to it, is manifestly impossible. In addition
to accordance with the formal conditions of experience, the understanding
requires a connection with some perception; but that which is connected with
this perception is real, even although it is not immediately perceived. But
that another series of phenomena, in complete coherence with that which is
given in perception, consequently more than one all-embracing experience is
possible, is an inference which cannot be concluded from the data given us by
experience, and still less without any data at all. That which is possible only
under conditions which are themselves merely possible, is not possible in any
respect. And yet we can find no more certain ground on which to base the
discussion of the question whether the sphere of possibility is wider than that
of experience.

I have merely mentioned these questions, that in treating of the conception of
the understanding, there might be no omission of anything that, in the common
opinion, belongs to them. In reality, however, the notion of absolute
possibility (possibility which is valid in every respect) is not a mere
conception of the understanding, which can be employed empirically, but belongs
to reason alone, which passes the bounds of all empirical use of the
understanding. We have, therefore, contented ourselves with a merely critical
remark, leaving the subject to be explained in the sequel.

Before concluding this fourth section, and at the same time the system of all
principles of the pure understanding, it seems proper to mention the reasons
which induced me to term the principles of modality postulates. This expression
I do not here use in the sense which some more recent philosophers, contrary to
its meaning with mathematicians, to whom the word properly belongs, attach to
it—that of a proposition, namely, immediately certain, requiring neither
deduction nor proof. For if, in the case of synthetical propositions, however
evident they may be, we accord to them without deduction, and merely on the
strength of their own pretensions, unqualified belief, all critique of the
understanding is entirely lost; and, as there is no want of bold pretensions,
which the common belief (though for the philosopher this is no credential) does
not reject, the understanding lies exposed to every delusion and conceit,
without the power of refusing its assent to those assertions, which, though
illegitimate, demand acceptance as veritable axioms. When, therefore, to the
conception of a thing an à priori determination is synthetically added, such a
proposition must obtain, if not a proof, at least a deduction of the legitimacy
of its assertion.

The principles of modality are, however, not objectively synthetical, for the
predicates of possibility, reality, and necessity do not in the least augment
the conception of that of which they are affirmed, inasmuch as they contribute
nothing to the representation of the object. But as they are, nevertheless,
always synthetical, they are so merely subjectively. That is to say, they have
a reflective power, and apply to the conception of a thing, of which, in other
respects, they affirm nothing, the faculty of cognition in which the conception
originates and has its seat. So that if the conception merely agree with the
formal conditions of experience, its object is called possible; if it is in
connection with perception, and determined thereby, the object is real; if it
is determined according to conceptions by means of the connection of
perceptions, the object is called necessary. The principles of modality
therefore predicate of a conception nothing more than the procedure of the
faculty of cognition which generated it. Now a postulate in mathematics is a
practical proposition which contains nothing but the synthesis by which we
present an object to ourselves, and produce the conception of it, for
example—“With a given line, to describe a circle upon a plane, from
a given point”; and such a proposition does not admit of proof, because
the procedure, which it requires, is exactly that by which alone it is possible
to generate the conception of such a figure. With the same right, accordingly,
can we postulate the principles of modality, because they do not augment^[36] the conception of a thing but merely
indicate the manner in which it is connected with the faculty of cognition.

[36]
When I think the reality of a thing, I do really think more than the
possibility, but not in the thing; for that can never contain more in reality
than was contained in its complete possibility. But while the notion of
possibility is merely the notion of a position of thing in relation to the
understanding (its empirical use), reality is the conjunction of the thing with
perception.

GENERAL REMARK ON THE SYSTEM OF PRINCIPLES.

It is very remarkable that we cannot perceive the possibility of a thing from
the category alone, but must always have an intuition, by which to make evident
the objective reality of the pure conception of the understanding. Take, for
example, the categories of relation. How (1) a thing can exist only as a
subject, and not as a mere determination of other things, that is, can be
substance; or how (2), because something exists, some other thing must exist,
consequently how a thing can be a cause; or how (3), when several things exist,
from the fact that one of these things exists, some consequence to the others
follows, and reciprocally, and in this way a community of substances can be
possible—are questions whose solution cannot be obtained from mere
conceptions. The very same is the case with the other categories; for example,
how a thing can be of the same sort with many others, that is, can be a
quantity, and so on. So long as we have not intuition we cannot know whether we
do really think an object by the categories, and where an object can anywhere
be found to cohere with them, and thus the truth is established, that the
categories are not in themselves cognitions, but mere forms of thought for the
construction of cognitions from given intuitions. For the same reason is it
true that from categories alone no synthetical proposition can be made. For
example: “In every existence there is substance,” that is,
something that can exist only as a subject and not as mere predicate; or,
“Everything is a quantity”—to construct propositions such as
these, we require something to enable us to go out beyond the given conception
and connect another with it. For the same reason the attempt to prove a
synthetical proposition by means of mere conceptions, for example:
“Everything that exists contingently has a cause,” has never
succeeded. We could never get further than proving that, without this relation
to conceptions, we could not conceive the existence of the contingent, that is,
could not à priori through the understanding cognize the existence of such a
thing; but it does not hence follow that this is also the condition of the
possibility of the thing itself that is said to be contingent. If, accordingly;
we look back to our proof of the principle of causality, we shall find that we
were able to prove it as valid only of objects of possible experience, and,
indeed, only as itself the principle of the possibility of experience,
Consequently of the cognition of an object given in empirical intuition, and
not from mere conceptions. That, however, the proposition: “Everything
that is contingent must have a cause,” is evident to every one merely
from conceptions, is not to be denied. But in this case the conception of the
contingent is cogitated as involving not the category of modality (as that the
non-existence of which can be conceived) but that of relation (as that which
can exist only as the consequence of something else), and so it is really an
identical proposition: “That which can exist only as a consequence, has a
cause.” In fact, when we have to give examples of contingent existence,
we always refer to changes, and not merely to the possibility of conceiving the
opposite.^[37] But change is an event, which, as such,
is possible only through a cause, and considered per se its non-existence is
therefore possible, and we become cognizant of its contingency from the fact
that it can exist only as the effect of a cause. Hence, if a thing is assumed
to be contingent, it is an analytical proposition to say, it has a cause.

[37]
We can easily conceive the non-existence of matter; but the ancients did not
thence infer its contingency. But even the alternation of the existence and
non-existence of a given state in a thing, in which all change consists, by no
means proves the contingency of that state—the ground of proof being the
reality of its opposite. For example, a body is in a state of rest after
motion, but we cannot infer the contingency of the motion from the fact that
the former is the opposite of the latter. For this opposite is merely a logical
and not a real opposite to the other. If we wish to demonstrate the contingency
of the motion, what we ought to prove is that, instead of the motion which took
place in the preceding point of time, it was possible for the body to have been
then in rest, not, that it is afterwards in rest; for in this case, both
opposites are perfectly consistent with each other.

