Immanuel Kant's

trans. by Norman Kemp Smith

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P 276
APPENDIX
THE AMPHIBOLY OF CONCEPTS OF REFLECTION
ARISING FROM THE CONFUSION OF THE EMPIRICAL WITH THE
TRANSCENDENTAL EMPLOYMENT OF UNDERSTANDING
Reflection (reflexio) does not concern itself with objects 
themselves with a view to deriving concepts from them directly,
but is that state of mind in which we first set ourselves
to discover the subjective conditions under which [alone] we
are able to arrive at concepts. It is the consciousness of the 
relation of given representations to our different sources of 
knowledge; and only by way of such consciousness can the relation
of the sources of knowledge to one another be rightly determined.
Prior to all further treatment of our representations,
this question must first be asked: In which of our cognitive
faculties are our representations connected together? Is it the
understanding, or is it the senses, by which they are combined
or compared? Many a judgment is accepted owing to custom
or is grounded in inclination; but since no reflection precedes
it, or at least none follows critically upon it, it is taken as
having originated in the understanding. An examination
(i.e. the direction of our attention to the grounds of the truth
of a judgment) is not indeed required in every case; for if the
judgment is immediately certain (for instance, the judgment
that between two points there can only be one straight line),
there can be no better evidence of its truth than the judgment
itself. All judgments, however, and indeed all comparisons,
require reflection, i.e. distinction of the cognitive faculty to
which the given concepts belong. The act by which I confront
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the comparison of representations with the cognitive faculty
to which it belongs, and by means of which I distinguish
whether it is as belonging to the pure understanding or to
sensible intuition that they are to be compared with each
other, I call transcendental reflection. Now the relations in
which concepts in a state of mind can stand to one another are
those of identity and difference, of agreement and opposition,
of the inner and the outer, and finally of the determinable and
the determination (matter and form). The right determining
of the relation depends on the answer to the question, in which
faculty of knowledge they belong together subjectively -- in the
sensibility or in the understanding. For the difference between
the faculties makes a great difference to the mode in which we
have to think the relations.
Before constructing any objective judgment we compare
the concepts to find in them identity (of many representations
under one concept) with a view to universal judgments,
difference with a view to particular judgments, agreement
with a view to affirmative judgments, opposition with a view
to negative judgments, etc. For this reason we ought, it seems,
to call the above-mentioned concepts, concepts of comparison
(conceptus comparationis). If, however, the question is not
about the logical form, but about the content of the concepts,
i.e. whether things are themselves identical or different, in
agreement or in opposition, etc. , then since the things can have
a twofold relation to our faculty of knowledge, namely, to sensibility
and to understanding, it is the place to which they belong
in this regard that determines the mode in which they belong
to one another. For this reason the interrelations of given 
representations can be determined only through transcendental
reflection, that is, through [consciousness of] their relation to
one or other of the two kinds of knowledge. Whether things are
identical or different, in agreement or in opposition, etc. , 
cannot be established at once from the concepts themselves by
mere comparison (comparatio), but solely by means of transcendental
consideration (reflexio), through distinction of the
cognitive faculty to which they belong. We may therefore say
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that logical reflection is a mere act of comparison; for since
we take no account whatsoever of the faculty of knowledge to
which the given representations belong, the representations
must be treated as being, so far as their place in the mind is
concerned, all of the same order. Transcendental reflection, on
the other hand, since it bears on the objects themselves, contains
the ground of the possibility of the objective comparison
of representations with each other, and is therefore altogether
different from the former type of reflection. Indeed they do
not even belong to the same faculty of knowledge. This 
transcendental consideration is a duty from which nobody who
wishes to make any a priori judgments about things can claim
exemption. We shall now take it in hand, and in so doing shall
obtain no little light for the determining of the real business
of the understanding.
1. Identity and Difference. -- If an object is presented to us
on several occasions but always with the same inner determinations
(qualitas et quantitas), then if it be taken as object of
pure understanding, it is always one and the same, only one
thing (numerica identitas), not many. But if it is appearance,
we are not concerned to compare concepts; even if there is
no difference whatever as regards the concepts, difference of
spatial position at one and the same time is still an adequate
ground for the numerical difference of the object, that is, of the
object of the senses. Thus in the case of two drops of water
we can abstract altogether from all internal difference (of
quality and quantity), and the mere fact that they have been
intuited simultaneously in different spatial positions is sufficient
justification for holding them to be numerically different.
