Prolegomena to Any Future Metaphysics
                             (1783)
                                
                          Immanuel Kant
                                

Copyright 1997, James Fieser (jfieser@utm.edu). See endnote for
details on copyright and editing. The following is based on Paul
Carus's 1902 translation of the Prolegomena. Spelling has been
Americanized. A few of Lewis White Beck's conventions have been
adopted from his revision of Carus's translation, such as
replacing the word "cognise" with "knowledge."1

                            Contents:
                                
     Introduction.
     Preamble On The Peculiarities Of All Metaphysical Cognition.
     First Part Of The Transcendental Problem: How Is Pure
          Mathematics Possible?
     Second Part Of The Transcendental Problem: How Is The
          Science Of Nature Possible?
     Third Part Of The Main Transcendental Problem: How Is
          Metaphysics In General Possible?
     Conclusion: On The Determination Of The Bounds Of Pure
          Reason.
     Solution Of The General Question Of The Prolegomena:  "How
          Is Metaphysics Possible As A Science?"
     Appendix: On What Can Be Done To Make Metaphysics Actual As
          A Science.

                             * * * *
                                
                          INTRODUCTION.

     These Prolegomena are destined for the use, not of pupils,
but of future teachers, and even the latter should not expect
that they will be serviceable for the systematic exposition of a
ready-made science, but merely for the discovery of the science
itself.

     There are scholarly men, to whom the history of philosophy
(both ancient and modern) is philosophy itself; for these the
present Prolegomena are not written. They must wait till those
who endeavor to draw from the fountain of reason itself have
completed their work; it will then be the historian's turn to
inform the world of what has been done. Unfortunately, nothing
can be said, which in their opinion has not been said before, and
truly the same prophecy applies to all future time; for since the
human reason has for many centuries speculated upon innumerable
objects in various ways, it is hardly to be expected that we
should not be able to discover analogies for every new idea among
the old sayings of past ages.

     My object is to persuade all those who think Metaphysics
worth studying, that it is absolutely necessary to pause a
moment, and, neglecting all that has been done, to propose first
the preliminary question, 'Whether such a thing as metaphysics be
at all possible?'

     If it be a science, how comes it that it cannot, like other
sciences, obtain universal and permanent recognition ? If not,
how can it maintain its pretensions, and keep the human mind in
suspense with hopes, never ceasing, yet never fulfilled? Whether
then we demonstrate our knowledge or our ignorance in this field,
we must come once for all to a definite conclusion respecting the
nature of this so-called science, which cannot possibly remain on
its present footing. It seems almost ridiculous, while every
other science is continually advancing, that in this, which
pretends to be Wisdom incarnate, for whose oracle every one
inquires, we should constantly move round the same spot, without
gaining a single step. And so its followers having melted away,
we do not find men confident of their ability to shine in other
sciences venturing their reputation here, where everybody,
however ignorant in other matters, may deliver a final verdict,
as in this domain there is as yet no standard weight and measure
to distinguish sound knowledge from shallow talk.

     After all it is nothing extraordinary in the elaboration of
a science, when men begin to wonder how far it has advanced, that
the question should at last occur, whether and how such a science
is possible? Human reason so delights in constructions, that it
has several times built up a tower, and then razed it to examine
the nature of the foundation. It is never too late to become
wise; but if the change comes late, there is always more
difficulty in starting a reform.

     The question whether a science be possible, presupposes a
doubt as to its actuality. But such a doubt offends the men whose
whole possessions consist of this supposed jewel; hence he who
raises the doubt must expect opposition from all sides. Some, in
the proud consciousness of their possessions, which are ancient,
and therefore considered legitimate, will take their metaphysical
compendia in their hands, and look down on him with contempt;
others, who never see anything except it be identical with what
they have seen before, will not understand him, and everything
will remain for a time, as if nothing had happened to excite the
concern, or the hope, for an impending change.

     Nevertheless, I venture to predict that the independent
reader of these Prolegomena will not only doubt his previous
science, but ultimately be fully persuaded, that it cannot exist
unless the demands here stated on which its possibility depends,
be satisfied; and, as this has never been done, that there is, as
yet, no such thing as Metaphysics. But as it can never cease to
be in demand,2 -- since the interests of common sense are
intimately interwoven with it, he must confess that a radical
reform, or rather a new birth of the science after an original
plan, are unavoidable, however men may struggle against it for a
while.

     Since the Essays of Locke and Leibniz, or rather since the
origin of metaphysics so far as we know its history, nothing has
ever happened which was more decisive to its fate than the attack
made upon it by David Hume. He threw no light on this species of
knowledge, but he certainly struck a spark from which light might
have been obtained, had it caught some inflammable substance and
had its smoldering fire been carefully nursed and developed.

     Hume started from a single but important concept in
Metaphysics, viz., that of Cause and Effect (including its
derivatives force and action, etc.). He challenges reason, which
pretends to have given birth to this idea from herself, to answer
him by what right she thinks anything to be so constituted, that
if that thing be posited, something else also must necessarily be
posited; for this is the meaning of the concept of cause. He
demonstrated irrefutably that it was perfectly impossible for
reason to think a priori and by means of concepts a combination
involving necessity. We cannot at all see why, in consequence of
the existence of one thing, another must necessarily exist, or
how the concept of such a combination can arise a priori. Hence
he inferred, that reason was altogether deluded with reference to
this concept, which she erroneously considered as one of her
children, whereas in reality it was nothing but a bastard of
imagination, impregnated by experience, which subsumed certain
representations under the Law of Association, and mistook the
subjective necessity of habit for an objective necessity arising
from insight. Hence he inferred that reason had no power to think
such, combinations, even generally, because her concepts would
then be purely fictitious, and all her pretended a priori
cognitions nothing but common experiences marked with a false
stamp. In plain language there is not, and cannot be, any such
thing as metaphysics at all.3

     However hasty and mistaken Hume's conclusion may appear, it
was at least founded upon investigation, and this investigation
deserved the concentrated attention of the brighter spirits of
his day as well as determined efforts on their part to discover,
if possible, a happier solution of the problem in the sense
proposed by him, all of which would have speedily resulted in a
complete reform of the science.

     But Hume suffered the usual misfortune of metaphysicians, of
not being understood. It is positively painful to see bow utterly
his opponents, Reid, Oswald, Beattie, and lastly Priestley,
missed the point of the problem; for while they were ever taking
for granted that which he doubted, and demonstrating with zeal
and often with impudence that which he never thought of doubting,
they so misconstrued his valuable suggestion that everything
remained in its old condition, as if nothing had happened.

     The question was not whether the concept of cause was right,
useful, and even indispensable for our knowledge of nature, for
this Hume had never doubted; but whether that concept could be
thought by reason a priori, and consequently whether it possessed
an inner truth, independent of all experience, implying a wider
application than merely to the objects of experience. This was
Hume's problem. It was a question concerning the origin, not
concerning the indispensable need of the concept. Were the former
decided, the conditions of the use and the sphere of its valid
application would have been determined as a matter of course.

     But to satisfy the conditions of the problem, the opponents
of the great thinker should have penetrated very deeply into the
nature of reason, so far as it is concerned with pure thinking,-a
task which did not suit them. They found a more convenient method
of being defiant without any insight, viz., the appeal to common
sense. It is indeed a great gift of God, to possess right, or (as
they now call it) plain common sense. But this common sense must
be shown practically, by well-considered and reasonable thoughts
and words, not by appealing to it as an oracle, when no rational
justification can be advanced. To appeal to common sense, when
insight and science fail, and no sooner-this is one of the subtle
discoveries of modern times, by means of which the most
superficial ranter can safely enter the lists with the most
thorough thinker, and hold his own. But as long as a particle of
insight remains, no one would think of having recourse to this
subterfuge. For what is it but an appeal to the opinion of the
multitude, of whose applause the philosopher is ashamed, while
the popular charlatan glories and confides in it? I should think
that Hume might fairly have laid as much claim to common sense as
Beattie, and in addition to a critical reason (such as the latter
did not possess), which keeps common sense in check and prevents
it from speculating, or, if speculations are under discussion
restrains the desire to decide because it cannot satisfy itself
concerning its own arguments. By this means alone can common
sense remain sound. Chisels and hammers may suffice to work a
piece of wood, but for steel-engraving we require an engraver's
needle. Thus common sense and speculative understanding are each
serviceable in their own way, the former in judgments which apply
immediately to experience, the latter when we judge universally
from mere concepts, as in metaphysics, where sound common sense,
so called in spite of the inapplicability of the word, has no
right to judge at all.

     I openly confess, the suggestion of David Hume was the very
thing, which many years ago first interrupted my dogmatic
slumber, and gave my investigations in the field of speculative
philosophy quite a new direction. I was far from following him in
the conclusions at which he arrived by regarding, not the whole
of his problem, but a part, which by itself can give us no
information. If we start from a well-founded, but undeveloped,
thought, which another has bequeathed to us, we may well hope by
continued reflection to advance farther than the acute man, to
whom we owe the first spark of light.

     I therefore first tried whether Hume's objection could not
be put into a general form, and soon found that the concept of
the connection of cause and effect was by no means the only idea
by which the understanding thinks the connection of things a
priori, but rather that metaphysics consists altogether of such
connections. I sought to ascertain their number, and when I had
satisfactorily succeeded in this by starting from a single
principle, I proceeded to the deduction of these concepts, which
I was now certain were not deduced from experience, as Hume had
apprehended, but sprang from the pure understanding. This
deduction (which seemed impossible to my acute predecessor, which
bad never even occurred to any one else, though no one had
hesitated to use the concepts without investigating the basis of
their objective validity) was the most difficult task ever
undertaken in the service of metaphysics; and the worst was that
metaphysics, such as it then existed, could not assist me in the
least, because this deduction alone can render metaphysics
possible. But as soon as I had succeeded in solving Hume's
problem not merely in a particular case, but with respect to the
whole faculty of pure reason, I could proceed safely, though
slowly, to determine the whole sphere of pure reason completely
and from general principles, in its circumference as well as in
its contents. This was required for metaphysics in order to
construct its system according to a reliable method.

     But I fear that the execution of Hume's problem in its
widest extent (viz., my Critique of the Pure Reason) will fare as
the problem itself fared, when first proposed. It will be
misjudged because it is misunderstood, and misunderstood because
men choose to skim through the book, and not to think through it-
a disagreeable task, because the work is dry, obscure, opposed to
all ordinary notions, and moreover long-winded. I confess,
however, I did not expect, to hear from philosophers complaints
of want of popularity, entertainment, and facility, when the
existence of a highly prized and indispensable cognition is at
stake, which cannot be established otherwise, than by the
strictest rules of methodic precision. Popularity may follow, but
is inadmissible at the beginning. Yet as regards a certain
obscurity, arising partly from the diffuseness of the plan, owing
to which. the principal points of the investigation are easily
lost sight of, the complaint is just, and I intend to remove it
by the present Prolegomena.

     The first-mentioned work, which discusses the pure faculty
of reason in its whole compass and bounds, will remain the
foundation, to which the Prolegomena, as a preliminary, exercise,
refer; for our critique must first be established as a complete
and perfected science, before we can think of letting Metaphysics
appear on the scene, or even have the most distant hope of
attaining it.

     We have been long accustomed to seeing antiquated knowledge
produced as new by taking it out of its former context, and
reducing it to system in a new suit of any fancy pattern under
new titles. Most readers will set out by expecting nothing else
from the Critique; but these Prolegomena may persuade him that it
is a perfectly new science, of which no one has ever even
thought, the very idea of which was unknown, and for which
nothing hitherto accomplished can be of the smallest use, except
it be the suggestion of Hume's doubts. Yet even he did not
suspect such a formal science, but ran his ship ashore, for
safety's sake, landing on skepticism, there to let it lie and
rot; whereas my object is rather to give it a pilot, who, by
means of safe astronomical principles drawn from a knowledge of
the globe, and provided with a complete chart and compass, may
steer the ship safely, whither he listeth.

     If in a new science, which is wholly isolated and unique in
its kind, we started with the prejudice that we can judge of
things by means of our previously acquired knowledge, which., is
precisely what has first to be called in question, we should only
fancy we saw everywhere what we had already known,. the
expressions, having a similar sound, only that all would appear
utterly metamorphosed, senseless and unintelligible, because we
should have as a foundation out own notions, made by long habit a
second nature, instead of the author's. But the longwindedness of
the work, so far as it depends on the subject, and not the
exposition, its consequent unavoidable dryness and its scholastic
precision are qualities which can only benefit the science,
though they may discredit the book.