But it is still more remarkable that, to understand the possibility of things
according to the categories and thus to demonstrate the objective reality of
the latter, we require not merely intuitions, but external intuitions. If, for
example, we take the pure conceptions of relation, we find that (1) for the
purpose of presenting to the conception of substance something permanent in
intuition corresponding thereto and thus of demonstrating the objective reality
of this conception, we require an intuition (of matter) in space, because space
alone is permanent and determines things as such, while time, and with it all
that is in the internal sense, is in a state of continual flow; (2) in order to
represent change as the intuition corresponding to the conception of causality,
we require the representation of motion as change in space; in fact, it is
through it alone that changes, the possibility of which no pure understanding
can perceive, are capable of being intuited. Change is the connection of
determinations contradictorily opposed to each other in the existence of one
and the same thing. Now, how it is possible that out of a given state one quite
opposite to it in the same thing should follow, reason without an example can
not only not conceive, but cannot even make intelligible without intuition; and
this intuition is the motion of a point in space; the existence of which in
different spaces (as a consequence of opposite determinations) alone makes the
intuition of change possible. For, in order to make even internal change
cognitable, we require to represent time, as the form of the internal sense,
figuratively by a line, and the internal change by the drawing of that line
(motion), and consequently are obliged to employ external intuition to be able
to represent the successive existence of ourselves in different states. The
proper ground of this fact is that all change to be perceived as change
presupposes something permanent in intuition, while in the internal sense no
permanent intuition is to be found. Lastly, the objective possibility of the
category of community cannot be conceived by mere reason, and consequently its
objective reality cannot be demonstrated without an intuition, and that
external in space. For how can we conceive the possibility of community, that
is, when several substances exist, that some effect on the existence of the one
follows from the existence of the other, and reciprocally, and therefore that,
because something exists in the latter, something else must exist in the
former, which could not be understood from its own existence alone? For this is
the very essence of community—which is inconceivable as a property of
things which are perfectly isolated. Hence, Leibnitz, in attributing to the
substances of the world—as cogitated by the understanding alone—a
community, required the mediating aid of a divinity; for, from their existence,
such a property seemed to him with justice inconceivable. But we can very
easily conceive the possibility of community (of substances as phenomena) if we
represent them to ourselves as in space, consequently in external intuition.
For external intuition contains in itself à priori formal external relations,
as the conditions of the possibility of the real relations of action and
reaction, and therefore of the possibility of community. With the same ease can
it be demonstrated, that the possibility of things as quantities, and
consequently the objective reality of the category of quantity, can be grounded
only in external intuition, and that by its means alone is the notion of
quantity appropriated by the internal sense. But I must avoid prolixity, and
leave the task of illustrating this by examples to the reader’s own
reflection.

The above remarks are of the greatest importance, not only for the confirmation
of our previous confutation of idealism, but still more when the subject of
self-cognition by mere internal consciousness and the determination of our own
nature without the aid of external empirical intuitions is under discussion,
for the indication of the grounds of the possibility of such a cognition.

The result of the whole of this part of the analytic of principles is,
therefore: “All principles of the pure understanding are nothing more
than à priori principles of the possibility of experience, and to experience
alone do all à priori synthetical propositions apply and relate”; indeed,
their possibility itself rests entirely on this relation.

Chapter III Of the Ground of the Division of all
Objects into Phenomena and Noumena

We have now not only traversed the region of the pure understanding and
carefully surveyed every part of it, but we have also measured it, and assigned
to everything therein its proper place. But this land is an island, and
enclosed by nature herself within unchangeable limits. It is the land of truth
(an attractive word), surrounded by a wide and stormy ocean, the region of
illusion, where many a fog-bank, many an iceberg, seems to the mariner, on his
voyage of discovery, a new country, and, while constantly deluding him with
vain hopes, engages him in dangerous adventures, from which he never can
desist, and which yet he never can bring to a termination. But before venturing
upon this sea, in order to explore it in its whole extent, and to arrive at a
certainty whether anything is to be discovered there, it will not be without
advantage if we cast our eyes upon the chart of the land that we are about to
leave, and to ask ourselves, firstly, whether we cannot rest perfectly
contented with what it contains, or whether we must not of necessity be
contented with it, if we can find nowhere else a solid foundation to build
upon; and, secondly, by what title we possess this land itself, and how we hold
it secure against all hostile claims? Although, in the course of our analytic,
we have already given sufficient answers to these questions, yet a summary
recapitulation of these solutions may be useful in strengthening our
conviction, by uniting in one point the momenta of the arguments.

We have seen that everything which the understanding draws from itself, without
borrowing from experience, it nevertheless possesses only for the behoof and
use of experience. The principles of the pure understanding, whether
constitutive à priori (as the mathematical principles), or merely regulative
(as the dynamical), contain nothing but the pure schema, as it were, of
possible experience. For experience possesses its unity from the synthetical
unity which the understanding, originally and from itself, imparts to the
synthesis of the imagination in relation to apperception, and in à priori
relation to and agreement with which phenomena, as data for a possible
cognition, must stand. But although these rules of the understanding are not
only à priori true, but the very source of all truth, that is, of the
accordance of our cognition with objects, and on this ground, that they contain
the basis of the possibility of experience, as the ensemble of all cognition,
it seems to us not enough to propound what is true—we desire also to be
told what we want to know. If, then, we learn nothing more by this critical
examination than what we should have practised in the merely empirical use of
the understanding, without any such subtle inquiry, the presumption is that the
advantage we reap from it is not worth the labour bestowed upon it. It may
certainly be answered that no rash curiosity is more prejudicial to the
enlargement of our knowledge than that which must know beforehand the utility
of this or that piece of information which we seek, before we have entered on
the needful investigations, and before one could form the least conception of
its utility, even though it were placed before our eyes. But there is one
advantage in such transcendental inquiries which can be made comprehensible to
the dullest and most reluctant learner—this, namely, that the
understanding which is occupied merely with empirical exercise, and does not
reflect on the sources of its own cognition, may exercise its functions very
well and very successfully, but is quite unable to do one thing, and that of
very great importance, to determine, namely, the bounds that limit its
employment, and to know what lies within or without its own sphere. This
purpose can be obtained only by such profound investigations as we have
instituted. But if it cannot distinguish whether certain questions lie within
its horizon or not, it can never be sure either as to its claims or
possessions, but must lay its account with many humiliating corrections, when
it transgresses, as it unavoidably will, the limits of its own territory, and
loses itself in fanciful opinions and blinding illusions.

That the understanding, therefore, cannot make of its à priori principles, or
even of its conceptions, other than an empirical use, is a proposition which
leads to the most important results. A transcendental use is made of a
conception in a fundamental proposition or principle, when it is referred to
things in general and considered as things in themselves; an empirical use,
when it is referred merely to phenomena, that is, to objects of a possible
experience. That the latter use of a conception is the only admissible one is
evident from the reasons following. For every conception are requisite,
firstly, the logical form of a conception (of thought) general; and, secondly,
the possibility of presenting to this an object to which it may apply. Failing
this latter, it has no sense, and utterly void of content, although it may
contain the logical function for constructing a conception from certain data.
Now, object cannot be given to a conception otherwise than by intuition, and,
even if a pure intuition antecedent to the object is à priori possible, this
pure intuition can itself obtain objective validity only from empirical
intuition, of which it is itself but the form. All conceptions, therefore, and
with them all principles, however high the degree of their à priori
possibility, relate to empirical intuitions, that is, to data towards a
possible experience. Without this they possess no objective validity, but are
mere play of imagination or of understanding with images or notions. Let us
take, for example, the conceptions of mathematics, and first in its pure
intuitions. “Space has three dimensions”—“Between two
points there can be only one straight line,” etc. Although all these
principles, and the representation of the object with which this science
occupies itself, are generated in the mind entirely à priori, they would
nevertheless have no significance if we were not always able to exhibit their
significance in and by means of phenomena (empirical objects). Hence it is
requisite that an abstract conception be made sensuous, that is, that an object
corresponding to it in intuition be forthcoming, otherwise the conception
remains, as we say, without sense, that is, without meaning. Mathematics
fulfils this requirement by the construction of the figure, which is a
phenomenon evident to the senses. The same science finds support and
significance in number; this in its turn finds it in the fingers, or in
counters, or in lines and points. The conception itself is always produced à
priori, together with the synthetical principles or formulas from such
conceptions; but the proper employment of them, and their application to
objects, can exist nowhere but in experience, the possibility of which, as
regards its form, they contain à priori.