Leibniz took the appearances for things-in-themselves, and so
for intelligibilia, i.e. objects of the pure understanding 
(although, on account of the confused character of our 
representations of them, he still gave them the name of phenomena),
and on that assumption his principle of the identity of 
indiscernibles (principium identitatis indiscernibilium) certainly
could not be disputed. But since they are objects of sensibility,
in relation to which the employment of the understanding is
not pure but only empirical, plurality and numerical difference
are already given us by space itself, the condition of outer
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appearances. For one part of space, although completely similar
and equal to another part, is still outside the other, and for
this very reason is a different part, which when added to it
constitutes with it a greater space. The same must be true of
all things which exist simultaneously in the different spatial
positions, however similar and equal they may otherwise be.
2. Agreement and Opposition. -- If reality is represented
only by the pure understanding (realitas noumenon), no opposition
can be conceived between the realities, i.e. no relation
of such a kind that, when combined in the same subject, they
cancel each other's consequences and take a form like 3 - 3 = 0.
On the other hand, the real in appearance (realitas phaenomenon)
may certainly allow of opposition. When such realities
are combined in the same subject, one may wholly or partially
destroy the consequences of another, as in the case of two
moving forces in the same straight line, in so far as they either
attract or impel a point in opposite directions, or again in the
case of a pleasure counterbalancing pain.
3. The Inner and the Outer. -- In an object of the pure
understanding that only is inward which has no relation whatsoever
(so far as its existence is concerned) to anything different
from itself. It is quite otherwise with a substantia phaenomenon
in space; its inner determinations are nothing but relations, and
it itself is entirely made up of mere relations. We are acquainted
with substance in space only through forces which are active
in this and that space, either bringing other objects to it 
(attraction), or preventing them penetrating into it (repulsion
and impenetrability). We are not acquainted with any other
properties constituting the concept of the substance which
appears in space and which we call matter. As object of pure
understanding, on the other hand, every substance must have
inner determinations and powers which pertain to its inner
reality. But what inner accidents can I entertain in thought,
save only those which my inner sense presents to me? They
must be something which is either itself a thinking or 
analogous to thinking. For this reason Leibniz, regarding 
substances as noumena, took away from them, by the manner in
which he conceived them, whatever might signify outer 
relation, including also, therefore, composition, and so made
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them all, even the constituents of matter, simple subjects with
powers of representation -- in a word, MONADS.
4. Matter and Form. -- These two concepts underlie all
other reflection, so inseparably are they bound up with all
employment of the understanding. The one [matter] signifies
the determinable in general, the other [form] its determination
-- both in the transcendental sense, abstraction being
made from all differences in that which is given and from the
mode in which it is determined Logicians formerly gave the
name 'matter' to the universal, and the name 'form' to the
specific difference. In any judgment we can call the given
concepts logical matter (i.e. matter for the judgment), and
their relation (by means of the copula) the form of the judgment.
In every being the constituent elements of it (essentialia)
are the matter, the mode in which they are combined in one
thing the essential form. Also as regards things in general
unlimited reality was viewed as the matter of all possibility,
and its limitation (negation) as being the form by which one
thing is distinguished from others according to transcendental
concepts. The understanding, in order that it may be in a 
position to determine anything in definite fashion, demands that
something be first given, at least in concept. Consequently in
the concept of the pure understanding matter is prior to form;
and for this reason Leibniz first assumed things (monads),
and within them a power of representation, in order afterwards
to found on this their outer relation and the community
of their states (i.e. of the representations). Space and time
-- the former through the relation of substances, the latter
through the connection of their determinations among themselves
-- were thus, on this view, possible as grounds and consequents.
This, in fact, is how it would necessarily be, if the
pure understanding could be directed immediately to objects,
and if space and time were determinations of things-in-themselves.
But if they are only sensible intuitions, in which we
determine all objects merely as appearances, then the form of
intuition (as a subjective property of sensibility) is prior to all
matter (sensations); space and time come before all appearances
and before all data of experience, and are indeed what
make the latter at all possible. The intellectualist 
philosopher could not endure to think of the form as preceding
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the things themselves and determining their possibility -- a
perfectly just criticism on the assumption that we intuit things
as they really are, although in confused representation. But
since sensible intuition is a quite specific subjective condition,
which lies a priori at the foundation of all perception, as its
original form, it follows that the form is given by itself, and that
so far is the matter (or the things themselves which appear)
from serving as the foundation (as we should have to judge
if we followed mere concepts) that on the contrary its own
possibility presupposes a formal intuition (time and space)
as antecedently given.