     Few writers are gifted with the subtlety, and at the same
time with the grace, of David Hume, or with the depth, as well as
the elegance, of Moses Mendelssohn. Yet I flatter myself I might
have made my own exposition popular, had my object been merely to
sketch out a plan and leave its completion to others instead of
having my heart in the welfare of the science, to which I had
devoted myself so long; in truth, it required no little
constancy, and even self-denial, to postpone the sweets of an
immediate success to the prospect of a slower, but more lasting,
reputation.

     Making plans is often the occupation of an opulent and
boastful mind, which thus obtains the reputation of a creative
genius, by demanding what it cannot itself supply; by censuring,
what it cannot improve; and by proposing, what it knows not where
to find. And yet something more should belong to a sound plan of
a general critique of pure reason than mere conjectures, if this
plan is to be other than the usual declamations of pious
aspirations. But pure reason is a sphere so separate and self-
contained, that we cannot touch a part without affecting all the
rest. We can therefore do nothing without first determining the
position; of each part, and its relation to the rest; for, as our
judgment cannot be corrected by anything without, the validity
and use of every part depends upon the relation in which it
stands to all the rest within the domain of reason.

     So in the structure of an organized body, the end of each
member can only be deduced from the full conception of the whole.
It may, then, be said of such a critique that it is never
trustworthy except it be perfectly complete, down to the smallest
elements of pure reason. In the sphere of this faculty you can
determine either everything or nothing.

     But although a mere sketch, preceding the Critique of Pure
Reason, would be unintelligible, unreliable, and useless, it is
all the more useful as a sequel. For so we are able to grasp the
whole, to examine in detail the chief points of importance in the
science, and to improve in many respects our exposition, as
compared with the first execution of the work.

     After the completion of the work I offer here such a plan
which is sketched out after an analytical method, while the work
itself had to be executed in the synthetical style, in order that
the science may present all its articulations, as the structure
of a peculiar cognitive faculty, in their natural combination.
But should any reader find this plan, which I publish as the
Prolegomena to any future Metaphysics, still obscure, let him
consider that not every one is bound to study Metaphysics, that
many minds will succeed very well, in the exact and even in deep
sciences, more closely allied to practical experience,4 while
they cannot succeed in investigations dealing exclusively with
abstract concepts. In such cases men should apply their talents
to other subjects. But he who undertakes to judge, or still more,
to construct, a system of Metaphysics, must satisfy the demands
here made, either by adopting my solution, or by thoroughly
refuting it, and substituting another. To evade it is impossible.

     In conclusion, let it be remembered that this much-abused
obscurity (frequently serving as a mere pretext under which
people hide their own indolence or dullness) has its uses, since
all who in other sciences observe a judicious silence, speak
authoritatively in metaphysics and make bold decisions, because
their ignorance is not here contrasted with the knowledge of
others. Yet it does contrast with sound critical principles,
which we may therefore commend in the words of Virgil:

     " Ignavum, fucos, pecus a praesepibus arcent. "
     "Bees are defending their hives against drones, those
     indolent creatures. "

                             * * * *
                                
                          PROLEGOMENA.
                                
  PREAMBLE ON THE PECULIARITIES OF ALL METAPHYSICAL COGNITION.

             Sect. 1: Of the Sources of Metaphysics

     If it becomes desirable to formulate any cognition as
science, it will be necessary first to determine accurately those
peculiar features which no other science has in common with it,
constituting its characteristics; otherwise the. boundaries of
all sciences become confused, and none of them can be treated
thoroughly according to its nature.

     The characteristics of a science may consist of a simple
difference of object, or of the sources of cognition, or of the
kind of cognition, or perhaps of all three conjointly. On this,
therefore, depends the idea of a possible science and its
territory.

     First, as concerns the sources of metaphysical cognition,
its very concept implies that they cannot be empirical. Its
principles (including not only its maxims but its basic notions)
must never be derived from experience. It must not be physical
but metaphysical knowledge, viz., knowledge lying beyond
experience. It can therefore have for its basis neither external
experience, which is the source of physics proper, nor internal,
which is the basis of empirical psychology. It is therefore a
priori knowledge, coming from pure Understanding and pure Reason.

     But so far Metaphysics would not be distinguishable from
pure Mathematics; it must therefore be called pure philosophical
cognition; and for the meaning of this term I refer to the
Critique of the Pure Reason (II. "Method of Transcendentalism,"
Chap. I., Sec. 1), where the distinction between these two
employments of the reason is sufficiently explained. So far
concerning the sources of metaphysical cognition.

            Sect. 2. Concerning the Kind of Cognition which can
                       alone be called Metaphysical

     a. Of the Distinction between Analytical and Synthetical
judgments in general. -- The peculiarity of its sources demands
that metaphysical cognition must consist of nothing but a priori
judgments. But whatever be their origin, or their logical form,
there is a distinction in judgments, as to their content,
according to which they are either merely explicative, adding
nothing to the content of the cognition, or expansive, increasing
the given cognition: the former may be called analytical, the
latter synthetical, judgments.

     Analytical judgments express nothing in the predicate but
what has been already actually thought in the concept of the
subject, though not so distinctly or with the same (full)
consciousness. When I say: All bodies are extended, I have not
amplified in the least my concept of body, but have only analyzed
it, as extension was really thought to belong to that concept
before the judgment was made, though it was not expressed, this
judgment is therefore analytical. On the contrary, this judgment,
All bodies have weight, contains in its predicate something not
actually thought in the general concept of the body; it amplifies
my knowledge by adding something to my concept, and must
therefore be called synthetical.

     b. The Common Principle of all Analytical Judgments is the
Law of Contradiction. -- All analytical judgments depend wholly
on the law of Contradiction, and are in their nature a priori
cognitions, whether the concepts that supply them with matter be
empirical or not. For the predicate of an affirmative analytical
judgment is already contained in the concept of the subject, of
which it cannot be denied without contradiction. In the same way
its opposite is necessarily denied of the subject in an
analytical, but negative, judgment, by the same law of
contradiction. Such is the nature of the judgments: all bodies
are extended, and no bodies are unextended (i. e., simple).

     For this very reason all analytical judgments are a .priori
even when the concepts are empirical, as, for example, Gold is a
yellow metal; for to know this I require no experience beyond my
concept of gold as a yellow metal: it is, in fact, the very
concept, and I need only analyze it, without looking beyond it
elsewhere.

     c. Synthetical judgments require a different Principle from
the Law of Contradiction.-There are synthetical a posteriori
judgments of empirical origin; but there are also others which
are proved to be certain a priori, and which spring from pure
Understanding and Reason. Yet they both agree in this, that they
cannot possibly spring from the principle of analysis, viz., the
law of contradiction, alone; they require a quite different
principle, though, from whatever they may be deduced, they must
be subject to the law of contradiction, which must never be
violated, even though everything cannot be deduced from it. I
shall first classify synthetical judgments.

     1. Empirical judgments are always synthetical. For it would
be absurd to base an analytical judgment on experience, as our
concept suffices for the purpose without requiring any testimony
from experience. That body is extended, is a judgment established
a priori, and not an empirical judgment. For before appealing to
experience, we already have all the conditions of the judgment in
the concept, from which we have but to elicit the predicate
according to the law of contradiction, and thereby to become
conscious of the necessity of the judgment, which experience
could not even teach us.

     2. Mathematical judgments are all synthetical. This fact
seems hitherto to have altogether escaped the observation of
those who have analyzed human reason; it even seems directly
opposed to all their conjectures, though incontestably certain,
and most important in its consequences. For as it was found that
the conclusions of mathematicians all proceed according to the
law of contradiction (as is demanded by all apodictic certainty),
men persuaded themselves that the fundamental principles were
known from the same law. This was a great mistake, for a
synthetical proposition can indeed be comprehended according to
the law of contradiction, but only by presupposing another
synthetical proposition from which it follows, but never in
itself.

     First of all, we must observe that all proper mathematical
judgments are a priori, and not empirical, because they carry
with them necessity, which cannot be obtained from experience.
But if this be not conceded to me, very good; I shall confine my
assertion pure Mathematics, the very notion of which implies that
it contains pure a priori and not empirical cognitions.

     It might at first be thought that the proposition 7 + 5 = 12
is a mere analytical judgment, following from the concept of the
sum of seven and five, according to the law of contradiction. But
on closer examination it appears that the concept of the sum Of
7+5 contains merely their union in a single number, without its
being at all thought what the particular number is that unites
them. The concept of twelve is by no means thought by merely
thinking of the combination of seven and five; and analyze this
possible sum as we may, we shall not discover twelve in the
concept. We must go beyond these concepts, by calling to our aid
some concrete image [Anschauung], i.e., either our five fingers,
or five points (as Segner has it in his Arithmetic), and we must
add successively the units of the five, given in some concrete
image [Anschauung], to the concept of seven. Hence our concept is
really amplified by the proposition 7 + 5 = I 2, and we add to
the first a second, not thought in it. Arithmetical judgments are
therefore synthetical, and the more plainly according as we take
larger numbers; for in such cases it is clear that, however
closely we analyze our concepts without calling visual images
(Anscliauung) to our aid, we can never find the sum by such mere
dissection.

     All principles of geometry are no less analytical. That a
straight line is the shortest path between two points, is a
synthetical proposition. For my concept of straight contains
nothing of quantity, but only a quality. The attribute of
shortness is therefore altogether additional, and cannot be
obtained by any analysis of the concept. Here, too, visualization
[Anschauung] must come to aid us. It alone makes the synthesis
possible.

     Some other principles, assumed by geometers, are indeed
actually analytical, and depend on the law of contradiction; but
they only serve, as identical propositions, as a method of
concatenation, and not as principles, e. g., a=a, the whole is
equal to itself, or a + b > a, the whole is greater than its
part. And yet even these, though they are recognized as valid
from mere concepts, are only admitted in mathematics, because
they can be represented in some visual form [Anschauung]. What
usually makes us believe that the predicate of such apodictic5
judgments is already contained in our concept, and that the
judgment is therefore analytical, is the duplicity of the
expression, requesting us to think a certain predicate as of
necessity implied in the thought of a given concept, which
necessity attaches to the concept. But the question is not what
we are requested to join in thought to the given concept, but
what we actually think together with and in it, though obscurely;
and so it appears that the predicate belongs to these concepts
necessarily indeed, yet not directly but indirectly by an added
visualization [Anschauung].

   Sect. 3. A Remark on the General Division of judgments into
                   Analytical and Synthetical

     This division is indispensable, as concerns the Critique of
human understanding, and therefore deserves to be called
classical, though otherwise it is of little use, but this is the
reason why dogmatic philosophers, who always seek the sources of
metaphysical judgments in Metaphysics itself, and not apart from
it, in the pure laws of reason generally, altogether neglected
this apparently obvious distinction. Thus the celebrated Wolf,
and his acute follower Baumgarten, came to seek the proof of the
principle of Sufficient Reason, which is clearly synthetical, in
the principle of Contradiction. In Locke's Essay, however, I find
an indication of my division. For in the fourth book (chap. iii.
Sect. 9, seq.), having discussed the various connections of
representations in judgments, and their sources, one of which he
makes -I identity and contradiction" (analytical judgments), and
another the coexistence of representations in a subject, he
confesses (Sect. 10) that our a priori knowledge of the latter is
very narrow, and almost nothing. But in his remarks on this
species of cognition, there is so little of what is definite, and
reduced to rules, that we cannot wonder if no one, not even Hume,
was led to make investigations concerning this sort of judgments.
For such general and yet definite principles are not easily
learned from other men, who have had them obscurely in their
minds. We must hit on them first by our own reflection, then we
find them elsewhere, where we could not possibly nave found them
at first, because the authors themselves did not know that such
an idea lay at the basis of their observations. Men who never
think independently have nevertheless the acuteness to discover
everything, after it has been once shown them, in what was said
long since, though no one ever saw it there before.

     Sect. 4. The General Question of the Prolegemena. - Is
                  Metaphysics at all Possible?