That this is also the case with all of the categories and the principles based
upon them is evident from the fact that we cannot render intelligible the
possibility of an object corresponding to them without having recourse to the
conditions of sensibility, consequently, to the form of phenomena, to which, as
their only proper objects, their use must therefore be confined, inasmuch as,
if this condition is removed, all significance, that is, all relation to an
object, disappears, and no example can be found to make it comprehensible what
sort of things we ought to think under such conceptions.

The conception of quantity cannot be explained except by saying that it is the
determination of a thing whereby it can be cogitated how many times one is
placed in it. But this “how many times” is based upon successive
repetition, consequently upon time and the synthesis of the homogeneous
therein. Reality, in contradistinction to negation, can be explained only by
cogitating a time which is either filled therewith or is void. If I leave out
the notion of permanence (which is existence in all time), there remains in the
conception of substance nothing but the logical notion of subject, a notion of
which I endeavour to realize by representing to myself something that can exist
only as a subject. But not only am I perfectly ignorant of any conditions under
which this logical prerogative can belong to a thing, I can make nothing out of
the notion, and draw no inference from it, because no object to which to apply
the conception is determined, and we consequently do not know whether it has
any meaning at all. In like manner, if I leave out the notion of time, in which
something follows upon some other thing in conformity with a rule, I can find
nothing in the pure category, except that there is a something of such a sort
that from it a conclusion may be drawn as to the existence of some other thing.
But in this case it would not only be impossible to distinguish between a cause
and an effect, but, as this power to draw conclusions requires conditions of
which I am quite ignorant, the conception is not determined as to the mode in
which it ought to apply to an object. The so-called principle:
“Everything that is contingent has a cause,” comes with a gravity
and self-assumed authority that seems to require no support from without. But,
I ask, what is meant by contingent? The answer is that the non-existence of
which is possible. But I should like very well to know by what means this
possibility of non-existence is to be cognized, if we do not represent to
ourselves a succession in the series of phenomena, and in this succession an
existence which follows a non-existence, or conversely, consequently, change.
For to say, that the non-existence of a thing is not self-contradictory is a
lame appeal to a logical condition, which is no doubt a necessary condition of
the existence of the conception, but is far from being sufficient for the real
objective possibility of non-existence. I can annihilate in thought every
existing substance without self-contradiction, but I cannot infer from this
their objective contingency in existence, that is to say, the possibility of
their non-existence in itself. As regards the category of community, it may
easily be inferred that, as the pure categories of substance and causality are
incapable of a definition and explanation sufficient to determine their object
without the aid of intuition, the category of reciprocal causality in the
relation of substances to each other (commercium) is just as little susceptible
thereof. Possibility, existence, and necessity nobody has ever yet been able to
explain without being guilty of manifest tautology, when the definition has
been drawn entirely from the pure understanding. For the substitution of the
logical possibility of the conception—the condition of which is that it
be not self-contradictory, for the transcendental possibility of
things—the condition of which is that there be an object corresponding to
the conception, is a trick which can only deceive the inexperienced.^[38]

[38]
In one word, to none of these conceptions belongs a corresponding object, and
consequently their real possibility cannot be demonstrated, if we take away
sensuous intuition—the only intuition which we possess—and there
then remains nothing but the logical possibility, that is, the fact that the
conception or thought is possible—which, however, is not the question;
what we want to know being, whether it relates to an object and thus possesses
any meaning.

It follows incontestably, that the pure conceptions of the understanding are
incapable of transcendental, and must always be of empirical use alone, and
that the principles of the pure understanding relate only to the general
conditions of a possible experience, to objects of the senses, and never to
things in general, apart from the mode in which we intuite them.

Transcendental analytic has accordingly this important result, to wit, that the
understanding is competent effect nothing à priori, except the anticipation of
the form of a possible experience in general, and that, as that which is not
phenomenon cannot be an object of experience, it can never overstep the limits
of sensibility, within which alone objects are presented to us. Its principles
are merely principles of the exposition of phenomena, and the proud name of an
ontology, which professes to present synthetical cognitions à priori of things
in general in a systematic doctrine, must give place to the modest title of
analytic of the pure understanding.

Thought is the act of referring a given intuition to an object. If the mode of
this intuition is unknown to us, the object is merely transcendental, and the
conception of the understanding is employed only transcendentally, that is, to
produce unity in the thought of a manifold in general. Now a pure category, in
which all conditions of sensuous intuition—as the only intuition we
possess—are abstracted, does not determine an object, but merely
expresses the thought of an object in general, according to different modes.
Now, to employ a conception, the function of judgement is required, by which an
object is subsumed under the conception, consequently the at least formal
condition, under which something can be given in intuition. Failing this
condition of judgement (schema), subsumption is impossible; for there is in
such a case nothing given, which may be subsumed under the conception. The
merely transcendental use of the categories is therefore, in fact, no use at
all and has no determined, or even, as regards its form, determinable object.
Hence it follows that the pure category is incompetent to establish a
synthetical à priori principle, and that the principles of the pure
understanding are only of empirical and never of transcendental use, and that
beyond the sphere of possible experience no synthetical à priori principles are
possible.

It may be advisable, therefore, to express ourselves thus. The pure categories,
apart from the formal conditions of sensibility, have a merely transcendental
meaning, but are nevertheless not of transcendental use, because this is in
itself impossible, inasmuch as all the conditions of any employment or use of
them (in judgements) are absent, to wit, the formal conditions of the
subsumption of an object under these conceptions. As, therefore, in the
character of pure categories, they must be employed empirically, and cannot be
employed transcendentally, they are of no use at all, when separated from
sensibility, that is, they cannot be applied to an object. They are merely the
pure form of the employment of the understanding in respect of objects in
general and of thought, without its being at the same time possible to think or
to determine any object by their means. But there lurks at the foundation of
this subject an illusion which it is very difficult to avoid. The categories
are not based, as regards their origin, upon sensibility, like the forms of
intuition, space, and time; they seem, therefore, to be capable of an
application beyond the sphere of sensuous objects. But this is not the case.
They are nothing but mere forms of thought, which contain only the logical
faculty of uniting à priori in consciousness the manifold given in intuition.
Apart, then, from the only intuition possible for us, they have still less
meaning than the pure sensuous forms, space and time, for through them an
object is at least given, while a mode of connection of the manifold, when the
intuition which alone gives the manifold is wanting, has no meaning at all. At
the same time, when we designate certain objects as phenomena or sensuous
existences, thus distinguishing our mode of intuiting them from their own
nature as things in themselves, it is evident that by this very distinction we
as it were place the latter, considered in this their own nature, although we
do not so intuite them, in opposition to the former, or, on the other hand, we
do so place other possible things, which are not objects of our senses, but are
cogitated by the understanding alone, and call them intelligible existences
(noumena). Now the question arises whether the pure conceptions of our
understanding do possess significance in respect of these latter, and may
possibly be a mode of cognizing them.