NOTE TO THE AMPHIBOLY 0F CONCEPTS OF REFLECTION
Let me call the place which we assign to a concept, either
in sensibility or in pure understanding, its transcendental
location. Thus the decision as to the place which belongs to
every concept according to difference in the use to which it
is put, and the directions for determining this place for all
concepts according to rules, is a transcendental topic. This
doctrine, in distinguishing the cognitive faculty to which in
each case the concepts properly belong, will provide a sure
safeguard against the surreptitious employment of pure 
understanding and the delusions which arise therefrom. We may
call every concept, every heading, under which many items of
knowledge fall, a logical location. On this is based the logical
topic of Aristotle, of which teachers and orators could make
use in order under given headings of thought to find what
would best suit the matter in hand, and then, with some
appearance of thoroughness, to argue or be eloquent about it.
The transcendental topic, on the other hand, contains no
more than the above-mentioned four headings of all comparison
and distinction. They are distinguished from categories
by the fact that they do not present the object according
to what constitutes its concept (quantity, reality), but
only serve to describe in all its manifoldness the comparison
of the representations which is prior to the concept of things.
But this comparison requires in the first place a reflection,
that is, a determination of the location to which the 
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representations of the things that are being compared belong,
namely, whether they are thought by the pure understanding
or given in appearance by sensibility.
Concepts can be compared logically without our troubling
to which faculty their objects belong, that is, as to whether
their objects are noumena for the understanding, or are
phenomena for the sensibility. But if we wish to advance
to the objects with these concepts, we must first resort to 
transcendental reflection, in order to determine for which cognitive
faculty they are to be objects, whether for pure understanding
or for sensibility. In the absence of such reflection, the use of
these concepts is very unsafe, giving birth to alleged synthetic
principles, which the critical reason cannot recognise, and
which are based on nothing better than a transcendental
amphiboly, that is, a confounding of an object of pure 
understanding with appearance.
Having no such transcendental topic, and being therefore
deceived by the amphiboly of the concepts of reflection, the
celebrated Leibniz erected an intellectual system of the world,
or rather believed that he could obtain knowledge of the
inner nature of things by comparing all objects merely with
the understanding and with the separated, formal concepts
of its thought. Our table of concepts of reflection gives us the
unexpected advantage of putting before our eyes the distinctive
features of his system in all its parts, and at the same time
the chief ground of this peculiar way of thinking, which indeed
rested on nothing but a misunderstanding. He compared all
things with each other by means of concepts alone, and 
naturally found no other differences save those through which
the understanding distinguishes its pure concepts from one
another. The conditions of sensible intuition, which carry
with them their own differences, he did not regard as original,
sensibility being for him only a confused mode of representation,
and not a separate source of representations. Appearance
was, on his view, the representation of the thing in
itself. Such representation is indeed, as he recognised,
different in logical form from knowledge through the understanding,
since, owing to its usual lack of analysis, it introduces
a certain admixture of accompanying representations
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into the concept of the thing, an admixture which the 
understanding knows how to separate from it. In a word, Leibniz
intellectualised appearances, just as Locke, according to his
system of noogony (if I may be allowed the use of such 
expressions), sensualised all concepts of the understanding, i.e.
interpreted them as nothing more than empirical or abstracted
concepts of reflection. Instead of seeking in understanding
and sensibility two sources of representations which, while
quite different, can supply objectively valid judgments of
things only in conjunction with each other, each of these great
men holds to one only of the two, viewing it as in immediate
relation to things in themselves. The other faculty is then
regarded as serving only to confuse or to order the 
representations which this selected faculty yields.