     Were a metaphysics, which could maintain its place as a
science, really in existence; could we say, here is metaphysics,
learn it, and it will convince you irresistibly and irrevocably
of its truth: this question would be useless, and there would
only remain that other question (which would rather be a test of
our acuteness, than a proof of the existence of the thing
itself), "How is the science possible, and how does reason come
to attain it?" But human reason has not been so fortunate in this
case. There is no single book to which you can point as you do to
Euclid, and say: This is Metaphysics; here you may find the
noblest objects of this science, the knowledge of a highest
Being, and of a future existence, proved from principles of pure
reason. We can be shown indeed many judgments, demonstrably
certain, and never questioned; but these are all analytical, and
rather concern the materials and the scaffolding for Metaphysics,
than the extension of knowledge, which is our proper object in
studying it (Sect 2). Even supposing you produce synthetical
judgments (such as the law of Sufficient Reason, which you have
never proved, as you ought to, from pure reason a priori, though
we gladly concede its truth), you lapse when they come to be
employed for your principal object, into such doubtful
assertions, that in all ages one Metaphysics has contradicted
another, either in its assertions, or their proofs, and thus has
itself destroyed its own claim to lasting assent. Nay, the very
attempts to set up such a science are the main cause of the early
appearance of skepticism, a mental attitude in which reason
treats itself with such violence that it could never have arisen
save from complete despair of ever satisfying our most important
aspirations. For long before men began to inquire into nature
methodically, they consulted abstract reason, which had to some
extent been exercised by means of ordinary experience; for reason
is ever present, while laws of nature must usually be discovered
with labor. So Metaphysics floated to the surface, like foam,
which dissolved the moment it was scooped off. But immediately
there appeared a new supply on the surface, to be ever eagerly
gathered up by some, while others, instead of seeking in the
depths the cause of the phenomenon, thought they showed their
wisdom by ridiculing the idle labor of their neighbors.

     The essential and distinguishing feature of pure
mathematical cognition among all other a priori cognitions is,
that it cannot at all proceed from concepts, but only by means of
the construction of concepts (see Critique II., Method of
Transcendentalism, Chap. I., sect. 1). As therefore in its
judgments it must proceed beyond the concept to that which its
corresponding visualization [Anschauung] contains, these
judgments neither can, nor ought to, arise analytically, by
dissecting the concept, but are all synthetical.

     I cannot refrain from pointing out the disadvantage
resulting to philosophy from the neglect of this easy and
apparently insignificant observation. Hume being prompted (a task
worthy of a philosopher) to cast his eye over the whole field of
a priori cognitions in which human understanding claims such
mighty possessions, heedlessly severed from it a whole, and
indeed its most valuable, province, viz., pure mathematics; for
he thought its nature, or, so to speak, the state-constitution of
this empire, depended on totally different principles, namely, on
the law of contradiction alone; and although he did not divide
judgments in this manner formally and universally as I have done
here, what he said was equivalent to this: that mathematics
contains only analytical, but metaphysics synthetical, a priori
judgments. In this, however, he was greatly mistaken, and the
mistake had a decidedly injurious effect upon his whole
conception. But for this, he would have extended his question
concerning the origin of our synthetical judgments far beyond the
metaphysical concept of Causality, and included in it the
possibility of mathematics a priori also, for this latter he must
have assumed to be equally synthetical. And then he could not
have based his metaphysical judgments on mere experience without
subjecting the axioms of mathematics equally to experience, a
thing which he was far too acute to do. The good company into
which metaphysics would thus have been brought, would have saved
it from the danger of a contemptuous ill-treatment, for the
thrust intended for it must have reached mathematics, which was
not and could not have been Hume's intention. Thus that acute man
would have been led into considerations which must needs be
similar to those that now occupy us, but which would have gained
inestimably by his inimitably elegant style.

     Metaphysical judgments, properly so called, are all
synthetical. We must distinguish judgments pertaining to
metaphysics from metaphysical judgments properly so called. Many
of the former are analytical, but they only afford the means for
metaphysical judgments, which are the whole end of the science,
and which are always synthetical. For if there be concepts
pertaining to metaphysics (as, for example, that of substance),
the judgments springing from simple analysis of them also pertain
to metaphysics, as, for example, substance is that which only
exists as subject; and by means of several such analytical
judgments, we seek to approach the definition of the concept. But
as the analysis of a pure concept of the understanding pertaining
to metaphysics, does not proceed in any different manner from the
dissection of any other, even empirical, concepts, not pertaining
to metaphysics (such as: air is an elastic fluid, the elasticity
of which is not destroyed by any known degree of cold), it
follows that the concept indeed, but not the analytical judgment,
is properly metaphysical. This science has something peculiar in
the production of its a priori cognitions, which must therefore
be distinguished from the features it has in common with other
rational knowledge. Thus the judgment, that all the substance in
things is permanent, is a synthetical and properly metaphysical
judgment.

     If the a priori principles, which constitute the materials
of metaphysics, have first been collected according to fixed
principles, then their analysis will be of great value; it might
be taught as a particular part (as a philosophia definitiva),
containing nothing but analytical judgments pertaining to
metaphysics, and could be treated separately from the synthetical
which constitute metaphysics proper. For indeed these analyses
are not elsewhere of much value, except in metaphysics, i.e., as
regards the synthetical judgments, which are to be generated by
these previously analyzed concepts.

     The conclusion drawn in this section then is, that
metaphysics is properly concerned with synthetical propositions a
priori, and these alone constitute its end, for which it indeed
requires various dissections of its concepts, viz., of its
analytical judgments, but wherein the procedure is not different
from that in every other kind of knowledge, in which we merely
seek to render our concepts distinct by analysis. But the
generation of a priori cognition by concrete images as well as by
concepts, in fine of synthetical propositions a priori in
philosophical cognition, constitutes the essential subject of
Metaphysics.

     Weary therefore as well of dogmatism, which teaches us
nothing, as of skepticism, which does not even promise us
anything, not even the quiet state of a contented ignorance;
disquieted by the importance of knowledge so much needed; and
lastly, rendered suspicious by long experience of all knowledge
which we believe we possess, or which offers itself, under the
title of pure reason: there remains but one critical question on
the answer to which our future procedure depends, viz., Is
Metaphysics at all possible? But this question must be answered
not by skeptical objections to the asseverations of some actual
system of metaphysics (for we do not as yet admit such a thing to
exist), but from the conception, as yet only problematical, of a
science of this sort.

     In the Critique of Pure Reason I have treated this question
synthetically, by making inquiries into pure reason itself, and
endeavoring in this source to determine the elements as well as
the laws of its pure use according to principles. The task is
difficult, and requires a resolute reader to penetrate by degrees
into a system, based on no data except reason itself, and which
therefore seeks, without resting upon any fact, to unfold
knowledge from its original germs. Prolegomena, however, are
designed for preparatory exercises; they are intended rather to
point out what we have to do in order if possible to actualize a
science, than to propound it. They must therefore rest upon
something already known as trustworthy, from which we can set out
with confidence, and ascend to sources as yet unknown, the
discovery of which will not only explain to us what we knew, but
exhibit a sphere of many cognitions which all spring from the
same sources. The method of Prolegomena, especially of those
designed as a preparation for future metaphysics, is consequently
analytical.

     But it happens fortunately, that though we cannot assume
metaphysics to be an actual science, we can say with confidence
that certain pure a priori synthetical cognitions, pure
Mathematics and pure Physics are actual and given; for both
contain propositions, which are thoroughly recognized as
apodictically certain, partly by mere reason, partly by general
consent arising from experience, and yet as independent of
experience. We have therefore some at least uncontested
synthetical knowledge a priori, and need not ask whether it be
possible, for it is actual, but how it is possible, in order that
we may deduce from the principle which makes the given cognitions
possible the possibility of all the rest.

 Sect. 5. The General Problem: How is Cognition from Pure Reason
                            Possible?

     We have above learned the significant distinction between
analytical and synthetical judgments. The possibility of
analytical propositions was easily comprehended, being entirely
founded on the law of Contradiction. The possibility of
synthetical a posteriori judgments, of those which are gathered
from experience, also requires no particular explanation; for
experience is nothing but a continual synthesis of perceptions.
There remain therefore only synthetical propositions a priori, of
which the possibility must be sought or investigated, because
they must depend upon other principles than the law of
contradiction.

     But here we need not first establish the possibility of such
propositions so as to ask whether they are possible. For there
are enough of them which indeed are of undoubted certainty, and
as our present method is analytical, we shall start from the
fact, that such synthetical but purely rational cognition
actually exists; but we must now inquire into the reason of this
possibility, and ask, how such cognition is possible, in order
that we may from the principles of its possibility be enabled to
determine the conditions of its use, its sphere and its limits.
The proper problem upon which all depends, when expressed with
scholastic precision, is therefore: How are Synthethetic
Propositions a priori possible?

     For the sake of popularity I have above expressed this
problem somewhat differently, as an inquiry into purely rational
cognition, which I could do for once without detriment to the
desired comprehension, because, as we have only to do here with
metaphysics and its sources, the reader will, I hope, after the
foregoing remarks, keep in mind that when we speak of purely
rational cognition, we do not mean analytical, but synthetical
cognition.6

     Metaphysics stands or falls with the solution of this
problem: its very existence depends upon it. Let any one make
metaphysical assertions with ever so much plausibility, let him
overwhelm us with conclusions, if he has not previously proved
able to answer this question satisfactorily, I have a right to
say this is all vain baseless philosophy and false wisdom. You
speak through pure reason, and claim, as it were to create
cognitions a priori. by not only dissecting given concepts, but
also by asserting connections which do not rest upon the law of
contradiction, and which you believe you conceive quite
independently of all experience; how do you arrive at this, and
how will you justify your pretensions? An appeal to the consent
of the common sense of mankind cannot be allowed; for that is a
witness whose authority depends merely upon rumor. Says Horace:

     " Quodcunque ostendis mihi sic, incredulus odi."
     "To all that which thou provest me thus, I refuse to give
     credence. "

     The answer to this question, though indispensable, is
difficult; and though the principal reason that it was not made
long ago is, that the possibility of the question never occurred
to anybody, there is yet another reason, which is this that a
satisfactory answer to this one question requires a much more
persistent, profound, and painstaking reflection, than the most
diffuse work on Metaphysics, which on its first appearance
promised immortality to its author. And every intelligent reader,
when he carefully reflects what this problem requires, must at
first be struck with its difficulty, and would regard it as
insoluble and even impossible, did there not actually exist pure
synthetical cognitions a priori. This actually happened to David
Hume, though he did not conceive the question in its entire
universality as is done here, and as must be done, should the
answer be decisive for all Metaphysics. For how is it possible,
says that acute man, that when a concept is given me, I can go
beyond it and connect with it another, which is not contained in
it, in such a manner as if the latter necessarily belonged to the
former? Nothing but experience can furnish us with such
connections (thus he concluded from the difficulty which he took
to be an impossibility), and all that vaunted necessity, or, what
is the same thing, all cognition assumed to be a priori, is
nothing but a long habit of accepting something as true, and
hence of mistaking subjective necessity for objective.

     Should my reader complain of the difficulty and the trouble
which I occasion him in the solution of this problem, he is at
liberty to solve it himself in an easier way. Perhaps he will
then feel under obligation to the person who has undertaken for
him a labor of so profound research, and will rather be surprised
at the facility with which, considering the nature of the
subject, the solution has been attained. Yet it has cost years of
work to solve the problem in its whole universality (using the
term in the mathematical sense, viz., for that which is
sufficient for all cases), and finally to exhibit it in the
analytical form, as the reader finds it here.

     All metaphysicians are therefore solemnly and legally
suspended from their occupations till they shall have answered in
a satisfactory manner the question, "How are synthetic cognitions
a priori possible?" For the answer contains the only credentials
which they must show when they have anything to offer in the name
of pure reason. But if they do not possess these credentials,
they can expect nothing else of reasonable people, who have been
deceived so often, than to be dismissed without further ado.

     If they on the other hand desire to carry on their business,
not as a science, but as an art of wholesome oratory suited to
the common sense of man, they cannot in justice be prevented.
They will then speak the modest language of a rational belief,
they will grant that they are not allowed even to conjecture, far
less to know, anything which lies beyond the bounds of all
possible experience, but only to assume (not for speculative use,
which they must abandon, but for practical purposes only) the
existence of something that is possible and even indispensable
for the guidance of the understanding and of the will in life. In
this mariner alone can they be called useful and wise men, and
the more so as they renounce the title of metaphysicians; for the
latter profess to be speculative philosophers, and since, when
judgments a prior: are under discussion, poor probabilities
cannot be admitted (for what is declared to be known a priori is
thereby announced as necessary), such men cannot be permitted to
play with conjectures, but their assertions must be either
science, or are worth nothing at all.

