Critique of Pure Reason (Phenomena and Noumena)

Immanuel Kant's
Critique
trans. by Norman Kemp Smith
P 257
TRANSCENDENTAL DOCTRINE OF JUDGMENT
 (ANALYTIC OF PRINCIPLES)
 CHAPTER III
 THE GROUND OF THE DISTINCTION OF ALL OBJECTS
 IN GENERAL INTO PHENOMENA AND NOUMENA
WE have now not merely explored the territory of pure 
understanding, and carefully surveyed every part of it, but have
also measured its extent, and assigned to everything in it its
rightful place. This domain is an island, enclosed by nature
itself within unalterable limits. It is the land of truth -- 
enchanting name! -- surrounded by a wide and stormy ocean,
the native home of illusion, where many a fog bank and many
a swiftly melting iceberg give the deceptive appearance of
farther shores, deluding the adventurous seafarer ever anew
with empty hopes, and engaging him in enterprises which
he can never abandon and yet is unable to carry to 
completion. Before we venture on this sea, to explore it in
all directions and to obtain assurance whether there be any
ground for such hopes, it will be well to begin by casting
a glance upon the map of the land which we are about
to leave, and to enquire, first, whether we cannot in any
case be satisfied with what it contains -- are not, indeed,
under compulsion to be satisfied, inasmuch as there may be
no other territory upon which we can settle; and, secondly,
by what title we possess even this domain, and can consider
ourselves as secured against all opposing claims. Although
we have already given a sufficient answer to these questions
in the course of the Analytic, a summary statement of its
solutions may nevertheless help to strengthen our conviction,
by focussing the various considerations in their bearing on
the questions now before us.
P 258
We have seen that everything which the understanding
derives from itself is, though not borrowed from experience,
at the disposal of the understanding solely for use in 
experience. The principles of pure understanding, whether 
constitutive a priori, like the mathematical principles, or merely
regulative, like the dynamical, contain nothing but what
may be called the pure schema of possible experience. For
experience obtains its unity only from the synthetic unity
which the understanding originally and of itself confers
upon the synthesis of imagination in its relation to 
apperception; and the appearances, as data for a possible knowledge,
must already stand a priori in relation to, and in agreement
with, that synthetic unity. But although these rules of
understanding are not only true a priori, but are indeed
the source of all truth (that is, of the agreement of our 
knowledge with objects), inasmuch as they contain in themselves
the ground of the possibility of experience viewed as the sum
of all knowledge wherein objects can be given to us, we are
not satisfied with the exposition merely of that which is true,
but likewise demand that account be taken of that which we
desire to know. If, therefore, from this critical enquiry we
learn nothing more than what, in the merely empirical 
employment of understanding, we should in any case have
practised without any such subtle enquiry, it would seem
as if the advantage derived from it by no means repays
the labour expended. The reply may certainly be made that
in the endeavour to extend our knowledge a meddlesome
curiosity is far less injurious than the habit of always insisting,
before entering on any enquiries, upon antecedent proof of
the utility of the enquiries -- an absurd demand, since prior
to completion of the enquiries we are not in a position to form
the least conception of this utility, even if it were placed before
our eyes. There is, however, one advantage which may be
made comprehensible and of interest even to the most refractory
and reluctant learner, the advantage, that while the
understanding, occupied merely with its empirical employment,
and not reflecting upon the sources of its own knowledge,
may indeed get along quite satisfactorily, there is yet
one task to which it is not equal, that, namely, of determining
the limits of its employment, and of knowing what it is that
P 259
may lie within and what it is that lies without its own proper
sphere. This demands just those deep enquiries which we have
instituted. If the understanding in its empirical employment
cannot distinguish whether certain questions lie within its
horizon or not, it can never be assured of its claims or of its
possessions, but must be prepared for many a humiliating
disillusionment, whenever, as must unavoidably and constantly
happen, it oversteps the limits of its own domain,
and loses itself in opinions that are baseless and 
misleading. 