Leibniz therefore compared the objects of the senses
with each other merely in regard to understanding, taking
them as things in general. First, he compared them in so far
as they are to be judged by understanding to be identical or
to be different. And since he had before him only their 
concepts and not their position in intuition (wherein alone the
objects can be given), and left entirely out of account the
transcendental place of these concepts (whether the object is
to be reckoned among appearances or things in themselves),
it inevitably followed that he should extend his principle of
the identity of indiscernibles, which is valid only of concepts
of things in general, to cover also the objects of the senses
(mundus phaenomenon), and that he should believe that in
so doing he had advanced our knowledge of nature in no
small degree. Certainly, if I know a drop of water in all its
internal determinations as a thing in itself, and if the whole
concept of any one drop is identical with that of every other,
I cannot allow that any drop is different from any other. But
if the drop is an appearance in space, it has its location not
only in understanding (under concepts) but in sensible outer
intuition (in space), and the physical locations are there quite
indifferent to the inner determinations of the things. A 
location b can contain a thing which is completely similar and
equal to another in a location a, just as easily as if the things
were inwardly ever so different. Difference of locations, without
any further conditions, makes the plurality and distinction
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of objects, as appearances, not only possible but also 
necessary. Consequently, the above so-called law is no law of
nature. It is only an analytic rule for the comparison of
things through mere concepts.
Secondly, the principle that realities (as pure assertions)
never logically conflict with each other is an entirely true
proposition as regards the relation of concepts, but has not
the least meaning in regard either to nature or to anything
in itself. For real conflict certainly does take place; there are
cases where A - B = 0, that is, where two realities combined
in one subject cancel one another's effects. This is brought
before our eyes incessantly by all the hindering and 
counteracting processes in nature, which, as depending on forces,
must be called realitates phaenomena. General mechanics can
indeed give the empirical condition of this conflict in an a -
priori rule, since it takes account of the opposition in the
direction of forces, a condition totally ignored by the 
transcendental concept of reality. Although Herr von Leibniz did
not indeed announce the above proposition with all the pomp
of a new principle, he yet made use of it for new assertions,
and his successors expressly incorporated it into their Leibnizian
- Wolffian system. Thus, according to this principle all
evils are merely consequences of the limitations of created
beings, that is, negations, since negations alone conflict
with reality. (This is indeed the case as regards the mere
concept of a thing in general, but not as regards things as
appearances. ) Similarly his disciples consider it not only 
possible, but even natural, to combine all reality in one being,
without fear of any conflict. For the only conflict which they
recognise is that of contradiction, whereby the concept of a
thing is itself removed. They do not admit the conflict of 
reciprocal injury, in which each of two real grounds destroys the
effect of the other -- a conflict which we can represent to ourselves
only in terms of conditions presented to us in sensibility.
Thirdly, Leibniz's monadology has no basis whatsoever
save his mode of representing the distinction of inner and
outer merely in relation to the understanding. Substances in
general must have some internal nature, which is therefore
free from all outer relations, and consequently also from 
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composition. The simple is therefore the basis of that which is
inner in things-in-themselves. But that which is inner in the
state of a substance cannot consist in place, shape, contact,
or motion (these determinations being all outer relations), and
we can therefore assign to substances no inner state save that
through which we ourselves inwardly determine our sense,
namely, the state of the representations. This, therefore, 
completed the conception of the monads, which, though they have
to serve as the basic material of the whole universe, have no
other active power save only that which consists in representations,
the efficacy of which is confined, strictly speaking, to
themselves.
For this very reason his principle of the possible reciprocal
community of substances had to be a pre-established harmony,
and could not be a physical influence. For since everything is
merely inward, i.e. concerned with its own representations, the
state of the representations of one substance could not stand
in any effective connection whatever with that of another.
There had to be some third cause, determining all substances
whatsoever, and so making their states correspond to each
other, not indeed by an occasional special intervention in each
particular case (systema assistentiae), but by the unity of the
idea of a cause valid for all substances, and in which they
must one and all obtain their existence and permanence, and
consequently also their reciprocal correspondence, according
to universal laws.
Fourthly, Leibniz's famous doctrine of time and space, in
which he intellectualised these forms of sensibility, owed its
origin entirely to this same fallacy of transcendental reflection.
If I attempt, by the mere understanding, to represent to
myself outer relations of things, this can only be done by means
of a concept of their reciprocal action; and if I seek to connect
two states of one and the same thing, this can only be in the
order of grounds and consequences. Accordingly, Leibniz
conceived space as a certain order in the community of 
substances, and time as the dynamical sequence of their states.
That which space and time seem to possess as proper to themselves,
in independence of things, he ascribed to the confusion
in their concepts, which has led us to regard what is a mere
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form of dynamical relations as being a special intuition, self-
subsistent and antecedent to the things themselves. Thus space
and time were for him the intelligible form of the connection
of things (substances and their states) in themselves; and the
things were intelligible substances (substantiae noumena).