     It may be said, that the entire transcendental philosophy,
which necessarily precedes all metaphysics, is nothing but the
complete solution of the problem here propounded, in systematical
order and completeness, and hitherto we have never had any
transcendental philosophy; for what goes by its name is properly
a part of metaphysics, whereas the former sciences intended first
to constitute the possibility of the 'matter, and must therefore
precede all metaphysics. And it is not surprising that when a
whole science, deprived of all help from other sciences, and
consequently in itself quite new, is required to answer a -single
question satisfactorily, we should find the answer troublesome
and difficult, nay even shrouded in obscurity.

     As we now proceed to this solution according to the
analytical method, in which we assume that such cognitions from
pure reasons actually exist, we can only appeal to two sciences
of theoretical cognition . which alone is under consideration
here), pure mathematics and pure natural science (physics). For
these alone can exhibit to us objects in a definite and
actualizable form (in der Anschauung), and consequently (if there
should occur in them a cognition a priori) can show the truth or
conformity of the cognition to the object in concrete, that is,
its actuality, from which we could proceed to the reason of its
possibility by the analytic method. This facilitates our work
greatly for here universal considerations are not only applied to
facts, but even start from them, while in a synthetic procedure
they must strictly be derived in abstracts from concepts.

     But, in order to rise from these actual and at the same time
well-grounded pure cognitions a priori to such a possible
cognition of the same as we are seeking, viz., to metaphysics as
a science, we must comprehend that which occasions it, I mean the
mere natural, though in spite of its truth not unsuspected,
cognition a priori which lies at the bottom of that science, the
elaboration of which without any critical investigation of its
possibility is commonly called metaphysics. In a word, we must
comprehend the natural conditions of such a science as a part of
our inquiry, and thus the transcendental problem will be
gradually answered by a division into four questions:

     1. How is pure mathematics possible?
     2. How is pure natural science possible?
     3. How is metaphysics in general possible?
     4. How is metaphysics as a science possible?
   
     It may be seen that the solution of these problems, though
chiefly designed to exhibit the essential matter of the Critique,
has yet something peculiar, which for itself alone deserves
attention. This is the search for the sources of given sciences
in reason itself, so that its faculty of knowing something a
priori may by its own deeds be investigated and measured. By this
procedure these sciences gain, if not with regard to their
contents, yet as to their proper use, and while they throw light
on the higher question concerning their common origin, they give,
at the same time, an occasion better to explain their own nature.

                             * * * *

            FIRST PART OF THE TRANSCENDENTAL PROBLEM:
                HOW IS PURE MATHEMATICS POSSIBLE?

     Here is a great and established branch of knowledge,
encompassing even now a wonderfully large domain and promising an
unlimited extension in the future. Yet it carries with it
thoroughly apodictical certainty, i.e., absolute necessity, which
therefore rests upon no empirical grounds. Consequently it is a
pure product of reason, and moreover is thoroughly synthetical.
[Here the question arises:] "How then is it possible for human
reason to produce a cognition of this nature entirely a priori?"

     Does not this faculty [which produces mathematics], as it
neither is nor can be based upon experience, presuppose some
ground of cognition a priori, which lies deeply hidden, b,.--,
which might reveal itself by these its effects, if their first
beginnings were but diligently ferreted out?

     Sect. 7. But we find that all mathematical cognition has
this peculiarity: it must first exhibit its concept in a visual
form [Anschauung] and indeed a priori, therefore in a visual form
which is not empirical, but pure. Without this mathematics cannot
take a single step; hence its judgments are always visual, viz.,
"Intuitive"; whereas philosophy must be satisfied with discursive
judgments from mere concepts, and though it may illustrate its
doctrines through a visual figure, can never derive them from it.
This observation on the nature of mathematics gives us a clue to
the first and highest condition of its possibility, which is,
that some non-sensuous visualization [called pure intuition, or
reine Anschauung] must form its basis, in which all its concepts
can be exhibited or constructed, in concrete and yet a priori. If
we can find out this pure intuition and its possibility, we may
thence easily explain how synthetical propositions a priori are
possible in pure mathematics, and consequently how this science
itself is possible. Empirical intuition [viz., sense-perception]
enables us without difficulty to enlarge the concept which we
frame of an object of intuition [or sense-perception], by new
predicates, which intuition [i.e., sense-perception] itself
presents synthetically in experience. Pure intuition [viz., the
visualization of forms in our imagination, from which every thing
sensual, i.e., every thought of material qualities, is excluded]
does so likewise, only with this difference, that in the latter
case the synthetical judgment is a priori certain and
apodictical, in the former, only a posteriori and empirically
certain; because this latter contains only that which occurs in
contingent empirical intuition, but the former, that which must
necessarily be discovered in pure intuition. He.-e intuition,
being an intuition a priori, is before all experience, viz.,
before any perception of particular objects, inseparably
conjoined with its concept.

     Sect. 8. But with this step our perplexity seems rather to
increase than to lessen. For the question now is, "How is it
possible to intuit [in a visual form] anything a priori" An
intuition [viz., a visual sense perception] is such a
representation as immediately depends upon the presence of the
object. Hence it seems impossible to intuit from the outset a
priori, because intuition would in that event take place without
either a former or a present object to refer to, and by
consequence could not be intuition. Concepts indeed are such,
that we can easily form some of them a priori, viz., such as
contain nothing but the thought of an object in general; and we
need not find ourselves in an immediate relation to the object.
Take, for instance, the concepts of Quantity, of Cause, etc. But
even these require, in order to make them understood, a certain
concrete use-that is, an application to some sense-experience
[Anschauung], by which an object of them is given us. But how can
the intuition of the object [its visualization] precede the
object itself?

     Sect. 9. If our intuition [i.e., our sense-experience] were
perforce of such a nature as to represent things as they are in
themselves, there would not be any intuition a priori, but
intuition would be always empirical. For I can only know what is
contained in the object in itself when it is present and given to
me. It is indeed even then incomprehensible how the visualizing
[Anschauung] of a present thing should make me know this thing as
it is in itself, as its properties cannot migrate into my faculty
of representation. But even granting this possibility, a
visualizing of that sort would not take place a priori, that is,
before the object were presented to me; for without this latter
fact no reason of a relation between my representation and the
object can be imagined, unless it depend upon a direct
inspiration.

     Therefore in one way only can my intuition [Anschauung]
anticipate the actuality of the object, and be a cognition a
priori, viz.: if my intuition contains nothing but the form of
sensibility, antedating in my subjectivity all the actual
impressions through which I am affected by objects.

     For that objects of sense can only be intuitd according to
this form of sensibility I can know a priori. Hence it follows:
that propositions, which concern this form of sensuous intuition
only, are possible and valid for objects of the senses; as also,
conversely, that intuitions which are possible a priori can never
concern any other things than objects of our senses.7

     Sect. 10. Accordingly, it is only the form of sensuous
intuition by which we can intuit things a priori, but by which we
can know objects only as they appear to us (to our senses), not
as they are in themselves; and this assumption is absolutely
necessary if synthetical propositions a priori be granted as
possible, or if, in case they actually occur, their possibility
is to be comprehended and determined beforehand.

     Now, the intuitions which pure mathematics lays at the
foundation of all its cognitions and judgments which appear at
once apodictic and necessary are Space and Time. For mathematics
must first have all its concepts in intuition, and pure
mathematics in pure intuition, that is, it must construct them.
If it proceeded in any other way, it would be impossible to make
any headway, for mathematics proceeds, not analytically by
dissection of concepts, but synthetically, and if pure intuition
be wanting, there is nothing in which the matter for synthetical
judgments a priori can be given. Geometry is based upon the pure
intuition of space. Arithmetic accomplishes its concept of number
by the successive addition of units in time; and pure mechanics
especially cannot attain its concepts of motion without employing
the representation of time. Both representations, however, are
only intuitions; for if we omit from the empirical intuitions of
bodies and their alterations (motion) everything empirical, or
belonging to sensation, space and time still remain, which are
therefore pure intuitions that lie a priori at the basis of the
empirical. Hence they can never be omitted, but at the same time,
by their being pure intuitions a priori, they prove that they are
mere forms of our sensibility, which must precede all empirical
intuition, or perception of actual objects, and conformably to
which objects can be known a priori, but only as they appear to
us.

     Sect. 11. The problem of the present section is therefore
solved. Pure mathematics, as synthetical cognition a priori, is
only possible by referring to no other objects than those of the
senses. At the basis of their empirical intuition lies a pure
intuition (of space and of time) which is a priori. This is
possible, because the latter intuition is nothing but the mere
form of sensibility, which precedes the actual appearance of the
objects, in, that it, in fact, makes them possible. Yet this
faculty of intuiting a priori affects not the matter of the
phenomenon (that is, the sense-element in it, for this
constitutes that which is empirical), but its form, viz., space
and time. Should any man venture to doubt that these are
determinations adhering not to things in themselves, but to their
relation to our sensibility, I should be glad to know how it can
be possible to know the constitution of things a priori, viz.,
before we have any acquaintance with them and before they are
presented to us. Such, however, is the case with space and time.
But this is quite comprehensible as soon as both count for
nothing more than formal conditions of our sensibility, while the
objects count merely as phenomena; for then the form of the
phenomenon, i.e., pure intuition, can by all means be represented
as proceeding from ourselves, that is, a priori.

     Sect. 12. In order to add something by way of illustration
and confirmation, we need only watch the ordinary and necessary
procedure of geometers. All proofs of the complete congruence of
two given figures (where the one can in every respect be
substituted for the other) come ultimately to this that they may
be made to coincide; which is evidently nothing else than a
synthetical proposition resting upon immediate intuition, and
this intuition must be pure, or given a priori, otherwise the
proposition could not rank as apodictically certain, but would
have empirical certainty only. In that case, it could only be
said that it is always found to be so, and holds good only as far
as our perception reaches. That everywhere space (which (in its
entirety] is itself no longer the boundary of another space) has
three dimensions, and that space cannot in any way have more, is
based on the proposition that not more than three lines can
intersect at right angles in one point; but this proposition
cannot by any means be shown from concepts, but rests immediately
on intuition, and indeed on pure and a priori intuition, because
it is apodictically certain. That we can require a line to be
drawn to infinity (in indefinitum), or that a series of changes
(for example, spaces traversed by motion) shall be infinitely
continued, presupposes a representation of space and time, which
can only attach to intuition, namely, so far as it in itself is
bounded by nothing, for from concepts it could never be inferred.
Consequently, the basis of mathematics actually are pure
intuitions, which make its synthetical and apodictically valid
propositions possible. Hence our transcendental deduction of the
notions of space and of time explains at the same time the
possibility of pure mathematics. Without some such deduction its
truth may be granted, but its existence could by no means be
understood, and we must assume II that everything which can be
given to our senses (to the external senses in space, to the
internal one in time) is intuitd by us as it appears to us, not
as it is in itself."

     Sect. 13. Those who cannot yet rid themselves of the notion
that space and time are actual qualities inhering in things in
themselves, may exercise their acumen on the following paradox.
When they have in vain attempted its solution, and are free from
prejudices at least for a few moments, they will suspect that the
degradation of space and of time to mere forms of @ur sensuous
intuition may perhaps be well founded,

     If two things are quite equal in all respects ask much as
can be ascertained by all means possible, quantitatively and
qualitatively, it must follow, that the one can in all cases and
under all circumstances replace the other, and this substitution
would not occasion the least perceptible difference. This in fact
is true of plane figures in geometry; but some spherical figures
exhibit, notwithstanding a complete internal agreement, such a
contrast in their external relation, that the one figure cannot
possibly be put in the place of the other. For instance, two
spherical triangles on opposite hemispheres, which have an arc of
the equator as their common base, may be quite equal, both as
regards sides and angles, so that nothing is to be found in
either, if it be described for itself alone and completed, that
would not equally be applicable to both; and yet the one cannot
be put in the place of the other (being situated upon the
opposite hemisphere). Here then is an internal difference between
the two triangles, which difference our understanding cannot
describe as internal, and which only manifests itself by external
relations in space.

     But I shall adduce examples, taken from common life, that
are more obvious still.