If the assertion, that the understanding can employ its
various principles and its various concepts solely in an 
empirical and never in a transcendental manner, is a proposition
which can be known with certainty, it will yield important
consequences. The transcendental employment of a concept
in any principle is its application to things in general and in
themselves; the empirical employment is its application merely
to appearances; that is, to objects of a possible experience. That
the latter application of concepts is alone feasible is evident
from the following considerations. We demand in every concept,
first, the logical form of a concept (of thought) in general,
and secondly, the possibility of giving it an object to which
it may be applied. In the absence of such object, it has no
meaning and is completely lacking in content, though it may
still contain the logical function which is required for making
a concept out of any data that may be presented. Now the
object cannot be given to a concept otherwise than in intuition;
for though a pure intuition can indeed precede the object
a priori, even this intuition can acquire its object, and 
therefore objective validity, only through the empirical intuition
of which it is the mere form. Therefore all concepts, and
with them all principles, even such as are possible a priori,
relate to empirical intuitions, that is, to the data for a
possible experience. Apart from this relation they have no
objective validity, and in respect of their representations are
a mere play of imagination or of understanding. Take, for
instance, the concepts of mathematics, considering them first
of all in their pure intuitions. Space has three dimensions;
between two points there can be only one straight line, etc.
Although all these principles, and the representation of the
P 260
object with which this science occupies itself, are generated
in the mind completely a priori, they would mean nothing,
were we not always able to present their meaning in 
appearances, that is, in empirical objects. We therefore demand
that a bare concept be made sensible, that is, that an object
corresponding to it be presented in intuition. Otherwise the
concept would, as we say, be without sense, that is, without
meaning. The mathematician meets this demand by the construction
of a figure, which, although produced a priori, is an
appearance present to the senses. In the same science the
concept of magnitude seeks its support and sensible meaning
in number, and this in turn in the fingers, in the beads of the
abacus, or in strokes and points which can be placed before
the eyes. The concept itself is always a priori in origin, and
so likewise are the synthetic principles or formulas derived
from such concepts; but their employment and their relation
to their professed objects can in the end be sought nowhere
but in experience, of whose possibility they contain the formal
conditions.
 That this is also the case with all categories and the 
principles derived from them, appears from the following 
consideration. We cannot define any one of them in any real
fashion, that is, make the possibility of their object 
understandable, without at once descending to the conditions of
sensibility, and so to the form of appearances -- to which, as
their sole objects, they must consequently be limited. For if
this condition be removed, all meaning, that is, relation to the
object, falls away; and we cannot through any example make
comprehensible to ourselves what sort of a thing is to be meant
by such a concept.
++ In the above statement of the table of categories, we relieved
ourselves of the task of defining each of them, as our purpose,
which concerned only their synthetic employment, did not
require such definition, and we are not called upon to incur
any responsibility through unnecessary undertakings from
which we can be relieved.
P 261
The concept of magnitude in general can never be explained
except by saying that it is that determination of a thing
whereby we are enabled to think how many times a unit is posited
in it. But this how-many-times is based on successive repetition,
and therefore on time and the synthesis of the homogeneous
in time. Reality, in contradistinction to negation, can be 
explained only if we think time (as containing all being) as either
filled with being or as empty. If I leave out permanence (which
is existence in all time), nothing remains in the concept of 
substance save only the logical representation of a subject -- a 
representation which I endeavour to realise by representing to
myself something which can exist only as subject and never as predicate.
++ It was no evasion but an important
prudential maxim, not to embark upon the task of definition,
attempting or professing to attain completeness and precision
in the determination of a concept, so long as we can achieve our
end with one or other of its properties, without requiring a
complete enumeration of all those that constitute the 
complete concept. But we now perceive that the ground of this
precaution lies still deeper. We realise that we are unable to
define them even if we wished. For if we remove all those
conditions of sensibility which mark them out as concepts of
possible empirical employment, and view them as concepts of
things in general and therefore of transcendental employment,
all that we can then do with them is to regard the logical
function in judgments [to which they give expression] as the
condition of the possibility of the things themselves, without
in the least being able to show how they can have application
to an object, that is, how in pure understanding, apart from
sensibility, they can have meaning and objective validity.