And since he allowed sensibility no mode of intuition peculiar
to itself but sought for all representation of objects, even the
empirical, in the understanding, and left to the senses nothing
but the despicable task of confusing and distorting the 
representations of the former, he had no option save to treat the
[intellectualised] concepts as being likewise valid of 
appearances. 
But even if we could by pure understanding say anything
synthetically in regard to things-in-themselves (which, however,
is impossible), it still could not be applied to appearances,
which do not represent things-in-themselves. In dealing
with appearances I shall always be obliged to compare my
concepts, in transcendental reflection, solely under the 
conditions of sensibility; and accordingly space and time will not
be determinations of things-in-themselves but of appearances.
What the things-in-themselves may be I do not know, nor do
I need to know, since a thing can never come before me except
in appearance.
The remaining concepts of reflection have to be dealt with
in the same manner. Matter is substantia phaenomenon. That
which inwardly belongs to it I seek in all parts of the space
which it occupies, and in all effects which it exercises, though
admittedly these can only be appearances of outer sense. I
have therefore nothing that is absolutely, but only what is
comparatively inward and is itself again composed of outer
relations. The absolutely inward [nature] of matter, as it would
have to be conceived by pure understanding, is nothing but
a phantom; for matter is not among the objects of pure
understanding, and the transcendental object which may be
the ground of this appearance that we call matter is a mere
something of which we should not understand what it is, even
if someone were in a position to tell us. For we can understand
only that which brings with it, in intuition, something 
corresponding to our words. If by the complaints -- that we have no
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insight whatsoever into the inner [nature] of things -- it be
meant that we cannot conceive by pure understanding what
the things which appear to us may be in themselves, they are
entirely illegitimate and unreasonable. For what is demanded
is that we should be able to know things, and therefore to
intuit them, without senses, and therefore that we should have
a faculty of knowledge altogether different from the human,
and this not only in degree but as regards intuition likewise
in kind -- in other words, that we should be not men but
beings of whom we are unable to say whether they are even
possible, much less how they are constituted. Through 
observation and analysis of appearances we penetrate to nature's
inner recesses, and no one can say how far this knowledge
may in time extend. But with all this knowledge, and even if
the whole of nature were revealed to us, we should still never
be able to answer those transcendental questions which go
beyond nature. The reason of this is that it is not given to us
to observe our own mind with any other intuition than that
of inner sense; and that it is yet precisely in the mind that
the secret of the source of our sensibility is located. The 
relation of sensibility to an object and what the transcendental
ground of this [objective] unity may be, are matters undoubtedly
so deeply concealed that we, who after all know even ourselves
only through inner sense and therefore as appearance, can
never be justified in treating sensibility as being a suitable
instrument of investigation for discovering anything save
always still other appearances -- eager as we yet are to explore
their non-sensible cause.
What makes this critique of conclusions based merely on
acts of reflection so exceedingly useful is that it renders 
manifest the nullity of all conclusions about objects which are
compared with each other solely in the understanding, and at
the same time confirms our principal contention, namely, that
although appearances are not included as things-in-themselves
among the objects of pure understanding, they are yet
the only objects in regard to which our knowledge can possess
objective reality, that is, in respect of which there is an 
intuition corresponding to the concepts.
If we reflect in a merely logical fashion, we are only 
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comparing our concepts with each other in the understanding, to
find whether both have the same content, whether they are
contradictory or not, whether something is contained within
the concept or is an addition from outside, which of the two
is given and which should serve only as a mode of thinking
what is given. But if I apply these concepts to an object in
general (in the transcendental sense), without determining
whether it be an object of sensible or of intellectual intuition,
limitations are at once revealed in the very notion of this
object which forbid any non-empirical employment of the
concepts, and by this very fact prove that the representation
of an object as a thing in general is not only insufficient, but,
when taken without sensible determination, and independently
of any empirical condition, self-contradictory. The 
conclusion is that we must either abstract from any and every
object (as in logic), or, if we admit an object, must think it
under the conditions of sensible intuition. For the intelligible
would require a quite peculiar intuition which we do not
possess, and in the absence of this would be for us nothing at
all; and, on the other hand, it is also evident that appearances
could not be objects in themselves. If I think to myself merely
things in general, the difference in their outer relations cannot
constitute a difference in the things themselves; on the contrary,
it presupposes this difference. And if there is no inward
difference between the concept of the one and the concept of the
other, I am only positing one and the same thing in different
relations. Further, the addition of one sheer affirmation
(reality) to another increases the positive in them; nothing is
withdrawn or inhibited; accordingly the real in things cannot
be in conflict with itself -- and so on.