     What can be more similar in every respect and in every part
more alike to my hand and to my ear, than their images in a
mirror? And yet I cannot put such a hand as is seen in the glass
in the place of its archetype; for if this is a right hand, that
in the glass is a left one, and the image or reflection of the
right ear is a left one which never can serve as a substitute for
the other. There are in this case no internal differences which
our understanding could determine by thinking alone. Yet the
differences are internal as the senses teach, for,
notwithstanding their complete equality and similarity, the left
hand cannot be enclosed in the same bounds as the right one (they
are not congruent); the glove of one hand cannot be used for the
other. What is the solution? These objects are not
representations of things as they are in themselves, and as the
pure understanding would know them, but sensuous intuitions, that
is, appearances, the possibility of which rests upon the relation
of certain things unknown in themselves to something else, viz.,
to our sensibility. Space is the form of the external intuition
of this sensibility, and the internal determination of every
space is only possible by the determination of its external
relation to the whole space, of which it is a part (in other
words, by its relation to the external sense). That is to say,
the part is only possible through the whole, which is never the
case with things in themselves, as objects of the mere
understanding, but with appearances only. Hence the difference
between similar and equal things, which are yet not congruent
(for instance, two symmetric helices), cannot be made
intelligible by any concept, but only by the relation to the
right and the left hands which immediately refers to intuition.

                            REMARK 1.

     Pure Mathematics, and especially pure geometry, can only
have objective reality on condition that they refer to objects of
sense. But in regard to the latter the principle holds good, that
our sense representation is not a representation of things in
themselves but of the way in which they appear to us. Hence it
follows, that the propositions of geometry are not the results of
a mere creation of our poetic imagination, and that therefore
they cannot be referred with assurance to actual objects; but
rather that they are necessarily valid of space, and consequently
of all that may be found in space, because space is nothing else
than the form of all external appearances, and it is this form
alone in which objects of sense can be given. Sensibility, the
form of which is the basis of geometry, is that upon which the
possibility of external appearance depends. Therefore these
appearances can never contain anything but what geometry
prescribes to them.

     It would be quite otherwise if the senses were so
constituted as to represent objects as they are in themselves.
For then it would not by any means follow from the conception of
space, which with all its properties serves to the geometer as an
a priori foundation, together with what is thence inferred, must
be so in nature. The space of the geometer would be considered a
mere fiction, and it would not be credited with objective
validity, because we cannot see how things must of necessity
agree with an image of them, which we make spontaneously and
previous to our acquaintance with them. But if this image, or
rather this formal intuition, is the essential property of our
sensibility, by means of which alone objects are given to us, and
if this sensibility represents not things in themselves, but
their appearances: we shall easily comprehend, and at the same
time indisputably prove, that all external objects of our world
of sense must necessarily coincide in the most rigorous way with
the propositions of geometry; because sensibility by means of its
form of external intuition, viz., by space, the same with which
the geometer is occupied, makes those objects at all possible as
mere appearances.

     It will always remain a remarkable phenomenon in the history
of philosophy, that there was a time, when even mathematicians,
who at the same time were philosophers, began to doubt, not of
the accuracy of their geometrical propositions so far as they
concerned space, but of their objective validity and the
applicability of this concept itself, and of all its corollaries,
to nature. They showed much concern whether a-line in nature
might not consist of physical points, and consequently that true
space in the object might consist of simple [discrete] parts,
while the space which the geometer has in his mind [being
continuous] cannot be such. They did not recognize that this
mental space renders possible the physical space, i.e., the
extension of matter; that this pure space is not at all a quality
of things in themselves, but a form of our sensuous faculty of
representation; and that all objects in space are mere
appearances, i.e., not things in themselves but representations
of our sensuous intuition. But such is the case, for the space of
the geometer is exactly the form of sensuous intuition which we
find a priori in us, and contains the ground of the possibility
of all external appearances (according to their form), and the
latter must necessarily and most rigidly agree with the
propositions of the geometer, which he draws not from any
fictitious concept, but from the subjective basis of all external
phenomena, which is sensibility itself. In this and no other way
can geometry be made secure as to the undoubted objective reality
of its propositions against all the intrigues of a shallow
Metaphysics, which is surprised at them [the geometrical
propositions], because it has not traced them to the sources of
their concepts.

                           REMARK II.

     Whatever is given us as object, must be given us in
intuition. All our intuition however takes place by means of the
senses only; the understanding intuits nothing, but only
reflects. And as we have just shown that the senses never and in
no manner enable us to know things in themselves, but only their
appearances, which are mere representations of the sensibility,
we conclude that all bodies, together with the space in which
they are, must be considered nothing but mere representations in
us, and exist nowhere but in our thoughts.' You will say: Is not
this manifest idealism?

     Idealism consists in the assertion, that there are none but
thinking beings, all other things, which we think are perceived
in intuition, being nothing but representations in the thinking
beings, to which no object external to them corresponds in fact.
Whereas I say, that things as objects of our senses existing
outside us are given, but we know nothing of what they may be in
themselves, knowing only their appearances, 1. e., the
representations which they cause in us by affecting our senses.
Consequently I grant by all means that there are bodies without
us, that is, things which, though quite unknown to us as to what
they are in themselves, we yet know by the representations which
their influence on our sensibility procures us, and which we call
bodies, a term signifying merely the appearance of the thing
which is unknown to us, but not therefore less actual. Can this
be termed idealism? It is the very contrary.

     Long before Locke's time, but assuredly since him, it has
been generally assumed and granted without detriment to the
actual existence of external things, that many of their
predicates may be said to belong not to the things in themselves,
but to their appearances, and to have no proper existence outside
our representation. Heat, color, and taste, for instance, are of
this kind. Now, if I go farther, and for weighty reasons rank as
mere appearances the remaining qualities of bodies also, which
are called primary, such as extension, place, and in general
space, with all that which belongs to it (impenetrability or
materiality, space, etc.)-no one in the least can adduce the
reason of its being inadmissible. As little as the man who admits
colors not to be properties of the object in itself, but only as
modifications of the sense of sight, should on that account be
called an idealist, so little can my system be named idealistic,
merely because I find that more, nay, A11 the properties which
constitute the intuition of a body belong merely to its
appearance.

     The existence of the thing that appears is thereby not
destroyed, as in genuine idealism, but it is only shown, that we
cannot possibly know it by the senses as it is in itself.

     I should be glad to know what my assertions must be in order
to avoid all idealism. Undoubtedly, I should say, that the
representation of space is not only perfectly conformable to the
relation which our sensibility has to objects-that I have said-
but that it is quite similar to the object,-an assertion in which
I can find as little meaning as if I said that the sensation of
red has a similarity to the property of vermilion, which in me
excites this sensation.

                           REMARK III.

     Hence we may at once dismiss an easily foreseen but futile
objection, "that by admitting the ideality of space and of time
the whole sensible world would be turned into mere sham." At
first all philosophical insight into the nature of sensuous
cognition was spoiled, by making the sensibility merely a
confused mode of representation, according to which we still know
things as they are, but without being able to reduce everything
in this our representation to a clear consciousness; whereas
proof is offered by us that sensibility consists, not in this
logical distinction of clearness and obscurity, but in the
genetical one of the origin of cognition itself. For sensuous
perception represents things not at all as they are, but only the
mode in which they affect our senses, and consequently by
sensuous perception appearances only and not things themselves
are given to the understanding for reflection. After this
necessary corrective, an objection rises from an unpardonable and
almost intentional misconception, as if my doctrine turned all
the things of the world of sense into mere illusion.

     When an appearance is given us, we are still quite free as
to how we should judge the matter. The appearance depends upon
the senses, but the judgment upon the understanding, and the only
question is, whether in the determination of the object there is
truth or not. But the difference between truth and dreaming is
not ascertained by the nature of the representations, which are
referred to objects (for they are the same in both cases), but by
their connection according to those rules, which determine the
coherence of the representations in the concept of an object, and
by ascertaining whether they can subsist together in experience
or not. And it is not the fault of the appearances if our
cognition takes illusion for truth, i.e., if the intuition, by
which an object is given us, is considered a concept of the thing
or of its existence also, which the understanding can only think.
The senses represent to us the paths of the planets as now
progressive, now retrogressive, and herein is neither falsehood
nor truth, because as long as we hold this path to be nothing but
appearance, we do not judge of the objective nature of their
motion. But as a false judgment may easily arise when the
understanding is not on its guard against this subjective mode of
representation being considered objective, we say they appear to
move backward; it is not the senses however which must be charged
with the illusion, but the understanding, whose province alone it
is to give an objective judgment on appearances.

     Thus, even if we did not at all reflect on the origin of our
representations, whenever we connect our intuitions of sense
(whatever they may contain), in space and in time, according to
the rules of the coherence of all cognition in experience,
illusion or truth will arise according as we are negligent or
careful. It is merely a question of the use of sensuous
representations in the understanding, and not of their origin. In
the same way, if I consider all the representations of the
senses, together with their form, space and time, to be nothing
but appearances, and space and time to be a mere form of the
sensibility, which is not to be met with in objects out of it,
and if I make use of these representations in reference to
possible experience only, there is nothing in my regarding them
as appearances that can lead astray or cause illusion. For all
that they can correctly cohere according to rules of truth in
experience. Thus all the propositions of geometry hold good of
space as well as of all the objects of the senses, consequently
of all possible experience, whether I consider space as a mere
form of the sensibility, or as something cleaving to the things
themselves. In the former case however I comprehend how I can
know a priori these propositions concerning all the objects of
external intuition. Otherwise, everything else as regards all
possible experience remains just as if I had not departed from
the vulgar view.

     But if I venture to go beyond all possible experience with
my notions of space and time, which I cannot refrain from doing
if I proclaim them qualities inherent in things in themselves
(for what should prevent me from letting them hold good of the
same things, even though my senses might be different, and
unsuited to them?), then a grave error may arise due to illusion,
for thus I would proclaim to be universally valid what is merely
a subjective condition of the intuition of things and sure only
for all objects of sense, viz., for all possible experience; I
would refer this condition to things in themselves, and do not
limit it to the conditions of experience.

     My doctrine of the ideality of space and of time, therefore,
far from reducing the whole sensible world to mere illusion, is
the only means of securing the application of one of the most
important cognitions (that which mathematics propounds a priori)
to actual objects, and of preventing its being regarded as mere
illusion. For without this observation it would be quite
impossible to make out whether the intuitions of space and time,
which we borrow from no experience, and which yet lie in our
representation a priori, are not mere phantasms of our brain, to
which objects do not correspond, at least not adequately, and
consequently, whether we have been able to show its
unquestionable validity with regard to all the objects of the
sensible world just because they are mere appearances.

     Secondly, though these my principles make appearances of the
representations of the senses, they are so far from turning the
truth of experience into mere illusion, that they are rather the
only means of preventing the transcendental illusion, by which
metaphysics has hitherto been deceived, leading to the childish
endeavor of catching at bubbles, because appearances, which are
mere representations, were taken for things in themselves. Here
originated the remarkable event of the antimony of Reason which I
shall mention by and by, and which is destroyed by the single
observation, that appearance, as long as it is employed in
experience, produces truth, but the moment it transgresses the
bounds of experience, and consequently becomes transcendent,
produces nothing but illusion.

     Inasmuch therefore, as I leave to things as we obtain them
by the senses their actuality, and only limit our sensuous
intuition of these things to this, that they represent in no
respect, not even in the pure intuitions of space and of time,
anything more than mere appearance of those thin-s, but never
their constitution in themselves, this is not a sweeping illusion
invented for nature by me. My protestation too against all
charges of idealism is so valid and clear as even to seem
superfluous, were there not incompetent judges, who, while they
would have an old name for every deviation from their perverse
though common opinion, and never judge of the spirit of
philosophic nomenclature, but cling to the letter only, are ready
to put their own conceits in the place of well-defined notions,
and thereby deform and distort them. I have myself given this my
theory the name of transcendental idealism, but that cannot
authorize any one to confound it either with the empirical
idealism of Descartes, (indeed, his was only an insoluble
problem, owing to which he thought every one at liberty to deny
the existence of the corporeal world, because it could never be
proved satisfactorily), or with the mystical and visionary
idealism of Berkeley, against which and other similar phantasms
our Critique contains the proper antidote. My idealism concerns
not the existence of things (the doubting of which, however,
constitutes idealism in the ordinary sense), since it never came
into my head to doubt it, but it concerns the sensuous
representation of things, to which space and time especially
belong. Of these [viz., space and time], consequently of all
appearances in general, I have only shown, that they are neither
things (but mere modes of representation), nor determinations
belonging to things in themselves. But the word "transcendental,"
which with me means a reference of our cognition, i.e., not to
things, but only to the cognitive faculty, was meant to obviate
this misconception. Yet rather than give further occasion to it
by this word, I now retract it, and desire this idealism of mine
to be called critical. But if it be really an objectionable
idealism to convert actual thin.-Is (not appearances) into mere
representations.. by what name shall we call him who conversely
changes mere representations to things? It may, I think, be
called "dreaming idealism," in contradistinction to the former,
which may be called "visionary," both of which are to be refuted
by my transcendental, or, better, critical idealism.