++ I here mean real definition -- which does not merely substitute
for the name of a thing other more intelligible words, but contains
a clear property by which the defined object can always be known
with certainty, and which makes the explained concept serviceable
in application. Real explanation would be that which makes clear
not only the concept but also its objective reality. Mathematical
explanations which present the object in intuition, in conformity
with the concept, are of this latter kind.
P 262
But not only am I ignorant of any conditions under
which this logical pre-eminence may belong to anything; I
can neither put such a concept to any use, nor draw the least
inference from it. For no object is thereby determined for
its employment, and consequently we do not know whether
it signifies anything whatsoever. If I omit from the concept
of cause the time in which something follows upon something
else in conformity with a rule, I should find in the pure
category nothing further than that there is something from
which we can conclude to the existence of something else. In
that case not only would we be unable to distinguish cause and
effect from one another, but since the power to draw such 
inferences requires conditions of which I know nothing, the 
concept would yield no indication how it applies to any object.
The so-called principle, that everything accidental has a cause,
presents itself indeed somewhat pompously, as self-sufficing
in its own high dignity. But if I ask what is understood by
accidental, and you reply, "That the not-being of which is
possible," I would gladly know how you can determine this
possibility of its not-being, if you do not represent a succession
in the series of appearances and in it a being which follows
upon not-being (or reversewise), that is, a change. For to say
that the not-being of a thing does not contradict itself, is a lame
appeal to a logical condition, which, though necessary to the
concept, is very far from being sufficient for real possibility.
I can remove in thought every existing substance without
contradicting myself, but I cannot infer from this their objective
contingency in existence, that is, that their non-existence
is possible. As regards the concept of community, it is easily
seen that inasmuch as the pure categories of substance
and causality admit of no explanation determinant of the
object, neither is any such explanation possible of reciprocal
causality in the relation of substances to one another 
(commercium). So long as the definition of possibility, existence,
and necessity is sought solely in pure understanding, they 
cannot be explained save through an obvious tautology. For to
substitute the logical possibility of the concept (namely, that
the concept does not contradict itself) for the transcendental
possibility of things (namely, that an object corresponds to
P 263
the concept) can deceive and leave satisfied only the simple-
minded.
++ There is something strange and even absurd in the assertion
that there should be a concept which possesses a meaning
and yet is not capable of any explanation. But the categories
have this peculiar feature, that only in virtue of the general
condition of sensibility can they possess a determinate meaning
and relation to any object. Now when this condition has
been omitted from the pure category, it can contain nothing but
the logical function for bringing the manifold under a concept.
By means of this function or form of the concept, thus taken
by itself, we cannot in any way know and distinguish what
object comes under it, since we have abstracted from the sensible
condition through which alone objects can come under it.
Consequently, the categories require, in addition to the pure
concept of understanding, determinations of their application to
sensibility in general (schemata). Apart from such application
they are not concepts through which an object is known and
distinguished from others, but only so many modes of thinking
an object for possible intuitions, and of giving it meaning,
under the requisite further conditions, in conformity with some
function of the understanding, that is, of defining it. But they
cannot themselves be defined. The logical functions of judgments
in general, unity and plurality, assertion and denial,
subject and predicate, cannot be defined without perpetrating
a circle, since the definition must itself be a judgment, and
so must already contain these functions. The pure categories
are nothing but representations of things in general, so far as
the manifold of their intuition must be thought through one or
other of these logical functions.
++ In a word, if all sensible intuition, the only kind of intuition
which we possess, is removed, not one of these concepts can in any
fashion verify itself, so as to show its real possibility. Only logical
possibility then remains, that is, that the concept or thought is 
possible. That, however, is not what we are discussing, but whether
the concept relates to an object and so signifies something.