***
As we have shown, the concepts of reflection, owing to a
certain misinterpretation, have exercised so great an influence
upon the employment of the understanding that they have
misled even one of the most acute of all philosophers into a
supposititious system of intellectual knowledge, which undertakes
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to determine its objects without any assistance from the
senses. For this reason the exposition of the cause of what is
deceptive -- occasioning these false principles -- in the amphiboly
of these concepts, is of great utility as a reliable method of
determining and securing the limits of the understanding.
It is indeed true that whatever universally agrees with or
contradicts a concept also agrees with or contradicts every
particular which is contained under it (dictum de omni et
nullo); but it would be absurd to alter this logical principle so
as to read: -- what is not contained in a universal concept is also
not included in the particular concepts which stand under it.
For these are particular concepts just because they include in
themselves more than is thought in the universal. Nevertheless
it is upon this latter principle that the whole intellectual 
system of Leibniz is based; and with this principle it therefore
falls, together with all the ambiguities (in the employment of
the understanding) that have thence arisen.
The principle of the identity of indiscernibles is really based
on the presupposition, that if a certain distinction is not found
in the concept of a thing in general, it is also not to be found
in the things themselves, and consequently that all things
which are not distinguishable from one another in their concepts
(in quality or quantity) are completely identical (numero
eadem). Because in the mere concept of a thing in general we
abstract from the many necessary conditions of its intuition,
the conditions from which we have abstracted are, with strange
presumption, treated as not being there at all, and nothing is
allowed to the thing beyond what is contained in its concept.
The concept of a cubic foot of space, wherever and however
often I think it, is in itself throughout one and the same.
But two cubic feet are nevertheless distinguished in space by
the mere difference of their locations (numero diversa); these
locations are conditions of the intuition wherein the object of
this concept is given; they do not, however, belong to the concept
but entirely to sensibility. Similarly there is no conflict
in the concept of a thing unless a negative statement is combined
with an affirmative; merely affirmative concepts cannot,
when combined, produce any cancellation. But in the sensible
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intuition, wherein reality (e.g. motion) is given, there are
conditions (opposite directions), which have been omitted in
the concept of motion in general, that make possible a conflict
(though not indeed a logical one), namely, as producing from
what is entirely positive a zero (=0). We are not, therefore, in
a position to say that since conflict is not to be met with in
the concepts of reality, all reality is in agreement with itself.
 According to mere concepts the inner is the substratum of
all relational or outer determinations. If, therefore, I abstract
from all conditions of intuition and confine myself to the concept
of a thing in general, I can abstract from all outer relation,
and there must still be left a concept of something which
signifies no relation, but inner determinations only. From this
it seems to follow that in whatever is a thing (substance) there
is something which is absolutely inward and precedes all outer
determinations, inasmuch as it is what first makes them
possible; and consequently, that this substratum, as no longer
containing in itself any outer relations, is simple. (Corporeal
things are never anything save relations only, at least of
their parts external to each other. ) And since we know of no
determinations which are absolutely inner except those [given]
through our inner sense, this substratum is not only simple;
it is likewise (in analogy with our inner sense) determined
through representations; in other words, all things are really
monads, simple beings endowed with representations. These
contentions would be entirely justified, if beyond the concept
of a thing in general there were no further conditions
under which alone objects of outer intuition can be given us
-- those from which the pure concept has [as a matter of fact] made abstraction.

++ If we here wished to resort to the usual subterfuge, maintaining
as regards realitates noumena that they at least do not act in 
opposition to each other, it would be incumbent on us to produce an 
example of such pure and non-sensuous reality, that it may be 
discerned whether such a concept represents something or nothing.
But no example can be obtained otherwise than from experience,
which never yields more than phenomena. This proposition has
therefore no further meaning than that a concept which only 
includes affirmation includes no negation -- a proposition which we
have never doubted.