                             * * * *
                                
           SECOND PART OF THE TRANSCENDENTAL PROBLEM:
             HOW IS THE SCIENCE OF NATURE POSSIBLE?

                                
     Sect. 14. Nature is the existence of things, so far as it is
determined according to universal laws. Should nature signify the
existence of things in themselves, we could never know it either
a priori or a posteriori. Not a priori, for how can we know what
belongs to things in themselves, since this never can be done by
the dissection of our concepts (in analytical judgments)? We do
not want to know what is contained in our concept of a thing (for
the [concept describes what] belongs to its logical being), but
what is in the actuality of the thing superadded to our concept,
and by what the thing itself is determined in its existence
outside the concept. Our understanding, and the conditions on
which alone it can connect the determinations of things in their
existence, do not prescribe any rule to things themselves; these
do not conform to our understanding, but it must conform itself
to them; they must therefore be first given us in order to gather
these determinations from them, wherefore they would not be known
a priori.

     A cognition of the nature of things in themselves a
posteriori would be equally impossible. For, if experience is to
teach us laws, to which the existence of things is subject, these
laws, if they regard things in themselves, must belong to them of
necessity even outside our experience. But experience teaches us
what exists and how it exists, but never that it must necessarily
exist so and not otherwise. Experience therefore can never teach
us the nature of things in themselves.

     Sect. 15. We nevertheless actually possess a pure science of
nature in which are propounded, a priori and with all the
necessity requisite to apodictical propositions, laws to which
nature is subject. I need only call to witness that propaedeutic
of natural science which, under the title of the universal
Science of Nature, precedes all Physics (which is founded upon
empirical principles). In it we have Mathematics applied to
appearance, and also merely discursive principles (or those
derived from concepts), which constitute the philosophical part
of the pure cognition of nature. But there are several things in
it, which are not quite pure and independent of empirical
sources: such as the concept of motion, that of impenetrability
(upon which the empirical concept of matter rests), that of
inertia, and many others, which prevent its being called a
perfectly pure science of nature. Besides, it only refers to
objects of the external sense and therefore does not give an
example of a universal science of nature, in the strict sense,
for such a science must reduce nature in general, whether it
regards the object of the external or that of the internal sense
(the object of Physics as well as Psychology), to universal laws.
But among the principles of this universal physics there are a
few which actually have the required universality; for instance,
the propositions that "substance is permanent, " and that "every
event is determined by a cause according to constant laws," etc.
These are actually universal laws of nature, which subsist
completely a priori. There is then in fact a pure science of
nature, and the question arises, How is it possible?

     Sect. 16. The word "nature" assumes yet another meaning,
which determines the object, whereas in the former sense it only
denotes the conformity to law [Gesetzmdssigkeit] of the
determinations of the existence of things generally. If we
consider it materialiter (i.e., in the matter that forms its
objects) "nature is the complex of all the objects of
experience." And with this only are we now concerned, for
besides, things which can never be objects of experience, if they
must be known as to their nature, would oblige us to have
recourse to concepts whose meaning could never be given in
concrete (by any example of possible experience). Consequently we
must form for ourselves a list of concepts of their nature, the
reality whereof (i.e., whether they actually refer to objects, or
are mere creations of thought) could never be determined. The
cognition of what cannot be an object of experience would be
hyperphysical, and with things hyperphysical we are here not
concerned, but only with the cognition of nature, the actuality
of which can be confirmed by experience, though it [the cognition
of nature] is possible a priori and precedes all experience.

     Sect. 17. The formal [aspect] of nature in this narrower
sense is therefore the conformity to law of all the objects of
experience, and so far as it is known a priori, their necessary
conformity. But it has just been shown that the laws of nature
can never be known a priori in objects so far as they are
considered not in reference to possible experience, but as things
in themselves. And our inquiry here extends not to things in
themselves (the properties of which we pass by), but to things as
objects of possible experience, and the complex of these is what
we properly designate as nature. And now I ask, when the
possibility of a cognition of nature a priori is in question,
whether it is better to arrange the problem thus: How can we know
a priori that things as objects of experience necessarily conform
to law? or thus: How is it possible to know a priori the
necessary conformity to law of experience itself as regards all
its objects generally?

     Closely considered, the solution of the problem, represented
in either way, amounts, with regard to the pure cognition of
nature (which is the point of the question at issue), entirely to
the same thing. For the subjective laws, under which alone an
empirical cognition of things is possible, hold good of these
things, as objects of possible experience (not as things in
themselves, which are not considered here). Either of the
following statements means quite the same: "A judgment of
observation can never rank as experience, without the law, that
'whenever an event is observed, it is always referred to some
antecedent, which it follows according to a universal rule'";
alternatively, "Everything, of which experience teaches that it
happens, must have a cause."

     It is, however, more commendable to choose the first
formula. For we can a priori and previous to all given objects
have a cognition of those conditions, on which alone experience
is possible, but never of the laws to which things may in
themselves be subject, without reference to possible experience.
We cannot therefore study the nature of things a priori otherwise
than by investigating the conditions and the universal (though
subjective) laws, under which alone such a cognition as
experience (as to mere form) is possible, and we determine
accordingly the possibility of things, as objects of experience.
For if I should choose the second formula, and seek the
conditions a priori, on which nature as an object of experience
is possible, I might easily fall into error, and fancy that I was
speaking of nature as a thing in itself, and then move round in
endless circles, in a vain search for laws concerning things of
which nothing is given me.

     Accordingly we shall here be concerned with experience only,
and the universal conditions of its possibility which are given a
priori. Thence we shall determine nature as the whole object of
all possible experience. I think it will be understood that I
here do not mean the rules of the observation of a nature that is
already given, for these already presuppose experience. I do not
mean how (through experience) we can study the laws of nature;
for these would not then be laws a priori, and would yield us no
pure science of nature; but [I mean to ask] how the condi. tions
a priori of the possibility of experience are at the same time
the sources from which all the universal laws of nature must be
derived.

     Sect. 18. In the first place we must state that, while all
judgments of experience [Erfahrungsurtheile] are empirical (i.e.,
have their ground in immediate senseperception), vice versa, all
empirical judgments [empirische Urtheile] are not judgments of
experience, but, besides the empirical, and in general besides
what is given to the sensuous intuition, particular concepts must
yet be superadded-concepts which have their origin quite a priori
in the pure understanding, and under which every perception must
be first of all subsumed and then by their means changed into
experience.8

     Empirical judgments, so far as they have objective validity,
are judgments of experience; but those which are only
subjectively valid, I name mere judgments of perception. The
latter require no pure concept of the understanding, but only the
logical connection of perception in a thinking subject. But the
former always require, besides the representation of the sensuous
intuition, particular concepts originally begotten in the
understanding, which produce the objective validity of the
judgment of experience.

     All our judgments are at first merely judgments of
perception; they hold good only for us (i.e., for our subject),
and we do not till afterwards give them a new reference (to an
object), and desire that they shall always hold good for us and
in the same way for everybody else; for when a judgment agrees
with an object, all judgments concerning the same object must
likewise agree among themselves, and thus the objective validity
of the judgment of experience signifies nothing else than its
necessary universality of application. And conversely when we
have reason to consider a judgment necessarily universal (which
never depends upon perception, but upon the pure concept of the
understanding, under which the perception is subsumed), we must
consider it objective also, that is, that it expresses not merely
a reference of our perception to a subject, but a quality of the
object. For there would be no reason for the judgments of other
men necessarily agreeing with mine, if it were not the unity of
the object to which they all refer, and with which they accord;
hence they must all agree with one another.

     Sect. 19. Therefore objective validity and necessary
universality (for everybody) are equivalent terms, and though we
do not know the object in itself, yet when we consider a judgment
as universal, and also necessary, we understand it to have
objective validity. By this judgment we know the object (though
it remains unknown as it is in itself) by the universal and
necessary connection of the given perceptions. As this is the
case with all objects of sense, judgments of experience take
their objective validity not from the immediate cognition of the
object (which is impossible), but from the condition of universal
validity in empirical judgments, which, as already said, never
rests upon empirical, or, in short, sensuous conditions, but upon
a pure concept of the understanding. The object always remains
unknown in itself; but when by the concept of the understanding
the connection of the representations of the object, which are
given to our sensibility, is determined as universally valid, the
object is determined by this relation, and it is the judgment
that is objective.

     To illustrate the matter: When we say, "the room is warm,
sugar sweet, and wormwood bitter,"9 -- we have only subjectively
valid judgments, I do not at all expect that I or any other
person shall always find it as I now do; each of these sentences
only expresses a relation of two sensations to the same subject,
to myself, and that only in my present state of perception;
consequently they are not valid of the object. Such are judgments
of perception. judgments of experience are of quite a different
nature. What experience teaches me under certain circumstances,
it must always teach me and everybody; and its validity is not
limited to the subject nor to its state at a particular time.
Hence I pronounce all such judgments as being objectively valid.
For instance, when I say the air is elastic, this judgment is as
yet a judgment of perception only-I do nothing but refer two of
my sensations to one another. But, if I would have it called a
judgment of experience, I require this connection to stand under
a condition, which makes it universally valid. I desire therefore
that I and everybody else should always connect necessarily the
same perceptions under the same circumstances.

     Sect. 20. We must consequently analyze experience in order
to see what is contained in this product of the senses and of the
understanding, and how the judgment of experience itself is
possible. The foundation is the intuition of which I become
conscious, i.e., perception (perceptio), which pertains merely to
the senses. But in the next place, there are acts of judging
(which belong only to the understanding). But this judging may be
twofold-first, I may merely compare perceptions and connect them
in a particular state of my consciousness; or, secondly, I may
connect them in consciousness generally. The former judgment is
merely a judgment of perception, and of subjective validity only:
it is merely a connection of perceptions in my mental state,
without reference to the object. Hence it is not, as is commonly
imagined, enough for experience to compare perceptions and to
connect them in consciousness through judgment; there arises no
universality and necessity, for which alone judgments can become
objectively valid and be called experience.

     Quite another judgment therefore is required before
perception can become experience. The given intuition must be
subsumed under a concept, which determines the form of judging in
general relatively to the intuition, connects its empirical
consciousness in consciousness generally, and thereby procures
universal validity for empirical judgments. A concept of this
nature is a pure a priori concept of the Understanding, which
does nothing but determine for an intuition the general way in
which it can be used for judgments. Let the concept be that of
cause, then it determined the intuition which is subsumed under
it, e.g., that of air, relative to judgments in general, viz.,
the concept of air serves with regard to its expansion in the
relation of antecedent to consequent in a hypothetical judgment.
The concept of cause accordingly is a pure concept of the
understanding, which is totally disparate from all possible
perception, and only serves to determine the representation
subsumed under it, relatively to judgments in general, and so to
make a universally valid judgment possible.

     Before, therefore, a judgment of perception can become a
judgment of experience, it is requisite that the perception
should be subsumed under some such a concept of the
understanding.; for instance, air ranks under the concept of
causes, which determines our judgment about it in regard to its
expansion as hypothetical.10 Thereby the expansion of the air is
represented not as merely belonging to the perception of the air
in my present state or in several states of mine, or in the state
of perception of others, but as belonging to it necessarily. The
judgment, "the air is elastic," becomes universally valid, and a
judgment of experience, only by certain judgments preceding it,
which subsume the intuition of air under the concept of cause and
effect: and they thereby determine the perceptions not merely as
regards one another in me, but relatively to the form of judging
in general, which is here hypothetical, and in this way they
render the empirical judgment universally valid.