P 264
 From all this it undeniably follows that the pure concepts of
understanding can never admit of transcendental but always
only of empirical employment, and that the principles of pure
understanding can apply only to objects of the senses under
the universal conditions of a possible experience, never to
things in general without regard to the mode in which we are
able to intuit them.
Accordingly the Transcendental Analytic leads to this
important conclusion, that the most the understanding can
achieve a priori is to anticipate the form of a possible 
experience in general. And since that which is not appearance 
cannot be an object of experience, the understanding can never
transcend those limits of sensibility within which alone objects
can be given to us. Its principles are merely rules for the 
exposition of appearances; and the proud name of an Ontology
that presumptuously claims to supply, in systematic doctrinal
form, synthetic a priori knowledge of things in general (for
instance, the principle of causality) must, therefore, give place
to the modest title of a mere Analytic of pure understanding.
 Thought is the act which relates given intuition to an
object. If the mode of this intuition is not in any way
given, the object is merely transcendental, and the concept of
understanding has only transcendental employment, namely,
as the unity of the thought of a manifold in general. Thus no
object is determined through a pure category in which abstraction
is made of every condition of sensible intuition -- the
only kind of intuition possible to us.
P 263
Magnitude is the determination
P 264
which can be thought only through a judgment which has
quantity (judicium commune); reality is that determination
which can be thought only through an affirmative judgment;
substance is that which, in relation to intuition, must be the
last subject of all other determinations. But what sort of a
thing it is that demands one of these functions rather than
another, remains altogether undetermined. Thus the categories,
apart from the condition of sensible intuition, of
which they contain the synthesis, have no relation to any
determinate object, cannot therefore define any object, and
so do not in themselves have the validity of objective concepts.
P 264
It then expresses only the
P 265
thought of an object in general, according to different modes.
Now the employment of a concept involves a function of 
judgment whereby an object is subsumed under the concept, and
so involves at least the formal condition under which something
can be given in intuition. If this condition of judgment
(the schema) is lacking, all subsumption becomes impossible.
For in that case nothing is given that could be subsumed under
the concept. The merely transcendental employment of the 
categories is, therefore, really no employment at all, and has no
determinate object, not even one that is determinable in its
mere form. It therefore follows that the pure category does not
suffice for a synthetic a priori principle, that the principles
of pure understanding are only of empirical, never of 
transcendental employment, and that outside the field of possible
experience there can be no synthetic a priori principles.
It may be advisable, therefore, to express the situation as
follows. The pure categories, apart from formal conditions of
sensibility, have only transcendental meaning; nevertheless
they may not be employed transcendentally, such employment
being in itself impossible, inasmuch as all conditions of any
employment in judgments are lacking to them, namely, the
formal conditions of the subsumption of any ostensible object
under these concepts. Since, then, as pure categories merely,
they are not to be employed empirically, and cannot be employed
transcendentally, they cannot, when separated from all
sensibility, be employed in any manner whatsoever, that is,
they cannot be applied to any ostensible object. They are the
pure form of the employment of understanding in respect of
objects in general, that is, of thought; but since they are
merely its form, through them alone no object can be thought
or determined.
++ Appearances, so far as they are thought as objects according
to the unity of the categories, are called phaenomena. But
if I postulate things which are mere objects of understanding,
and which, nevertheless, can be given as such to an intuition,
P 266
although not to one that is sensible -- given therefore coram
intuitu intellectuali -- such things would be entitled noumena
(intelligibilia).