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For under these further conditions, as we
find, an abiding appearance in space (impenetrable extension)
can contain only relations and nothing at all that is absolutely
inward, and yet be the primary substratum of all outer 
perception. Through mere concepts I cannot, indeed, think what
is outer without thinking something that is inner; and this
for the sufficient reason that concepts of relation presuppose
things which are absolutely [i.e. independently] given, and
without these are impossible. But something is contained in
intuition which is not to be met with in the mere concept of a
thing; and this yields the substratum, which could never be
known through mere concepts, namely, a space which with all
that it contains consists solely of relations, formal or, it may be,
also real. Because, without an absolutely inner element, a thing
can never be represented by mere concepts, I may not therefore
claim that there is not also in the things themselves which are
subsumed under these concepts, and in their intuition, 
something external that has no basis in anything wholly inward.
Once we have abstracted from all conditions of intuition, there
is, I admit, nothing left in the mere concept but the inner in
general and its interrelations, through which alone the external
is possible. But this necessity, which is founded solely
on abstraction, does not arise in the case of things as given in
intuition with determinations that express mere relations, 
without having anything inward as their basis; for such are not
things in themselves but merely appearances. All that we
know in matter is merely relations (what we call the inner
determinations of it are inward only in a comparative sense),
but among these relations some are self-subsistent and 
permanent, and through these we are given a determinate object.
The fact that, if I abstract from these relations, there is 
nothing more left for me to think does not rule out the concept
of a thing as appearance, nor indeed the concept of an object
in abstracto. What it does remove is all possibility of an object
determinable through mere concepts, that is, of a noumenon.
It is certainly startling to hear that a thing is to be taken as
consisting wholly of relations. Such a thing is, however, mere
appearance, and cannot be thought through pure categories;
P 292
what it itself consists in is the mere relation of something in
general to the senses. Similarly, if we begin with mere concepts,
we cannot think the relations of things in abstracto in
any other manner than by regarding one thing as the cause of
determinations in another, for that is how our understanding
conceives of relations. But since we are in that case disregarding
all intuition, we have ruled ourselves out from any kind of
recognition of the special mode in which the different elements
of the manifold determine each other's positions, that is, of
the form of sensibility (space), which yet is presupposed in all
empirical causality.
If by merely intelligible objects we mean those things which
are thought through pure categories, without any schema
of sensibility, such objects are impossible. For the condition of
the objective employment of all our concepts of understanding
is merely the mode of our sensible intuition, by which objects
are given us; if we abstract from these objects, the concepts
have no relation to any object. Even if we were willing
to assume a kind of intuition other than this our sensible
kind, the functions of our thought would still be without
meaning in respect to it. If, however, we have in mind only
objects of a non-sensible intuition, in respect of which our
categories are admittedly not valid, and of which therefore
we can never have any knowledge whatsoever (neither intuition
nor concept), noumena in this purely negative sense
must indeed be admitted. For this is no more than saying
that our kind of intuition does not extend to all things, but
only to objects of our senses, that consequently its objective
validity is limited, and that a place therefore remains open
for some other kind of intuition, and so for things as its
objects. But in that case the concept of a noumenon is problematic,
that is, it is the representation of a thing of which we
can neither say that it is possible nor that it is impossible; for
we are acquainted with no kind of intuition but our own
sensible kind and no kind of concepts but the categories, and
neither of these is appropriate to a non-sensible object. We
cannot, therefore, positively extend the sphere of the objects
of our thought beyond the conditions of our sensibility, and
assume besides appearances objects of pure thought, that is,
P 293
noumena, since such objects have no assignable positive
meaning. For in regard to the categories we must admit that
they are not of themselves adequate to the knowledge of
things in themselves, and that without the data of sensibility
they would be merely subjective forms of the unity of 
understanding, having no object. Thought is in itself, indeed, no
product of the senses, and in so far is also not limited by
them; but it does not therefore at once follow that it has a
pure employment of its own, unaided by sensibility, since it is
then without an object. We cannot call the noumenon such
an object; signifying, as it does, the problematic concept of
an object for a quite different intuition and a quite different
understanding from ours, it is itself a problem. The concept
of the noumenon is, therefore, not the concept of an object,
but is a problem unavoidably bound up with the limitation
of our sensibility -- the problem, namely, as to whether there
may not be objects entirely disengaged from any such kind
of intuition. This is a question which can only be answered
in an indeterminate manner, by saying that as sensible 
intuition does not extend to all things without distinction, a
place remains open for other and different objects; and 
consequently that these latter must not be absolutely denied,
though -- since we are without a determinate concept of them
(inasmuch as no category can serve that purpose) -- neither
can they be asserted as objects for our understanding.