     If all our synthetical judgments are analyzed so far as they
are objectively valid, it will be found that they never consist
of mere intuitions connected only (as is commonly believed) by
comparison into a judgment; but that they would be impossible
were not a pure concept of the understanding superadded to the
concepts abstracted from intuition, under which concept these
latter are subsumed, and in this manner only combined into an
objectively valid judgment. Even the judgments of pure
mathematics in their simplest axioms are not exempt from this
condition. The principle, II a straight line is the shortest
between two points," presupposes that the line is subsumed under
the concept of quantity, which certainly is no mere intuition,
but bas its seat in the understanding alone, and serves to
determine the intuition (of the line) with regard to the
judgments which may be made about it, relatively to their
quantity, that is, to plurality (as judicia plurativa).11 For
under them it is understood that in a given intuition there is
contained a plurality of homogenous parts.

     Sect. 21. To prove, then, the possibility of experience so
far as it rests upon pure concepts of the understanding a priori,
we must first represent what belongs to judgments in general and
the various functions of the understanding, in a complete table.
For the pure concepts of the understanding must run parallel to
these functions, as such concepts are nothing more than concepts
of intuitions in general, so far as these are determined by one
or other of these functions of judging, in themselves, that is,
necessarily and universally. Hereby also the a priori principles
of the possibility of all experience, as of an objectively valid
empirical cognition, will be precisely determined. For they are
nothing but propositions by which all perception is (under
certain universal conditions of intuition) subsumed under those
pure concepts of the understanding.

LOGICAL TABLE OF JUDGMENTS.

1. As to Quantity.
     Universal.
     Particular.
     Singular.

2. As to Quality.
     Affirmative.
     Negative.
     Infinite.

3. As to Relation.
     Categorical.
     Hypothetical.
     Disjunctive.

4. As to Modality.
     Problematical.
     Assertorical.
     Apodictical.

TRANSCENDENTAL TABLE OF THE PURE CONCEFITS OF THE UNDERSTANDING.

1 . As to Quantity.
     Unity (the Measure).
     Plurality (the Quantity).
     Totality (the Whole).

2. As to Quality.
     Reality.
     Negation.
     Limitation.

3. As to Relation.
     Substance.
     Cause.
     Community.

4. As to Modality.
      Possibility.
     Existence.
     Necessity.

PURE PHYSICAL TABLE OF THE UNIVERSAL PRINCIPLES OF THE SCIENCE OF
NATURE.

1. Axioms of Intuition.
2. Anticipations of Perception.
3. Analogies of Experience.
4. Postulates of Empirical Thinking generally.

     Sect. 21a. In order to comprise the whole matter in one
idea, it is first necessary to remind the reader that we are
discussing not the origin of experience, but of that which lies
in experience. The former pertains to empirical psychology, and
would even then never be adequately explained without the latter,
which belongs to the Critique of cognition, and particularly of
the understanding.

     Experience consists of intuitions, which belong to the
sensibility, and of judgments, which are entirely a work of the
understanding. But the judgments, which the understanding forms
alone from sensuous intuitions, are far from being judgments of
experience. For in the one case the judgment connects only the
perceptions as they are given in the sensuous intuition, while in
the other the judgments must express what experience in general,
and not what the mere perception (which possesses only subjective
validity) contains. The judgment of experience must therefore add
to the sensuous intuition and its logical connection in a
judgment (after it has been rendered universal by comparison)
something that determines the synthetical judgment as necessary
and therefore as universally valid. This can be nothing else than
that concept which represents the intuition as determined in
itself with regard to one form of judgment rather than another,
viz., a concept of that synthetical unity of intuitions which can
only be represented by a given logical function of judgments.

     Sect. 22. The sum of the matter is this: the business of the
senses is to intuit -- that of the understanding is to think. But
thinking is uniting representations in one consciousness. This
union originates either merely relative to the subject, and is
accidental and subjective, or is absolute, and is necessary or
objective. The union of representations in one consciousness is
judgment. Thinking therefore is the same as judging, or referring
representations to judgments in general. Hence judgments are
either merely subjective, when representations are referred to a
consciousness in one subject only, and united in it, or
objective, when they are united in a consciousness generally,
that is, necessarily. The logical functions of all judgments are
but various modes of uniting representations in consciousness.
But if they serve for concepts, they are concepts of their
necessary union in a consciousness, and so principles of
objectively valid judgments. This union in a consciousness is
either analytical, by identity, or synthetical, by the
combination and addition of various representations one to
another. Experience consists in the synthetical connection of
phenomena (perceptions) in consciousness, so far as this
connection is necessary. Hence the pure concepts of the
understanding are those under which all perceptions must be
subsumed ere they can serve for judgments of experience, in which
the synthetical unity of the perceptions is represented as
necessary and universally valid.12

     Sect. 23. judgments, when considered merely as the condition
of the union of given representations in a consciousness, are
rules. These rules, so far as they represent the union as
necessary, are rules a priori, and so far as they cannot be
deduced from higher rules, are fundamental principles. But in
regard to the possibility of all experience, merely in relation
to the form of thinking in it, no conditions of judgments of
experience are higher than those which bring the phenomena,
according to the various form of their intuition, under pure
concepts of the understanding, and render the empirical judgment
objectively valid. These concepts are therefore the a priori
principles of possible experience.

     The principles of possible experience are then at the same
time universal laws of nature, which can be known a priori. And
thus the problem in our second question, "How is the pure Science
of Nature possible?" is solved. For the system which is required
for the form of a science is to be met with in perfection here,
because, beyond the above-mentioned formal conditions of all
judgments in general offered in logic, no others are possible,
and these constitute a logical system. The concepts grounded
thereupon, which contain the a priori conditions of all
synthetical and necessary judgments, accordingly constitute a
transcendental system. Finally the principles, by means of which
all phenomena are subsumed under these concepts, constitute a
physical13 system, that is, a system of nature, which precedes
all empirical cognition of nature, makes it even possible, and
hence may in strictness be denominated the universal and pure
science of nature.

     Sect. 24. The first one14 of the physiological principles
subsumes all phenomena, as intuitions in space and time, under
the concept of Quantity, and is so far a principle of the
application of Mathematics to experience. The second one subsumes
the empirical element, viz., sensation, which denotes the real in
intuitions, not indeed directly under the concept of quantity,
because sensation is not an intuition that contains either space
or time, though it places the respective object into both. But
still there is between reality (sense-representation) and the
zero, or total void of intuition in time, a difference which has
a quantity. For between every given degree of light and of
darkness, between every degree of beat and of absolute cold,
between every degree of weight and of absolute lightness, between
every degree of occupied space and of totally void space,
diminishing degrees can be conceived, in the same manner as
between consciousness and total unconsciousness (the darkness of
a psychological blank) ever diminishing degrees obtain. Hence
there is no perception that can prove an absolute absence of it;
for instance, no psychological darkness that cannot be considered
as a kind of consciousness, which is only out-balanced by a
stronger consciousness. This occurs in all cases of sensation,
and so the understanding can anticipate even sensations, which
constitute the peculiar quality of empirical representations
(appearances), by means of the principle: "that they all have
(consequently that what is real in all phenomena has) a degree."
Here is the second application of mathematics (mathesis
intensortim) to the science of nature.

     Sect. 25. Anent the relation of appearances merely with a
view to their existence, the determination is not mathematical
but dynamical, and can never be objectively valid, consequently
never fit for experience, if it does not come under a priori
principles by which the cognition of experience relative to
appearances becomes even possible. Hence appearances must be
subsumed under the concept of Substance, which is the foundation
of all determination of existence, as a concept of the thing
itself; or secondly so far as a succession is found among
phenomena, that is, an event-under the concept of an Effect with
reference to Cause; or lastly-so far as coexistence is to be
known objectively, that is, by a judgment of experience-under the
concept of Community (action and reaction).15 Thus a priori
principles form the basis of objectively valid, though empirical
judgments, that is, of the possibility of experience so far as it
must connect objects as existing in nature. These principles are
the proper laws of nature, which may be termed dynamical.

     Finally the cognition of the agreement and connection not
only of appearances among themselves in experience, but of their
relation to experience in general, belongs to the judgments of
experience. This relation contains either their agreement with
the formal conditions, which the understanding knows, or their
coherence with the materials of the senses and of perception, or
combines both into one concept. Consequently it contains
Possibility, Actuality, and Necessity according to universal laws
of nature; and this constitutes the physical doctrine of method,
or the distinction of truth and of hypotheses, and the bounds of
the certainty of the latter.

     Sect. 26. The third table of Principles drawn from the
nature of the understanding itself after the critical method,
shows an inherent perfection, which raises it far above every
other table which has hitherto though in vain been tried or may
yet be tried by analyzing the objects themselves dogmatically. It
exhibits all synthetical a priori principles completely and
according to one principle, viz., the faculty of judging in
general, constituting the essence of experience as regards the
understanding, so that we can be certain that there are no more
such principles, which affords a satisfaction such as can never
be attained by the dogmatical method. Yet is this not all: there
is a still greater merit in it.

     We must carefully bear in mind the proof which shows the
possibility of this cognition a priori, and at the same time
limits all such principles to a condition which must never be
lost sight of, if we desire it not to be misunderstood, and
extended in use beyond the original sense which the understanding
attaches to it. This limit is that they contain nothing but the
conditions of possible experience in general so far as it is
Subjected to laws a priori. Consequently I do not say, that
things in themselves possess a quantity, that their actuality
possesses a degree, their existence a connection of accidents in
a substance, etc. This nobody can prove, because such a
synthetical connection from mere concepts, without any reference
to sensuous intuition on the one side, or connection of it in a
possible experience on the other, is absolutely impossible. The
essential limitation of the concepts in these principles then is:
That all things stand necessarily a priori under the
aforementioned conditions, as objects of experience only.

     Hence there follows secondly a specifically peculiar mode of
proof of these principles: they are not directly referred to
appearances and to their relations, but to the possibility of
experience, of which appearances constitute the matter only, not
the form. Thus they are referred to objectively and universally
valid synthetical propositions, in which we distinguish judgments
of experience from those of perception. This takes place because
appearances, as mere intuitions, occupying a part of space and
time, come under the concept of Quantity, which unites their
multiplicity a priori according to rules synthetically. Again, so
far as the perception contains, besides intuition, sensibility,
and between the latter and nothing (i.e., the total disappearance
of sensibility), there is an ever-decreasing transition, it is
apparent that that which is in appearances must have a degree, so
far as it (viz., the perception) does not itself occupy any part
of space or of time.16 Still the transition to actuality from
empty time or empty space is only possible in time; consequently
though sensibility, as the quality of empirical intuition, can
never be known a priori, by its specific difference from other
sensibilities, yet it can, in a possible experience in general,
as a quantity of perception be intensely distinguished from every
other similar perception. Hence the application of mathematics to
nature, as regards the sensuous intuition by which nature is
given to us, becomes possible and is thus determined.

     Above all, the reader must pay attention to the mode of
proof of the principles which occur under the title of Analogies
of experience. For these do not refer to the genesis of
intuitions, as do the principles of applied mathematics, but to
the connection of their existence in experience; and this can be
nothing but the determination of their existence in time
according to necessary laws, under which alone the connection is
objectively valid, and thus becomes experience. The proof
therefore does not turn on the synthetical unity in the
connection of things in themselves, but merely of perceptions,
and of these not in regard to their matter, but to the
determination of time and of the relation of their existence in
it, according to universal laws. If the empirical determination
in relative time is indeed objectively valid (i.e., experience),
these universal laws contain the necessary determination of
existence in time generally (viz., according to a rule of the
understanding a priori).

     In these Prolegomena I cannot further descant on the
subject, but my reader (who has probably been long accustomed to
consider experience a mere empirical synthesis of perceptions,
and hence not considered that it goes much beyond them, as it
imparts to empirical judgments universal validity, and for that
purpose requires a pure and a priori unity of the understanding)
is recommended to pay special attention to this distinction of
experience from a mere aggregate of perceptions, and to judge the
mode of proof from this point of view.

     Sect. 27. Now we are prepared to remove Hume's doubt. He
justly maintains, that we cannot comprehend by reason the
possibility of Causality, that is, of the reference of the
existence of one thing to the existence of another, which is
necessitated by the former. I add, that we comprehend just as
little the concept of Subsistence, that is, the necessity that at
the foundation of the existence of things there lies a subject
which cannot itself be a predicate of any other thing; nay, we
cannot even form a notion of the possibility of such a thing
(though we can point out examples of its use in experience). The
very same incomprehensibility affects the Community of things, as
we cannot comprehend bow from the state of one thing an inference
to the state of quite another thing beyond it, and vice versa,
can be drawn, and how substances which have each their own
separate existence should depend upon one another necessarily.
But I am very far from holding these concepts to be derived
merely from experience, and the necessity represented in them, to
be imaginary and a mere illusion produced in us by long habit. On
the contrary, I have amply shown, that they and the theorems
derived from them are firmly established a priori, or before all
experience, and have their undoubted objective value, though only
with regard to experience.