P 266
But we are here subject to an illusion from which it is
difficult to escape. The categories are not, as regards their
origin, grounded in sensibility, like the forms of intuition,
space and time; and they seem, therefore, to allow of an
application extending beyond all objects of the senses. As a
matter of fact they are nothing but forms of thought, which
contain the merely logical faculty of uniting a priori in one 
consciousness the manifold given in intuition; and apart, therefore,
from the only intuition that is possible to us, they have even
less meaning than the pure sensible forms. Through these
forms an object is at least given, whereas a mode of combining
the manifold -- a mode peculiar to our understanding --
by itself, in the absence of that intuition wherein the 
manifold can alone be given, signifies nothing at all. At the
same time, if we entitle certain objects, as appearances,
sensible entities (phenomena), then since we thus distinguish
the mode in which we intuit them from the nature that
belongs to them in themselves,
++ Now we must bear in mind that the concept of appearances,
as limited by the Transcendental Aesthetic, already of
itself establishes the objective reality of noumena and justifies
the division of objects into phaenomena and noumena, and so
of the world into a world of the senses and a world of the 
understanding (mundus sensibilis et intelligibilis), and indeed in
such manner that the distinction does not refer merely to the
logical form of our knowledge of one and the same thing, according
as it is indistinct or distinct, but to the difference in
the manner in which the two worlds can be first given to our
knowledge, and in conformity with this difference, to the
manner in which they are in themselves generically distinct
from one another. For if the senses represent to us something
merely as it appears, this something must also in itself be a
P 267
thing, and an object of a non-sensible intuition, that is, of the
understanding.
P 267
it is implied in this distinction
that we place the latter, considered in their own nature,
although we do not so intuit them, or that we place other
possible things, which are not objects of our senses but are
thought as objects merely through the understanding, in
opposition to the former, and that in so doing we entitle them
intelligible entities (noumena). The question then arises,
whether our pure concepts of understanding have meaning
in respect of these latter, and so can be a way of knowing
them.
At the very outset, however, we come upon an ambiguity
which may occasion serious misapprehension. The understanding,
when it entitles an object in a [certain] relation
mere phenomenon, at the same time forms, apart from
that relation, a representation of an object in itself, and so
comes to represent itself as also being able to form 
concepts of such objects.
++
In other words, a [kind of] knowledge must be
possible, in which there is no sensibility, and which alone has
reality that is absolutely objective. Through it objects will be
represented as they are, whereas in the empirical employment
of our understanding things will be known only as they appear.
If this be so, it would seem to follow that we cannot assert,
what we have hitherto maintained, that the pure modes of
knowledge yielded by our understanding are never anything
more than principles of the exposition of appearance, and that
even in their a priori application they relate only to the formal
possibility of experience. On the contrary, we should have to
recognise that in addition to the empirical employment of the
categories, which is limited to sensible conditions, there is 
likewise a pure and yet objectively valid employment. For a field
quite different from that of the senses would here lie open to
us, a world which is thought as it were in the spirit (or even
perhaps intuited), and which would therefore be for the understanding
a far nobler, not a less noble, object of contemplation.
P 267
And since the understanding yields no
concepts additional to the categories, it also supposes that
the object in itself must at least be thought through these
P 268
pure concepts, and so is misled into treating the entirely
indeterminate concept of an intelligible entity, namely, of a
something in general outside our sensibility, as being a 
determinate concept of an entity that allows of being known in
a certain [purely intelligible] manner by means of the 
understanding. 
If by 'noumenon' we mean a thing so far as it is not an
object of our sensible intuition, and so abstract from our mode
of intuiting it, this is a noumenon in the negative sense of the
term. But if we understand by it an object of a non-sensible
intuition, we thereby presuppose a special mode of intuition,
namely, the intellectual, which is not that which we possess,
and of which we cannot comprehend even the possibility.
This would be 'noumenon' in the positive sense of the term.
The doctrine of sensibility is likewise the doctrine of the
noumenon in the negative sense, that is, of things which the
understanding must think without this reference to our mode
of intuition, therefore not merely as appearances but as
things in themselves.
++ All our representations are, it is true, referred by the 
understanding to some object; and since appearances are nothing
but representations, the understanding refers them to a something,
as the object of sensible intuition. But this something,
thus conceived, is only the transcendental object; and by that
is meant a something = X, of which we know, and with the
present constitution of our understanding can know, nothing
whatsoever, but which, as a correlate of the unity of apperception,
can serve only for the unity of the manifold in sensible
intuition. By means of this unity the understanding combines
the manifold into the concept of an object. This transcendental
object cannot be separated from the sense data, for nothing is
then left through which it might be thought. Consequently it
is not in itself an object of knowledge, but only the representation
of appearances under the concept of an object in general
-- a concept which is determinable through the manifold of
these appearances.