Understanding accordingly limits sensibility, but does
not thereby extend its own sphere. In the process of warning
the latter that it must not presume to claim applicability to
things-in-themselves but only to appearances, it does indeed
think for itself an object in itself, but only as transcendental
object, which is the cause of appearance and therefore not
itself appearance, and which can be thought neither as quantity
nor as reality nor as substance etc. (because these concepts
always require sensible forms in which they determine an
object). We are completely ignorant whether it is to be met
with in us or outside us, whether it would be at once removed
with the cessation of sensibility, or whether in the absence of
sensibility it would still remain. If we are pleased to name
this object noumenon for the reason that its representation
is not sensible, we are free to do so. But since we can apply
P 294
to it none of the concepts of our understanding, the 
representation remains for us empty, and is of no service except
to mark the limits of our sensible knowledge and to leave
open a space which we can fill neither through possible 
experience nor through pure understanding.
The critique of this pure understanding, accordingly,
does not permit us to create a new field of objects beyond those
which may be presented to it as appearances, and so to stray
into intelligible worlds; nay, it does not allow of our 
entertaining even the concept of them. The error, which quite 
obviously is the cause of this mistaken venture, and which indeed
excuses though it does not justify it, lies in employing the
understanding, contrary to its vocation, transcendentally, and
in making objects, that is, possible intuitions, conform to 
concepts, not concepts to possible intuitions, on which alone their
objective validity rests. This error, in turn, is due to the fact
that apperception, and with it thought, precedes all possible
determinate ordering of representations. Consequently what
we do is to think something in general; and while on the one
hand we determine it in sensible fashion, on the other hand we
distinguish from this mode of intuiting it the universal object
represented in abstracto. What we are then left with is a mode
of determining the object by thought alone -- a merely logical
form without content, but which yet seems to us to be a
mode in which the object exists in itself (noumenon) without
regard to intuition, which is limited to our senses.
 Before we leave the Transcendental Analytic we must
add some remarks which, although in themselves not of
special importance, might nevertheless be regarded as 
requisite for the completeness of the system. The supreme
concept with which it is customary to begin a transcendental
philosophy is the division into the possible and the impossible.
But since all division presupposes a concept to be divided, a
still higher one is required, and this is the concept of an object
in general, taken problematically, without its having been
decided whether it is something or nothing. As the categories
are the only concepts which refer to objects in general, the
P 295
distinguishing of an object, whether it is something or
nothing, will proceed according to the order and under the
guidance of the categories.
I. To the concepts of all, many, and one there is opposed
the concept which cancels everything, that is, none. Thus the
object of a concept to which no assignable intuition whatsoever
corresponds is = nothing. That is, it is a concept without
an object (ens rationis), like noumena, which cannot be
reckoned among the possibilities, although they must not for
that reason be declared to be also impossible; or like certain
new fundamental forces, which though entertained in thought
without self-contradiction are yet also in our thinking 
unsupported by any example from experience, and are therefore
not to be counted as possible.
2. Reality is something; negation is nothing, namely, a
concept of the absence of an object, such as shadow, cold
(nihil privativum).
3. The mere form of intuition, without substance, is in
itself no object, but the merely formal condition of an object
(as appearance), as pure space and pure time (ens imaginarium).
These are indeed something, as forms of intuition,
but are not themselves objects which are intuited.
4. The object of a concept which contradicts itself is
nothing, because the concept is nothing, is the impossible,
e.g. a two-sided rectilinear figure (nihil negativum).
The table of this division of the concept of nothing would
therefore have to be drawn up as follows. (The corresponding
division of something follows directly from it):
Nothing,
as
1
Empty concept without object,
ens rationis.
2
Empty object of a concept,
nihil privativum.
P 295
3
Empty intuition without object,
ens imaginarium.
4
Empty object without concept,
nihil negativum.
P 296
We see that the ens rationis (1) is distinguished from the
nihil negativum (4), in that the former is not to be counted
among possibilities because it is mere fiction (although not
self-contradictory), whereas the latter is opposed to possibility
in that the concept cancels itself. Both, however, are
empty concepts. On the other hand, the nihil privativum (2)
and the ens imaginarium (3) are empty data for concepts. If
light were not given to the senses we could not represent 
darkness, and if extended beings were not perceived we could not
represent space. Negation and the mere form of intuition, in
the absence of a something real, are not objects.

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