But we are met at the very commencement with an ambiguity, which may easily
occasion great misapprehension. The understanding, when it terms an object in a
certain relation phenomenon, at the same time forms out of this relation a
representation or notion of an object in itself, and hence believes that it can
form also conceptions of such objects. Now as the understanding possesses no
other fundamental conceptions besides the categories, it takes for granted that
an object considered as a thing in itself must be capable of being thought by
means of these pure conceptions, and is thereby led to hold the perfectly
undetermined conception of an intelligible existence, a something out of the
sphere of our sensibility, for a determinate conception of an existence which
we can cognize in some way or other by means of the understanding.

If, by the term noumenon, we understand a thing so far as it is not an object
of our sensuous intuition, thus making abstraction of our mode of intuiting it,
this is a noumenon in the negative sense of the word. But if we understand by
it an object of a non-sensuous intuition, we in this case assume a peculiar
mode of intuition, an intellectual intuition, to wit, which does not, however,
belong to us, of the very possibility of which we have no notion—and this
is a noumenon in the positive sense.

The doctrine of sensibility is also the doctrine of noumena in the negative
sense, that is, of things which the understanding is obliged to cogitate apart
from any relation to our mode of intuition, consequently not as mere phenomena,
but as things in themselves. But the understanding at the same time comprehends
that it cannot employ its categories for the consideration of things in
themselves, because these possess significance only in relation to the unity of
intuitions in space and time, and that they are competent to determine this
unity by means of general à priori connecting conceptions only on account of
the pure ideality of space and time. Where this unity of time is not to be met
with, as is the case with noumena, the whole use, indeed the whole meaning of
the categories is entirely lost, for even the possibility of things to
correspond to the categories is in this case incomprehensible. On this point, I
need only refer the reader to what I have said at the commencement of the
General Remark appended to the foregoing chapter. Now, the possibility of a
thing can never be proved from the fact that the conception of it is not
self-contradictory, but only by means of an intuition corresponding to the
conception. If, therefore, we wish to apply the categories to objects which
cannot be regarded as phenomena, we must have an intuition different from the
sensuous, and in this case the objects would be a noumena in the positive sense
of the word. Now, as such an intuition, that is, an intellectual intuition, is
no part of our faculty of cognition, it is absolutely impossible for the
categories to possess any application beyond the limits of experience. It may
be true that there are intelligible existences to which our faculty of sensuous
intuition has no relation, and cannot be applied, but our conceptions of the
understanding, as mere forms of thought for our sensuous intuition, do not
extend to these. What, therefore, we call noumenon must be understood by us as
such in a negative sense.

If I take away from an empirical intuition all thought (by means of the
categories), there remains no cognition of any object; for by means of mere
intuition nothing is cogitated, and, from the existence of such or such an
affection of sensibility in me, it does not follow that this affection or
representation has any relation to an object without me. But if I take away all
intuition, there still remains the form of thought, that is, the mode of
determining an object for the manifold of a possible intuition. Thus the
categories do in some measure really extend further than sensuous intuition,
inasmuch as they think objects in general, without regard to the mode (of
sensibility) in which these objects are given. But they do not for this reason
apply to and determine a wider sphere of objects, because we cannot assume that
such can be given, without presupposing the possibility of another than the
sensuous mode of intuition, a supposition we are not justified in making.

I call a conception problematical which contains in itself no contradiction,
and which is connected with other cognitions as a limitation of given
conceptions, but whose objective reality cannot be cognized in any manner. The
conception of a noumenon, that is, of a thing which must be cogitated not as an
object of sense, but as a thing in itself (solely through the pure
understanding), is not self-contradictory, for we are not entitled to maintain
that sensibility is the only possible mode of intuition. Nay, further, this
conception is necessary to restrain sensuous intuition within the bounds of
phenomena, and thus to limit the objective validity of sensuous cognition; for
things in themselves, which lie beyond its province, are called noumena for the
very purpose of indicating that this cognition does not extend its application
to all that the understanding thinks. But, after all, the possibility of such
noumena is quite incomprehensible, and beyond the sphere of phenomena, all is
for us a mere void; that is to say, we possess an understanding whose province
does problematically extend beyond this sphere, but we do not possess an
intuition, indeed, not even the conception of a possible intuition, by means of
which objects beyond the region of sensibility could be given us, and in
reference to which the understanding might be employed assertorically. The
conception of a noumenon is therefore merely a limitative conception and
therefore only of negative use. But it is not an arbitrary or fictitious
notion, but is connected with the limitation of sensibility, without, however,
being capable of presenting us with any positive datum beyond this sphere.

The division of objects into phenomena and noumena, and of the world into a
mundus sensibilis and intelligibilis is therefore quite inadmissible in a
positive sense, although conceptions do certainly admit of such a division; for
the class of noumena have no determinate object corresponding to them, and
cannot therefore possess objective validity. If we abandon the senses, how can
it be made conceivable that the categories (which are the only conceptions that
could serve as conceptions for noumena) have any sense or meaning at all,
inasmuch as something more than the mere unity of thought, namely, a possible
intuition, is requisite for their application to an object? The conception of a
noumenon, considered as merely problematical, is, however, not only admissible,
but, as a limitative conception of sensibility, absolutely necessary. But, in
this case, a noumenon is not a particular intelligible object for our
understanding; on the contrary, the kind of understanding to which it could
belong is itself a problem, for we cannot form the most distant conception of
the possibility of an understanding which should cognize an object, not
discursively by means of categories, but intuitively in a non-sensuous
intuition. Our understanding attains in this way a sort of negative extension.
That is to say, it is not limited by, but rather limits, sensibility, by giving
the name of noumena to things, not considered as phenomena, but as things in
themselves. But it at the same time prescribes limits to itself, for it
confesses itself unable to cognize these by means of the categories, and hence
is compelled to cogitate them merely as an unknown something.

I find, however, in the writings of modern authors, an entirely different use
of the expressions, mundus sensibilis and intelligibilis, which quite departs
from the meaning of the ancients—an acceptation in which, indeed, there
is to be found no difficulty, but which at the same time depends on mere verbal
quibbling. According to this meaning, some have chosen to call the complex of
phenomena, in so far as it is intuited, mundus sensibilis, but in so far as the
connection thereof is cogitated according to general laws of thought, mundus
intelligibilis. Astronomy, in so far as we mean by the word the mere
observation of the starry heaven, may represent the former; a system of
astronomy, such as the Copernican or Newtonian, the latter. But such twisting
of words is a mere sophistical subterfuge, to avoid a difficult question, by
modifying its meaning to suit our own convenience. To be sure, understanding
and reason are employed in the cognition of phenomena; but the question is,
whether these can be applied when the object is not a phenomenon and in this
sense we regard it if it is cogitated as given to the understanding alone, and
not to the senses. The question therefore is whether, over and above the
empirical use of the understanding, a transcendental use is possible, which
applies to the noumenon as an object. This question we have answered in the
negative.