P 268
At the same time the understanding is
P 269
well aware that in viewing things in this manner, as thus
apart from our mode of intuition, it cannot make any use of
the categories. For the categories have meaning only in relation
to the unity of intuition in space and time; and even this
unity they can determine, by means of general a priori 
connecting concepts, only because of the mere ideality of space
and time. In cases where this unity of time is not to be found,
and therefore in the case of the noumenon, all employment,
and indeed the whole meaning of the categories, entirely
vanishes; for we have then no means of determining whether
things in harmony with the categories are even possible. On
this point I need only refer the reader to what I have said in
the opening sentences of the General Note appended to the
preceding chapter. The possibility of a thing can never be
proved merely from the fact that its concept is not 
self-contradictory, but only through its being supported by some
corresponding intuition.
P 268a
Just for this reason the categories represent no special object,
given to the understanding alone, but only serve to determine
P 269a
the transcendental object, which is the concept of something
in general, through that which is given in sensibility, in
order thereby to know appearances empirically under concepts
of objects.
The cause of our not being satisfied with the substrate of
sensibility, and of our therefore adding to the phenomena 
noumena which only the pure understanding can think, is simply
as follows. The sensibility (and its field, that of the appearances)
is itself limited by the understanding in such fashion that
it does not have to do with things in themselves but only with
the mode in which, owing to our subjective constitution, they
appear. The Transcendental Aesthetic, in all its teaching, has
led to this conclusion; and the same conclusion also, of course,
follows from the concept of an appearance in general; namely,
that something which is not in itself appearance must correspond
to it. For appearance can be nothing by itself, outside
our mode of representation. Unless, therefore, we are to move
constantly in a circle, the word appearance must be recognised
as already indicating a relation to something, the immediate
P 270a
representation of which is, indeed, sensible, but which, even
apart from the constitution of our sensibility (upon which the
form of our intuition is grounded), must be something in itself,
that is, an object independent of sensibility.
P 269
If, therefore, we should attempt to
apply the categories to objects which are not viewed as being
appearances, we should have to postulate an intuition other
P 270
than the sensible, and the object would thus be a noumenon
in the positive sense. Since, however, such a type of intuition,
intellectual intuition, forms no part whatsoever of our
faculty of knowledge, it follows that the employment of
the categories can never extend further than to the objects
of experience. Doubtless, indeed, there are intelligible entities
corresponding to the sensible entities; there may also be 
intelligible entities to which our sensible faculty of intuition
has no relation whatsoever; but our concepts of understanding,
being mere forms of thought for our sensible intuition,
could not in the least apply to them. That, therefore, which
we entitle 'noumenon' must be understood as being such
only in a negative sense.
If I remove from empirical knowledge all thought (through
categories), no knowledge of any object remains. For through
mere intuition nothing at all is thought, and the fact that this
affection of sensibility is in me does not [by itself] amount to
a relation of such representation to any object. But if, on the
other hand, I leave aside all intuition, the form of thought still remains
++ There thus results the concept of a noumenon. It is not
of anything, but signifies only the thought of something in
general, in which I abstract from everything that belongs to
the form of sensible intuition. But in order that a noumenon
may signify a true object, distinguishable from all phenomena,
it is not enough that I free my thought from all conditions of
sensible intuition; I must likewise have ground for assuming
another kind of intuition, different from the sensible, in which
such an object may be given. For otherwise my thought, while
indeed without contradictions, is none the less empty. We have
not, indeed, been able to prove that sensible intuition is the only
possible intuition, but only that it is so for us. But neither have
we been able to prove that another kind of intuition is possible.