     Sect. 28. Though I have no notion of such a connection of
things in themselves, that they can either exist as substances,
or act as causes, or stand in community with others (as parts of
a real whole), and I can just as little conceive such properties
in appearances as such (because those concepts contain nothing
that lies in the appearances, but only what the understanding
alone must think): we have yet a notion of such a connection of
representations in our understanding, and in judgments generally;
consisting in this that representations appear in one sort of
judgments as subject in relation to predicates, in another as
reason in relation to consequences, and in a third as parts,
which constitute together a total possible cognition. Besides we
know a priori that without considering the representation of an
object as determined in some of these respects, we can have no
valid cognition of the object, and, if we should occupy ourselves
about the object in itself, there is no possible attribute, by
which I could know that it is determined under any of these
aspects, that is, under the concept either of substance, or of
cause, or (in relation to other substances) of community, for I
have no notion of the possibility of such a connection of
existence. But the question is not how things in themselves, but
how the empirical cognition of things is determined as regards
the above aspects of judgments in general, that is, how things,
as objects of experience, can and shall be subsumed under these
concepts of the understanding. And then it is clear, that I
completely comprehend not only the possibility, but also the
necessity of subsuming all phenomena under these concepts, that
is, of using them for principles of the possibility of
experience.

     Sect. 29. When making an experiment with Hume's
problematical concept (his crux metaphysicorum), the concept of
cause, we have, in the first place, given a priori, by means of
logic, the form of a conditional judgment in general, i.e., we
have one given cognition as antecedent and another as
consequence. But it is possible, that in perception we may meet
with a rule of relation, which runs thus: that a certain
phenomenon is constantly followed by another (though not
conversely), and this is a case for me to use the hypothetical
judgment, and, for instance, to say, if the sun shines long
enough upon a body, it grows warm. Here there is indeed as yet no
necessity of connection, or concept of cause. But I proceed and
say, that if this proposition, which is merely a subjective
connection of perceptions, is to be a judgment of experience, it
must be considered as necessary and universally valid. Such a
proposition would be, II the sun is by its light the cause of
heat." The empirical rule is now considered as a law, and as
valid not merely of appearances but valid of them for the
purposes of a possible experience which requires universal and
therefore necessarily valid rules. I therefore easily comprehend
the concept of cause, as a concept necessarily belonging to the
mere form of experience, and its possibility as a synthetical
union of perceptions in consciousness generally; but I do not at
all comprehend the possibility of a thing generally as a cause,
because the concept of cause denotes a condition not at all
belonging to things, but to experience. It is nothing in fact but
an objectively valid cognition of appearances and of their
succession, so far as the antecedent can be conjoined with the
consequent according to the rule of hypothetical judgments.

     Sect. 30. Hence if the pure concepts of the understanding do
not refer to objects of experience but to things in themselves
(noumena), they have no signification whatever. They serve, as it
were, only to decipher appearances, that we may be able to read
them as experience. The principles which arise from their
reference to the sensible world, only serve our understanding for
empirical use. Beyond this they are arbitrary combinations,
without objective reality, and we can neither know their
possibility a priori, nor verify their reference to objects, let
alone make it intelligible by any example; because examples can
only be borrowed from some possible experience, consequently the
objects of these concepts can be found nowhere but in a possible
experience.

     This complete (though to its originator unexpected) solution
of Hume's problem rescues for the pure concepts of the
understanding their a priori origin, and for the universal laws
of nature their validity, as laws of the understanding, yet in
such a way as to limit their use to experience, because their
possibility depends solely on the reference of the understanding
to experience, but with a completely reversed mode of connection
which never occurred to Hume, not by deriving them from
experience, but by deriving experience from them.

     This is therefore the result of all our foregoing inquiries:
"All synthetical principles a priori are nothing more than
principles of possible experience, and can never be referred to
things in themselves, but to appearances as objects of
experience. And hence pure mathematics as well as a pure science
of nature can never be referred to anything more than mere
appearances, and can only represent either that which makes
experience generally possible, or else that which, as it is
derived from these principles, must always be capable of being
represented in some possible experience."

     Sect. 31. And thus we have at last something definite, upon
which to depend in all metaphysical enterprises, which have
hitherto, boldly enough but always at random, attempted
everything without discrimination. That the aim of their
exertions should be so near, struck neither the dogmatical
thinkers nor those who, confident in their supposed sound common
sense, started with concepts and principles of pure reason (which
were legitimate and natural, but destined for mere empirical use)
in quest of fields of knowledge, to which they neither knew nor
could know any determinate bounds, because they bad never
reflected nor were able to reflect on the nature or even on the
possibility of such a pure understanding.

     Many a naturalist of pure reason (by which I mean the man
who believes he can decide in matters of metaphysics without any
science) may pretend, that lie long ago by the prophetic spirit
of his sound sense, not only suspected, but knew and
comprehended, what is here propounded with so much ado, or, if he
likes, with prolix and pedantic pomp: "that with all our reason
we can never reach beyond the field of experience." But when he
is questioned about his rational principles individually, he must
grant, that there are many of them which be has not taken from
experience, and which are therefore independent of it and valid a
priori. How then and on what grounds will he restrain both
himself and the dogmatist, who makes use of these concepts and
principles beyond all possible experience, because they are
recognized to be independent of it? And even he, this adept in
sound sense, in spite of all his assumed and cheaply acquired
wisdom, is not exempt from wandering inadvertently beyond objects
of experience into the field of chimeras. He is often deeply
enough involved in them, though in announcing everything as mere
probability, rational conjecture, or analogy, be gives by his
popular language a color to his groundless pretensions.

     Sect. 32. Since the oldest days of philosophy inquirers into
pure reason have conceived, besides the things of sense, or
appearances (phenomena), which make up the sensible world,
certain creations of the understanding (Verstandeswesen), called
noumena, which should constitute an intelligible world. And as
appearance and illusion were by those men identified (a thing
which we may well excuse in an undeveloped epoch), actuality was
only conceded to the creations of thought.

     And we indeed, rightly considering objects of sense as mere
appearances, confess thereby that they are based upon a thing in
itself, though we know not this thing in its internal
constitution, but only know its appearances, viz., the way in
which our senses are affected by this unknown something. The
understanding therefore, by assuming appearances, grants the
existence of things in themselves also, and so far we may say,
that the representation of such things as form the basis of
phenomena, consequently of mere creations of the understanding,
is not only admissible, but unavoidable.

     Our critical deduction by no means excludes things of that
sort (noumena), but rather limits the principles of the Aesthetic
(the science of the sensibility) to this, that they shall not
extend to all things, as everything would then be turned into
mere appearance, but that they shall only hold good of objects of
possible experience. Hereby then objects of the understanding are
granted, but with the inculcation of this rule which admits of no
exception: "that we neither know nor can know anything at all
definite of these pure objects of the understanding, because our
pure concepts of the understanding as well as our pure intuitions
extend to nothing but objects of possible experience,
consequently to mere things of sense, and as soon as we leave
this sphere these concepts retain no meaning whatever."

     Sect. 33. There is indeed something seductive in our pure
concepts of the understanding, which tempts us to a transcendent
use, -- a use which transcends all possible experience. Not only
are our concepts of substance, of power, of action, of reality,
and others, quite independent of experience, containing nothing
of sense appearance, and so apparently applicable to things in
themselves (noumena), but, what strengthens this conjecture, they
contain a necessity of determination in themselves, which
experience never attains. The concept of cause implies a rule,
according to which one state follows another necessarily; but
experience can only show us, that one state of things often, or
at most, commonly, follows another, an(i therefore affords
neither strict universality, nor necessity.

     Hence the Categories seem to have a deeper meaning and
import than can be exhausted by their empirical use, and so the
understanding inadvertently adds for itself to the house of
experience a much more extensive wing, which it fills with
nothing but creatures of thought, without ever observing that it
has transgressed with its otherwise lawful concepts the bounds of
their use.

     Sect. 34. Two important, and even indispensable, though very
dry, investigations had therefore become indispensable in the
Critique of Pure Reason,-viz., the two chapters "Vom Schematismus
der reinen Verstandsbegriffe," and "Vom Grunde der Unterscheidung
aller Verstandesbegriffe uberhaupt in Phenomena und Noumena. " In
the former it is shown, that the senses furnish not the pure
concepts of the understanding in concreto, but only the schedule
for their use, and that the object conformable to it occurs only
in experience (as the product of the understanding from materials
of the sensibility). In the latter it is shown, that, although
our pure concepts of the understanding and our principles are
independent of experience, and despite of the apparently greater
sphere of their use, still nothing whatever can be thought by
them beyond the field of experience, because they can do nothing
but merely determine the logical form of the judgment relatively
to given intuitions. But as there is no intuition at all beyond
the field of the sensibility, these pure concepts, as they cannot
possibly be exhibited in concrete, are void of all meaning;
consequently all these noumena, together with their complex, the
intelligible world,17 are nothing but representation of a
problem, of which the object in itself is possible, but the
solution, from the nature of our understanding, totally
impossible. For our understanding is not a faculty of intuition,
but of the connection of given intuitions in experience.
Experience must therefore contain all the objects for our
concepts; but beyond it no concepts have any significance, as
there is no intuition that might offer them a foundation.

     Sect. 35. The imagination may perhaps be forgiven for
occasional vagaries, and for not keeping carefully within the
limits of experience, since it gains life and vigor by such
flights, and since it is always easier to moderate its boldness,
than to stimulate its languor. But the understanding which ought
to think can never be forgiven for indulging in vagaries; for we
depend upon it alone for assistance to set bounds, when
necessary, to the vagaries of the imagination.

     But the understanding begins its aberrations very innocently
and modestly. It first elucidates the elementary cognitions,
which inhere in it prior to all experience, but yet must always
have their application in experience. It gradually drops these
limits, and what is there to prevent it, as it has quite freely
derived its principles from itself? And then it proceeds first to
newly-imagined powers in nature, then to beings outside nature;
in short to a world, for whose construction the materials cannot
be wanting, because fertile fiction furnishes them abundantly,
and though not confirmed, is never refuted, by experience. This
is the reason that young thinkers arc so partial to nietaph3,sics
of the truly dogmatical kind, and often sacrifice to it their
time and their talents, which might be otherwise better employed.

     But there is no use in trying to moderate these fruitless
endeavors of pure reason by all manner of cautions as to the
difficulties of solving questions so occult, by complaints of the
limits of our reason, and by degrading our assertions into mere
conjectures. For if their impossibility is not distinctly shown,
and reason's cognition of its own essence does not become a true
science, in which the field of its right use is distinguished, so
to say, with mathematical certainty from that of its worthless
and idle use, these fruitless efforts will never be abandoned for
good.

            Sect. 36. How is Nature itself possible?

     This question -- the highest point that transcendental
philosophy can ever reach, and to which, as its boundary and
completion, it must proceed-properly contains two questions.

     First: How is nature at all possible in the material sense,
by intuition, considered as the totality of appearances; how are
space, time, and that which fills both -- the object of
sensation, in general possible? The answer is: By means of the
constitution of our Sensibility, according to which it is
specifically affected by objects, which are in themselves unknown
to it, and totally distinct from those phenomena. This answer is
given in the Critique itself in the transcendental Aesthetic, and
in these Prolegomena by the solution of the first general
problem.

     Secondly: How is nature possible in the formal sense, as the
totality of the rules, under which all phenomena must come, in
order to be thought as connected in experience? The answer must
be this: it is only possible by means of the constitution of our
Understanding, according to which all the above representations
of the sensibility are necessarily referred to a consciousness,
and by which the peculiar way in which we think (viz., by rules),
and hence experience also, are possible, but must be clearly
distinguished from an insight into the objects in themselves.
This answer is given in the Critique itself in the transcendental
Logic, and in these Prolegomena, in the course of the solution of
the second main problem.

     But how this peculiar property of our sensibility itself is
possible, or that of our understanding and of the apperception
which is necessarily its basis and that of all thinking, cannot
be further analyzed or answered, because it is of them tha