When therefore we say, the senses represent objects as they appear, the
understanding as they are, the latter statement must not be understood in a
transcendental, but only in an empirical signification, that is, as they must
be represented in the complete connection of phenomena, and not according to
what they may be, apart from their relation to possible experience,
consequently not as objects of the pure understanding. For this must ever
remain unknown to us. Nay, it is also quite unknown to us whether any such
transcendental or extraordinary cognition is possible under any circumstances,
at least, whether it is possible by means of our categories. Understanding and
sensibility, with us, can determine objects only in conjunction. If we separate
them, we have intuitions without conceptions, or conceptions without
intuitions; in both cases, representations, which we cannot apply to any
determinate object.

If, after all our inquiries and explanations, any one still hesitates to
abandon the mere transcendental use of the categories, let him attempt to
construct with them a synthetical proposition. It would, of course, be
unnecessary for this purpose to construct an analytical proposition, for that
does not extend the sphere of the understanding, but, being concerned only
about what is cogitated in the conception itself, it leaves it quite undecided
whether the conception has any relation to objects, or merely indicates the
unity of thought—complete abstraction being made of the modi in which an
object may be given: in such a proposition, it is sufficient for the
understanding to know what lies in the conception—to what it applies is
to it indifferent. The attempt must therefore be made with a synthetical and
so-called transcendental principle, for example: “Everything that exists,
exists as substance,” or, “Everything that is contingent exists as
an effect of some other thing, viz., of its cause.” Now I ask, whence can
the understanding draw these synthetical propositions, when the conceptions
contained therein do not relate to possible experience but to things in
themselves (noumena)? Where is to be found the third term, which is always
requisite PURE site in a synthetical proposition, which may connect in the same
proposition conceptions which have no logical (analytical) connection with each
other? The proposition never will be demonstrated, nay, more, the possibility
of any such pure assertion never can be shown, without making reference to the
empirical use of the understanding, and thus, ipso facto, completely renouncing
pure and non-sensuous judgement. Thus the conception of pure and merely
intelligible objects is completely void of all principles of its application,
because we cannot imagine any mode in which they might be given, and the
problematical thought which leaves a place open for them serves only, like a
void space, to limit the use of empirical principles, without containing at the
same time any other object of cognition beyond their sphere.

APPENDIX

Of the Equivocal Nature or Amphiboly of the Conceptions of Reflection from the
Confusion of the Transcendental with the Empirical use of the Understanding.

Reflection (reflexio) is not occupied about objects themselves, for the purpose
of directly obtaining conceptions of them, but is that state of the mind in
which we set ourselves to discover the subjective conditions under which we
obtain conceptions. It is the consciousness of the relation of given
representations to the different sources or faculties of cognition, by which
alone their relation to each other can be rightly determined. The first
question which occurs in considering our representations is to what faculty of
cognition do they belong? To the understanding or to the senses? Many
judgements are admitted to be true from mere habit or inclination; but, because
reflection neither precedes nor follows, it is held to be a judgement that has
its origin in the understanding. All judgements do not require examination,
that is, investigation into the grounds of their truth. For, when they are
immediately certain (for example: “Between two points there can be only
one straight line”), no better or less mediate test of their truth can be
found than that which they themselves contain and express. But all judgement,
nay, all comparisons require reflection, that is, a distinction of the faculty
of cognition to which the given conceptions belong. The act whereby I compare
my representations with the faculty of cognition which originates them, and
whereby I distinguish whether they are compared with each other as belonging to
the pure understanding or to sensuous intuition, I term transcendental
reflection. Now, the relations in which conceptions can stand to each other are
those of identity and difference, agreement and opposition, of the internal and
external, finally, of the determinable and the determining (matter and form).
The proper determination of these relations rests on the question, to what
faculty of cognition they subjectively belong, whether to sensibility or
understanding? For, on the manner in which we solve this question depends the
manner in which we must cogitate these relations.

Before constructing any objective judgement, we compare the conceptions that
are to be placed in the judgement, and observe whether there exists identity
(of many representations in one conception), if a general judgement is to be
constructed, or difference, if a particular; whether there is agreement when
affirmative; and opposition when negative judgements are to be constructed, and
so on. For this reason we ought to call these conceptions, conceptions of
comparison (conceptus comparationis). But as, when the question is not as to
the logical form, but as to the content of conceptions, that is to say, whether
the things themselves are identical or different, in agreement or opposition,
and so on, the things can have a twofold relation to our faculty of cognition,
to wit, a relation either to sensibility or to the understanding, and as on
this relation depends their relation to each other, transcendental reflection,
that is, the relation of given representations to one or the other faculty of
cognition, can alone determine this latter relation. Thus we shall not be able
to discover whether the things are identical or different, in agreement or
opposition, etc., from the mere conception of the things by means of comparison
(comparatio), but only by distinguishing the mode of cognition to which they
belong, in other words, by means of transcendental reflection. We may,
therefore, with justice say, that logical reflection is mere comparison, for in
it no account is taken of the faculty of cognition to which the given
conceptions belong, and they are consequently, as far as regards their origin,
to be treated as homogeneous; while transcendental reflection (which applies to
the objects themselves) contains the ground of the possibility of objective
comparison of representations with each other, and is therefore very different
from the former, because the faculties of cognition to which they belong are
not even the same. Transcendental reflection is a duty which no one can neglect
who wishes to establish an à priori judgement upon things. We shall now proceed
to fulfil this duty, and thereby throw not a little light on the question as to
the determination of the proper business of the understanding.

1. Identity and Difference. When an object is presented to us several times,
but always with the same internal determinations (qualitas et quantitas), it,
if an object of pure understanding, is always the same, not several things, but
only one thing (numerica identitas); but if a phenomenon, we do not concern
ourselves with comparing the conception of the thing with the conception of
some other, but, although they may be in this respect perfectly the same, the
difference of place at the same time is a sufficient ground for asserting the
numerical difference of these objects (of sense). Thus, in the case of two
drops of water, we may make complete abstraction of all internal difference
(quality and quantity), and, the fact that they are intuited at the same time
in different places, is sufficient to justify us in holding them to be
numerically different. Leibnitz regarded phenomena as things in themselves,
consequently as intelligibilia, that is, objects of pure understanding
(although, on account of the confused nature of their representations, he gave
them the name of phenomena), and in this case his principle of the
indiscernible (principium identatis indiscernibilium) is not to be impugned.
But, as phenomena are objects of sensibility, and, as the understanding, in
respect of them, must be employed empirically and not purely or
transcendentally, plurality and numerical difference are given by space itself
as the condition of external phenomena. For one part of space, although it may
be perfectly similar and equal to another part, is still without it, and for
this reason alone is different from the latter, which is added to it in order
to make up a greater space. It follows that this must hold good of all things
that are in the different parts of space at the same time, however similar and
equal one may be to another.

2. Agreement and Opposition. When reality is represented by the pure
understanding (realitas noumenon), opposition between realities is
incogitable—such a relation, that is, that when these realities are
connected in one subject, they annihilate the effects of each other and may be
represented in the formula 3 -3 = 0. On the other hand, the real in a
phenomenon (realitas phaenomenon) may very well be in mutual opposition, and,
when united in the same subject, the one may completely or in part annihilate
the effect or consequence of the other; as in the case of two moving forces in
the same straight line drawing or impelling a point in opposite directions, or
in the case of a pleasure counterbalancing a certain amount of pain.