P 271
 -- that is, the mode of determining an object for
the manifold of a possible intuition. The categories accordingly
extend further than sensible intuition, since they think
objects in general, without regard to the special mode (the
sensibility) in which they may be given. But they do not
thereby determine a greater sphere of objects. For we cannot
assume that such objects can be given, without presupposing
the possibility of another kind of intuition than the sensible;
and we are by no means justified in so doing.
If the objective reality of a concept cannot be in any way
known, while yet the concept contains no contradiction and also
at the same time is connected with other modes of knowledge
that involve given concepts which it serves to limit, I entitle
that concept problematic. The concept of a noumenon -- that is,
of a thing which is not to be thought as object of the senses
but as a thing in itself, solely through a pure understanding --
is not in any way contradictory. For we cannot assert of 
sensibility that it is the sole possible kind of intuition.
P 270a
Consequently, although our thought can abstract from all
P 271a
++ sensibility, it is still an open question whether the notion of
a noumenon be not a mere form of a concept, and whether,
when this separation has been made, any object whatsoever
is left.
The object to which I relate appearance in general is
the transcendental object, that is, the completely 
indeterminate thought of something in general. This cannot be
entitled the noumenon; for I know nothing of what it is in
itself, and have no concept of it save as merely the object of
a sensible intuition in general, and so as being one and the
same for all appearances. I cannot think it through any category;
for a category is valid [only] for empirical intuition, as
bringing it under a concept of object in general. A pure use of
the category is indeed possible [logically], that is, without 
contradiction; but it has no objective validity, since the category
is not then being applied to any intuition so as to impart to it
the unity of an object. For the category is a mere function
of thought, through which no object is given to me, and by
which I merely think that which may be given in intuition.
P 272
Further, the concept of a noumenon is necessary, to prevent sensible intuition
from being extended to things in themselves, and thus to limit
the objective validity of sensible knowledge. The remaining
things, to which it does not apply, are entitled noumena, in
order to show that this knowledge cannot extend its domain
over everything which the understanding thinks. But none the
less we are unable to comprehend how such noumena can be
possible, and the domain that lies out beyond the sphere of
appearances is for us empty. That is to say, we have an
understanding which problematically extends further, but
we have no intuition, indeed not even the concept of a
possible intuition, through which objects outside the field
of sensibility can be given, and through which the 
understanding can be employed assertorically beyond that
field. The concept of a noumenon is thus a merely limiting
concept, the function of which is to curb the pretensions of
sensibility; and it is therefore only of negative employment.
At the same time it is no arbitrary invention; it is bound up
with the limitation of sensibility, though it cannot affirm 
anything positive beyond the field of sensibility.
The division of objects into phenomena and noumena, and
the world into a world of the senses and a world of the 
understanding, is therefore quite inadmissible in the positive sense
although the distinction of concepts as sensible and intellectual
is certainly legitimate. For no object can be determined for the
latter concepts, and consequently they cannot be asserted to be
objectively valid. If we abandon the senses, how shall we make
it conceivable that our categories, which would be the sole 
remaining concepts for noumena, should still continue to signify
something, since for their relation to any object more must be
given than merely the unity of thought -- namely, in addition,
a possible intuition, to which they may be applied. None the
less, if the concept of a noumenon be taken in a merely problematic
sense, it is not only admissible, but as setting limits
to sensibility is likewise indispensable. But in that case a 
noumenon is not for our understanding a special [kind of] object,
namely, an intelligible object; the [sort of] understanding to
which it might belong is itself a problem. For we cannot in
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the least represent to ourselves the possibility of an 
understanding which should know its object, not discursively
through categories, but intuitively in a non-sensible intuition.
What our understanding acquires through this concept of a
noumenon, is a negative extension; that is to say, understanding
is not limited through sensibility; on the contrary,
it itself limits sensibility by applying the term noumena to
things in themselves (things not regarded as appearances).
But in so doing it at the same time sets limits to itself, 
recognising that it cannot know these noumena through any of the
categories, and that it must therefore think them only under
the title of an unknown something.
In the writings of modern philosophers I find the expressions
mundus sensibilis and intelligibilis used with a meaning
altogether different from that of the ancients -- a meaning
which is easily understood, but which results merely in an
empty play upon words. According to this usage, some have
thought good to entitle the sum of appearances, in so far as
they are intuited, the world of the senses, and in so far as their
connection is thought in conformity with laws of understanding,
the world of the understanding. Observational astronomy,
which teaches merely the observation of the starry heavens,
would give an account of the former; theoretical astronomy,
on the other hand, as taught according to the Copernican
system, or according to Newton's laws of gravitation, would
give an account of the second, namely, of an intelligible
world. But such a twisting of words is a merely sophistical
subterfuge; it seeks to avoid a troublesome question by
changing its meaning to suit our own convenience. 
Understanding and reason are, indeed, employed in dealing with
appearances;
++ We must not, in place of the expression mundus intelligibilis,
use the expression 'an intellectual world', as is commonly done
in German exposition. For only modes of knowledge are either
intellectual or sensuous. What can only be an object of the one
or the other kind of intuition must be entitled (however harsh-
sounding) intelligible or sensible.
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but the question to be answered is whether they
have also yet another employment, when the object is not a
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phenomenon (that is, is a noumenon); and it is in this latter
sense that the object is taken, when it is thought as merely
intelligible, that is to say, as being given to the understanding
alone, and not to the senses. The question, therefore, is whether
in addition to the empirical employment of the understanding
-- to its employment even in the Newtonian account of the
structure of the universe -- there is likewise possible a 
transcendental employment, which has to do with the noumenon
as an object. This question we have answered in the negative.
 When, therefore, we say that the senses represent objects
as they appear, and the understanding objects as they are, the
latter statement is to be taken, not in the transcendental, but
in the merely empirical meaning of the terms, namely as
meaning that the objects must be represented as objects of
experience, that is, as appearances in thoroughgoing 
interconnection with one another, and not as they may be apart
from their relation to possible experience (and consequently
to any senses), as objects of the pure understanding. Such
objects of pure understanding will always remain unknown
to us; we can never even know whether such a transcendental
or exceptional knowledge is possible under any conditions
-- at least not if it is to be the same kind of knowledge
as that which stands under our ordinary categories.
Understanding and sensibility, with us, can determine objects
only when they are employed in conjunction. When we separate
them, we have intuitions without concepts, or concepts
without intuitions -- in both cases, representations which we
are not in a position to apply to any determinate object.
If, after all these explanations, any one still hesitates to
abandon the merely transcendental employment of the categories,
let him attempt to obtain from them a synthetic proposition.
An analytic proposition carries the understanding no
further; for since it is concerned only with what is already
thought in the concept, it leaves undecided whether this concept
has in itself any relation to objects, or merely signifies
the unity of thought in general -- complete abstraction being
made from the mode in which an object may be given. The
understanding [in its analytic employment] is concerned only
to know what lies in the concept; it is indifferent as to the
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object to which the concept may apply. The attempt must
therefore be made with a synthetic and professedly transcendental
principle, as, for instance, 'Everything that exists,
exists as substance, or as a determination inherent in it', or
'Everything contingent exists as an effect of some other thing,
namely, of its cause'. Now whence, I ask, can the understanding
obtain these synthetic propositions, when the concepts are
to be applied, not in their relation to possible experience, but
to things in themselves (noumena)? Where is here that third
something, which is always required for a synthetic proposition,
in order that, by its mediation, the concepts which have
no logical (analytic) affinity may be brought into connection
with one another? The proposition can never be established,
nay, more, even the possibility of any such pure assertion 
cannot be shown, without appealing to the empirical employment
of the understanding, and thereby departing completely from
the pure and non-sensible judgment. Thus the concept of pure
and merely intelligible objects is completely lacking in all
principles that might make possible its application. For we
cannot think of any way in which such intelligible objects
might be given. The problematic thought which leaves open
a place for them serves only, like an empty space, for the
limitation of empirical principles, without itself containing or
revealing any other object of knowledge beyond the sphere of
those principles.