3. The Internal and External. In an object of the pure understanding, only that
is internal which has no relation (as regards its existence) to anything
different from itself. On the other hand, the internal determinations of a
substantia phaenomenon in space are nothing but relations, and it is itself
nothing more than a complex of mere relations. Substance in space we are
cognizant of only through forces operative in it, either drawing others towards
itself (attraction), or preventing others from forcing into itself (repulsion
and impenetrability). We know no other properties that make up the conception
of substance phenomenal in space, and which we term matter. On the other hand,
as an object of the pure understanding, every substance must have internal
determination and forces. But what other internal attributes of such an object
can I think than those which my internal sense presents to me? That, to wit,
which in either itself thought, or something analogous to it. Hence Leibnitz,
who looked upon things as noumena, after denying them everything like external
relation, and therefore also composition or combination, declared that all
substances, even the component parts of matter, were simple substances with
powers of representation, in one word, monads.

4. Matter and Form. These two conceptions lie at the foundation of all other
reflection, so inseparably are they connected with every mode of exercising the
understanding. The former denotes the determinable in general, the second its
determination, both in a transcendental sense, abstraction being made of every
difference in that which is given, and of the mode in which it is determined.
Logicians formerly termed the universal, matter, the specific difference of
this or that part of the universal, form. In a judgement one may call the given
conceptions logical matter (for the judgement), the relation of these to each
other (by means of the copula), the form of the judgement. In an object, the
composite parts thereof (essentialia) are the matter; the mode in which they
are connected in the object, the form. In respect to things in general,
unlimited reality was regarded as the matter of all possibility, the limitation
thereof (negation) as the form, by which one thing is distinguished from
another according to transcendental conceptions. The understanding demands that
something be given (at least in the conception), in order to be able to
determine it in a certain manner. Hence, in a conception of the pure
understanding, the matter precedes the form, and for this reason Leibnitz first
assumed the existence of things (monads) and of an internal power of
representation in them, in order to found upon this their external relation and
the community their state (that is, of their representations). Hence, with him,
space and time were possible—the former through the relation of
substances, the latter through the connection of their determinations with each
other, as causes and effects. And so would it really be, if the pure
understanding were capable of an immediate application to objects, and if space
and time were determinations of things in themselves. But being merely sensuous
intuitions, in which we determine all objects solely as phenomena, the form of
intuition (as a subjective property of sensibility) must antecede all matter
(sensations), consequently space and time must antecede all phenomena and all
data of experience, and rather make experience itself possible. But the
intellectual philosopher could not endure that the form should precede the
things themselves and determine their possibility; an objection perfectly
correct, if we assume that we intuite things as they are, although with
confused representation. But as sensuous intuition is a peculiar subjective
condition, which is à priori at the foundation of all perception, and the form
of which is primitive, the form must be given per se, and so far from matter
(or the things themselves which appear) lying at the foundation of experience
(as we must conclude, if we judge by mere conceptions), the very possibility of
itself presupposes, on the contrary, a given formal intuition (space and time).

REMARK ON THE AMPHIBOLY OF THE CONCEPTIONS OF REFLECTION.

Let me be allowed to term the position which we assign to a conception either
in the sensibility or in the pure understanding, the transcendental place. In
this manner, the appointment of the position which must be taken by each
conception according to the difference in its use, and the directions for
determining this place to all conceptions according to rules, would be a
transcendental topic, a doctrine which would thoroughly shield us from the
surreptitious devices of the pure understanding and the delusions which thence
arise, as it would always distinguish to what faculty of cognition each
conception properly belonged. Every conception, every title, under which many
cognitions rank together, may be called a logical place. Upon this is based the
logical topic of Aristotle, of which teachers and rhetoricians could avail
themselves, in order, under certain titles of thought, to observe what would
best suit the matter they had to treat, and thus enable themselves to quibble
and talk with fluency and an appearance of profundity.

Transcendental topic, on the contrary, contains nothing more than the
above-mentioned four titles of all comparison and distinction, which differ
from categories in this respect, that they do not represent the object
according to that which constitutes its conception (quantity, reality), but set
forth merely the comparison of representations, which precedes our conceptions
of things. But this comparison requires a previous reflection, that is, a
determination of the place to which the representations of the things which are
compared belong, whether, to wit, they are cogitated by the pure understanding,
or given by sensibility.

Conceptions may be logically compared without the trouble of inquiring to what
faculty their objects belong, whether as noumena, to the understanding, or as
phenomena, to sensibility. If, however, we wish to employ these conceptions in
respect of objects, previous transcendental reflection is necessary. Without
this reflection I should make a very unsafe use of these conceptions, and
construct pretended synthetical propositions which critical reason cannot
acknowledge and which are based solely upon a transcendental amphiboly, that
is, upon a substitution of an object of pure understanding for a phenomenon.

For want of this doctrine of transcendental topic, and consequently deceived by
the amphiboly of the conceptions of reflection, the celebrated Leibnitz
constructed an intellectual system of the world, or rather, believed himself
competent to cognize the internal nature of things, by comparing all objects
merely with the understanding and the abstract formal conceptions of thought.
Our table of the conceptions of reflection gives us the unexpected advantage of
being able to exhibit the distinctive peculiarities of his system in all its
parts, and at the same time of exposing the fundamental principle of this
peculiar mode of thought, which rested upon naught but a misconception. He
compared all things with each other merely by means of conceptions, and
naturally found no other differences than those by which the understanding
distinguishes its pure conceptions one from another. The conditions of sensuous
intuition, which contain in themselves their own means of distinction, he did
not look upon as primitive, because sensibility was to him but a confused mode
of representation and not any particular source of representations. A
phenomenon was for him the representation of the thing in itself, although
distinguished from cognition by the understanding only in respect of the
logical form—the former with its usual want of analysis containing,
according to him, a certain mixture of collateral representations in its
conception of a thing, which it is the duty of the understanding to separate
and distinguish. In one word, Leibnitz intellectualized phenomena, just as
Locke, in his system of noogony (if I may be allowed to make use of such
expressions), sensualized the conceptions of the understanding, that is to say,
declared them to be nothing more than empirical or abstract conceptions of
reflection. Instead of seeking in the understanding and sensibility two
different sources of representations, which, however, can present us with
objective judgements of things only in conjunction, each of these great men
recognized but one of these faculties, which, in their opinion, applied
immediately to things in themselves, the other having no duty but that of
confusing or arranging the representations of the former.

Accordingly, the objects of sense were compared by Leibnitz as things in
general merely in the understanding.

1st. He compares them in regard to their identity or difference—as judged
by the understanding. As, therefore, he considered merely the conceptions of
objects, and not their position in intuition, in which alone objects can be
given, and left quite out of sight the transcendental locale of these
conceptions—whether, that is, their object ought to be classed among
phenomena, or among things in themselves, it was to be expected that he should
extend the application of the principle of indiscernibles, which is valid
solely of conceptions of things in general, to objects of sense (mundus
phaenomenon), and that he should believe that he had thereby contributed in no
small degree to extend our knowledge of nature. In truth, if I cognize in all
its inner determinations a drop of water as a thing in itself, I cannot look
upon one drop as different from another, if the conception of the one is
completely identical with that of the other. But if it is a phenomenon in
space, it has a place not merely in the understanding (among conceptions), but
also in sensuous external intuition (in space), and in this case, the physical
locale is a matter of indifference in regard to the internal determinations of
things, and one place, B, may contain a thing which is perfectly similar and
equal to another in a place, A, just as well as if the two things were in every
respect different from each other. Difference of place without any other
conditions, makes the plurality and distinction of objects as phenomena, not
only possible in itself, but even necessary. Consequently, the above so-called
law is not a law of nature. It is merely an analytical rule for the comparison
of things by means of mere conceptions.

2nd. The principle: “Realities (as simple affirmations) never logically
contradict each other,” is a proposition perfectly true respecting the
relation of conceptions, but, whether as regards nature, or things in
themselves (of which we have not the slightest conception), is without any the
least meaning. For real opposition, in which A -B is = 0, exists everywhere, an
opposition, that is, in which one reality united with another in the same
subject annihilates the effects of the other—a fact which is constantly
brought before our eyes by the different antagonistic actions and operations in
nature, which, nevertheless, as depending on real forces, must be called
realitates phaenomena. General mechanics can even present us with the empirical
condition of this opposition in an à priori rule, as it directs its attention
to the opposition in the direction of forces—a condition of which the
transcendental conception of reality can tell us nothing. Although M. Leibnitz
did not announce this proposition with precisely the pomp of a new principle,
he yet employed it for the establishment of new propositions, and his followers
introduced it into their Leibnitzio-Wolfian system of philosophy. According to
this principle, for example, all evils are but consequences of the limited
nature of created beings, that is, negations, because these are the only
opposite of reality. (In the mere conception of a thing in general this is
really the case, but not in things as phenomena.) In like manner, the upholders
of this system deem it not only possible, but natural also, to connect and
unite all reality in one being, because they acknowledge no other sort of
opposition than that of contradiction (by which the conception itself of a
thing is annihilated), and find themselves unable to conceive an opposition of
reciprocal destruction, so to speak, in which one real cause destroys the
effect of another, and the conditions of whose representation we meet with only
in sensibility.

3rd. The Leibnitzian monadology has really no better foundation than on this
philosopher’s mode of falsely representing the difference of the internal
and external solely in relation to the understanding. Substances, in general,
must have something inward, which is therefore free from external relations,
consequently from that of composition also. The simple—that which can be
represented by a unit—is therefore the foundation of that which is
internal in things in themselves. The internal state of substances cannot
therefore consist in place, shape, contact, or motion, determinations which are
all external relations, and we can ascribe to them no other than that whereby
we internally determine our faculty of sense itself, that is to say, the state
of representation. Thus, then, were constructed the monads, which were to form
the elements of the universe, the active force of which consists in
representation, the effects of this force being thus entirely confined to
themselves.

For the same reason, his view of the possible community of substances could not
represent it but as a predetermined harmony, and by no means as a physical
influence. For inasmuch as everything is occupied only internally, that is,
with its own representations, the state of the representations of one substance
could not stand in active and living connection with that of another, but some
third cause operating on all without exception was necessary to make the
different states correspond with one another. And this did not happen by means
of assistance applied in each particular case (systema assistentiae), but
through the unity of the idea of a cause occupied and connected with all
substances, in which they necessarily receive, according to the Leibnitzian
school, their existence and permanence, consequently also reciprocal
correspondence, according to universal laws.

4th. This philosopher’s celebrated doctrine of space and time, in which
he intellectualized these forms of sensibility, originated in the same delusion
of transcendental reflection. If I attempt to represent by the mere
understanding, the external relations of things, I can do so only by employing
the conception of their reciprocal action, and if I wish to connect one state
of the same thing with another state, I must avail myself of the notion of the
order of cause and effect. And thus Leibnitz regarded space as a certain order
in the community of substances, and time as the dynamical sequence of their
states. That which space and time possess proper to themselves and independent
of things, he ascribed to a necessary confusion in our conceptions of them,
whereby that which is a mere form of dynamical relations is held to be a
self-existent intuition, antecedent even to things themselves. Thus space and
time were the intelligible form of the connection of things (substances and
their states) in themselves. But things were intelligible substances
(substantiae noumena). At the same time, he made these conceptions valid of
phenomena, because he did not allow to sensibility a peculiar mode of
intuition, but sought all, even the empirical representation of objects, in the
understanding, and left to sense naught but the despicable task of confusing
and disarranging the representations of the former.

But even if we could frame any synthetical proposition concerning things in
themselves by means of the pure understanding (which is impossible), it could
not apply to phenomena, which do not represent things in themselves. In such a
case I should be obliged in transcendental reflection to compare my conceptions
only under the conditions of sensibility, and so space and time would not be
determinations of things in themselves, but of phenomena. What things may be in
themselves, I know not and need not know, because a thing is never presented to
me otherwise than as a phenomenon.

I must adopt the same mode of procedure with the other conceptions of
reflection. Matter is substantia phaenomenon. That in it which is internal I
seek to discover in all parts of space which it occupies, and in all the
functions and operations it performs, and which are indeed never anything but
phenomena of the external sense. I cannot therefore find anything that is
absolutely, but only what is comparatively internal, and which itself consists
of external relations. The absolutely internal in matter, and as it should be
according to the pure understanding, is a mere chimera, for matter is not an
object for the pure understanding. But the transcendental object, which is the
foundation of the phenomenon which we call matter, is a mere nescio quid, the
nature of which we could not understand, even though someone were found able to
tell us. For we can understand nothing that does not bring with it something in
intuition corresponding to the expressions employed. If, by the complaint of
being unable to perceive the internal nature of things, it is meant that we do
not comprehend by the pure understanding what the things which appear to us may
be in themselves, it is a silly and unreasonable complaint; for those who talk
thus really desire that we should be able to cognize, consequently to intuite,
things without senses, and therefore wish that we possessed a faculty of
cognition perfectly different from the human faculty, not merely in degree, but
even as regards intuition and the mode thereof, so that thus we should not be
men, but belong to a class of beings, the possibility of whose existence, much
less their nature and constitution, we have no means of cognizing. By
observation and analysis of phenomena we penetrate into the interior of nature,
and no one can say what progress this knowledge may make in time. But those
transcendental questions which pass beyond the limits of nature, we could never
answer, even although all nature were laid open to us, because we have not the
power of observing our own mind with any other intuition than that of our
internal sense. For herein lies the mystery of the origin and source of our
faculty of sensibility. Its application to an object, and the transcendental
ground of this unity of subjective and objective, lie too deeply concealed for
us, who cognize ourselves only through the internal sense, consequently as
phenomena, to be able to discover in our existence anything but phenomena, the
non-sensuous cause of which we at the same time earnestly desire to penetrate
to.

The great utility of this critique of conclusions arrived at by the processes
of mere reflection consists in its clear demonstration of the nullity of all
conclusions respecting objects which are compared with each other in the
understanding alone, while it at the same time confirms what we particularly
insisted on, namely, that, although phenomena are not included as things in
themselves among the objects of the pure understanding, they are nevertheless
the only things by which our cognition can possess objective reality, that is
to say, which give us intuitions to correspond with our conceptions.

When we reflect in a purely logical manner, we do nothing more than compare
conceptions in our understanding, to discover whether both have the same
content, whether they are self-contradictory or not, whether anything is
contained in either conception, which of the two is given, and which is merely
a mode of thinking that given. But if I apply these conceptions to an object in
general (in the transcendental sense), without first determining whether it is
an object of sensuous or intellectual intuition, certain limitations present
themselves, which forbid us to pass beyond the conceptions and render all
empirical use of them impossible. And thus these limitations prove that the
representation of an object as a thing in general is not only insufficient,
but, without sensuous determination and independently of empirical conditions,
self-contradictory; that we must therefore make abstraction of all objects, as
in logic, or, admitting them, must think them under conditions of sensuous
intuition; that, consequently, the intelligible requires an altogether peculiar
intuition, which we do not possess, and in the absence of which it is for us
nothing; while, on the other hand phenomena cannot be objects in themselves.
For, when I merely think things in general, the difference in their external
relations cannot constitute a difference in the things themselves; on the
contrary, the former presupposes the latter, and if the conception of one of
two things is not internally different from that of the other, I am merely
thinking the same thing in different relations. Further, by the addition of one
affirmation (reality) to the other, the positive therein is really augmented,
and nothing is abstracted or withdrawn from it; hence the real in things cannot
be in contradiction with or opposition to itself—and so on.

The true use of the conceptions of reflection in the employment of the
understanding has, as we have shown, been so misconceived by Leibnitz, one of
the most acute philosophers of either ancient or modern times, that he has been
misled into the construction of a baseless system of intellectual cognition,
which professes to determine its objects without the intervention of the
senses. For this reason, the exposition of the cause of the amphiboly of these
conceptions, as the origin of these false principles, is of great utility in
determining with certainty the proper limits of the understanding.

It is right to say whatever is affirmed or denied of the whole of a conception
can be affirmed or denied of any part of it (dictum de omni et nullo); but it
would be absurd so to alter this logical proposition as to say whatever is not
contained in a general conception is likewise not contained in the particular
conceptions which rank under it; for the latter are particular conceptions, for
the very reason that their content is greater than that which is cogitated in
the general conception. And yet the whole intellectual system of Leibnitz is
based upon this false principle, and with it must necessarily fall to the
ground, together with all the ambiguous principles in reference to the
employment of the understanding which have thence originated.

Leibnitz’s principle of the identity of indiscernibles or
indistinguishables is really based on the presupposition that, if in the
conception of a thing a certain distinction is not to be found, it is also not
to be met with in things themselves; that, consequently, all things are
completely identical (numero eadem) which are not distinguishable from each
other (as to quality or quantity) in our conceptions of them. But, as in the
mere conception of anything abstraction has been made of many necessary
conditions of intuition, that of which abstraction has been made is rashly held
to be non-existent, and nothing is attributed to the thing but what is
contained in its conception.

The conception of a cubic foot of space, however I may think it, is in itself
completely identical. But two cubic feet in space are nevertheless distinct
from each other from the sole fact of their being in different places (they are
numero diversa); and these places are conditions of intuition, wherein the
object of this conception is given, and which do not belong to the conception,
but to the faculty of sensibility. In like manner, there is in the conception
of a thing no contradiction when a negative is not connected with an
affirmative; and merely affirmative conceptions cannot, in conjunction, produce
any negation. But in sensuous intuition, wherein reality (take for example,
motion) is given, we find conditions (opposite directions)—of which
abstraction has been made in the conception of motion in general—which
render possible a contradiction or opposition (not indeed of a logical
kind)—and which from pure positives produce zero = 0. We are therefore
not justified in saying that all reality is in perfect agreement and harmony,
because no contradiction is discoverable among its conceptions.^[39] According to mere conceptions, that
which is internal is the substratum of all relations or external
determinations. When, therefore, I abstract all conditions of intuition, and
confine myself solely to the conception of a thing in general, I can make
abstraction of all external relations, and there must nevertheless remain a
conception of that which indicates no relation, but merely internal
determinations. Now it seems to follow that in everything (substance) there is
something which is absolutely internal and which antecedes all external
determinations, inasmuch as it renders them possible; and that therefore this
substratum is something which does not contain any external relations and is
consequently simple (for corporeal things are never anything but relations, at
least of their parts external to each other); and, inasmuch as we know of no
other absolutely internal determinations than those of the internal sense, this
substratum is not only simple, but also, analogously with our internal sense,
determined through representations, that is to say, all things are properly
monads, or simple beings endowed with the power of representation. Now all this
would be perfectly correct, if the conception of a thing were the only
necessary condition of the presentation of objects of external intuition. It
is, on the contrary, manifest that a permanent phenomenon in space
(impenetrable extension) can contain mere relations, and nothing that is
absolutely internal, and yet be the primary substratum of all external
perception. By mere conceptions I cannot think anything external, without, at
the same time, thinking something internal, for the reason that conceptions of
relations presuppose given things, and without these are impossible. But, as an
intuition there is something (that is, space, which, with all it contains,
consists of purely formal, or, indeed, real relations) which is not found in
the mere conception of a thing in general, and this presents to us the
substratum which could not be cognized through conceptions alone, I cannot say:
because a thing cannot be represented by mere conceptions without something
absolutely internal, there is also, in the things themselves which are
contained under these conceptions, and in their intuition nothing external to
which something absolutely internal does not serve as the foundation. For, when
we have made abstraction of all the conditions of intuition, there certainly
remains in the mere conception nothing but the internal in general, through
which alone the external is possible. But this necessity, which is grounded
upon abstraction alone, does not obtain in the case of things themselves, in so
far as they are given in intuition with such determinations as express mere
relations, without having anything internal as their foundation; for they are
not things of a thing of which we can neither for they are not things in
themselves, but only phenomena. What we cognize in matter is nothing but
relations (what we call its internal determinations are but comparatively
internal). But there are some self-subsistent and permanent, through which a
determined object is given. That I, when abstraction is made of these
relations, have nothing more to think, does not destroy the conception of a
thing as phenomenon, nor the conception of an object in abstracto, but it does
away with the possibility of an object that is determinable according to mere
conceptions, that is, of a noumenon. It is certainly startling to hear that a
thing consists solely of relations; but this thing is simply a phenomenon, and
cannot be cogitated by means of the mere categories: it does itself consist in
the mere relation of something in general to the senses. In the same way, we
cannot cogitate relations of things in abstracto, if we commence with
conceptions alone, in any other manner than that one is the cause of
determinations in the other; for that is itself the conception of the
understanding or category of relation. But, as in this case we make abstraction
of all intuition, we lose altogether the mode in which the manifold determines
to each of its parts its place, that is, the form of sensibility (space); and
yet this mode antecedes all empirical causality.

[39]
If any one wishes here to have recourse to the usual subterfuge, and to say,
that at least realitates noumena cannot be in opposition to each other, it will
be requisite for him to adduce an example of this pure and non-sensuous
reality, that it may be understood whether the notion represents something or
nothing. But an example cannot be found except in experience, which never
presents to us anything more than phenomena; and thus the proposition means
nothing more than that the conception which contains only affirmatives does not
contain anything negative—a proposition nobody ever doubted.