APPENDIX

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

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

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

1. Identity and Difference. When an object is presented to us several
Times, but always with the same internal determinations (qualitas et
Quantitas), it, if an object of pure understanding, is always the same
Not several things, but only one thing (numerica identitas); but if a
Phenomenon, we do not concern ourselves with comparing the conception of
The thing with the conception of some other, but, although they may be
In this respect perfectly the same, the difference of place at the same
Time is a sufficient ground for asserting the numerical difference of
These objects (of sense). Thus, in the case of two drops of water, we
May make complete abstraction of all internal difference (quality and
Quantity), and, the fact that they are intuited at the same time in
Different places, is sufficient to justify us in holding them to
Be numerically different. Leibnitz regarded phenomena as things in
Themselves, consequently as intelligibilia, that is, objects of pure
Understanding (although, on account of the confused nature of their
Representations, he gave them the name of phenomena), and in this
Case his principle of the indiscernible (principium identatis
Indiscernibilium) is not to be impugned. But, as phenomena are objects
Of sensibility, and, as the understanding, in respect of them, must be
Employed empirically and not purely or transcendentally, plurality
And numerical difference are given by space itself as the condition of
External phenomena. For one part of space, although it may be perfectly
Similar and equal to another part, is still without it, and for this
Reason alone is different from the latter, which is added to it in order
To make up a greater space. It follows that this must hold good of
All things that are in the different parts of space at the same time
However similar and equal one may be to another

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

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

4. Matter and Form. These two conceptions lie at the foundation of all
Other reflection, so inseparably are they connected with every mode of
Exercising the understanding. The former denotes the determinable in
General, the second its determination, both in a transcendental sense
Abstraction being made of every difference in that which is given, and
Of the mode in which it is determined. Logicians formerly termed the
Universal, matter, the specific difference of this or that part of
The universal, form. In a judgement one may call the given conceptions
Logical matter (for the judgement), the relation of these to each other
(by means of the copula), the form of the judgement. In an object, the
Composite parts thereof (essentialia) are the matter; the mode in which
They are connected in the object, the form. In respect to things
In general, unlimited reality was regarded as the matter of all
Possibility, the limitation thereof (negation) as the form, by which
One thing is distinguished from another according to transcendental
Conceptions. The understanding demands that something be given (at least
In the conception), in order to be able to determine it in a certain
Manner. Hence, in a conception of the pure understanding, the matter
Precedes the form, and for this reason Leibnitz first assumed the
Existence of things (monads) and of an internal power of representation
In them, in order to found upon this their external relation and the
Community their state (that is, of their representations). Hence, with
Him, space and time were possible--the former through the relation of
Substances, the latter through the connection of their determinations
With each other, as causes and effects. And so would it really be
If the pure understanding were capable of an immediate application
To objects, and if space and time were determinations of things in
Themselves. But being merely sensuous intuitions, in which we determine
All objects solely as phenomena, the form of intuition (as a subjective
Property of sensibility) must antecede all matter (sensations)
Consequently space and time must antecede all phenomena and all data
Of experience, and rather make experience itself possible. But the
Intellectual philosopher could not endure that the form should precede
The things themselves and determine their possibility; an objection
Perfectly correct, if we assume that we intuite things as they are
Although with confused representation. But as sensuous intuition is a
Peculiar subjective condition, which is a priori at the foundation of
All perception, and the form of which is primitive, the form must be
Given per se, and so far from matter (or the things themselves which
Appear) lying at the foundation of experience (as we must conclude
If we judge by mere conceptions), the very possibility of itself
Presupposes, on the contrary, a given formal intuition (space and time)

REMARK ON THE AMPHIBOLY OF THE CONCEPTIONS OF REFLECTION

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

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

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

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

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

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

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

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

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

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

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

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

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

When we reflect in a purely logical manner, we do nothing more than
Compare conceptions in our understanding, to discover whether both have
The same content, whether they are self-contradictory or not, whether
Anything is contained in either conception, which of the two is given
And which is merely a mode of thinking that given. But if I apply these
Conceptions to an object in general (in the transcendental sense)
Without first determining whether it is an object of sensuous or
Intellectual intuition, certain limitations present themselves, which
Forbid us to pass beyond the conceptions and render all empirical use
Of them impossible. And thus these limitations prove that the
Representation of an object as a thing in general is not only
Insufficient, but, without sensuous determination and independently of
Empirical conditions, self-contradictory; that we must therefore make
Abstraction of all objects, as in logic, or, admitting them, must think
Them under conditions of sensuous intuition; that, consequently, the
Intelligible requires an altogether peculiar intuition, which we do not
Possess, and in the absence of which it is for us nothing; while, on the
Other hand phenomena cannot be objects in themselves. For, when I merely
Think things in general, the difference in their external relations
Cannot constitute a difference in the things themselves; on the
Contrary, the former presupposes the latter, and if the conception of
One of two things is not internally different from that of the other
I am merely thinking the same thing in different relations. Further
By the addition of one affirmation (reality) to the other, the positive
Therein is really augmented, and nothing is abstracted or withdrawn
From it; hence the real in things cannot be in contradiction with or
Opposition to itself--and so on

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

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

Leibnitz's principle of the identity of indiscernibles or
Indistinguishables is really based on the presupposition that, if in the
Conception of a thing a certain distinction is not to be found, it is
Also not to be met with in things themselves; that, consequently
All things are completely identical (numero eadem) which are not
Distinguishable from each other (as to quality or quantity) in our
Conceptions of them. But, as in the mere conception of anything
Abstraction has been made of many necessary conditions of intuition
That of which abstraction has been made is rashly held to be
Non-existent, and nothing is attributed to the thing but what is
Contained in its conception

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

If by intelligible objects we understand things which can be thought
By means of the pure categories, without the need of the schemata of
Sensibility, such objects are impossible. For the condition of the
Objective use of all our conceptions of understanding is the mode of
Our sensuous intuition, whereby objects are given; and, if we make
Abstraction of the latter, the former can have no relation to an object
And even if we should suppose a different kind of intuition from our
Own, still our functions of thought would have no use or signification
In respect thereof. But if we understand by the term, objects of a
Non-sensuous intuition, in respect of which our categories are not
Valid, and of which we can accordingly have no knowledge (neither
Intuition nor conception), in this merely negative sense noumena must be
Admitted. For this is no more than saying that our mode of intuition is
Not applicable to all things, but only to objects of our senses
That consequently its objective validity is limited, and that room is
Therefore left for another kind of intuition, and thus also for things
That may be objects of it. But in this sense the conception of a
Noumenon is problematical, that is to say, it is the notion of that it
That it is possible, nor that it is impossible, inasmuch as we do not
Know of any mode of intuition besides the sensuous, or of any other sort
Of conceptions than the categories--a mode of intuition and a kind of
Conception neither of which is applicable to a non-sensuous object. We
Are on this account incompetent to extend the sphere of our objects
Of thought beyond the conditions of our sensibility, and to assume the
Existence of objects of pure thought, that is, of noumena, inasmuch as
These have no true positive signification. For it must be confessed
Of the categories that they are not of themselves sufficient for the
Cognition of things in themselves and, without the data of sensibility
Are mere subjective forms of the unity of the understanding. Thought is
Certainly not a product of the senses, and in so far is not limited by
Them, but it does not therefore follow that it may be employed purely
And without the intervention of sensibility, for it would then be
Without reference to an object. And we cannot call a noumenon an object
Of pure thought; for the representation thereof is but the problematical
Conception of an object for a perfectly different intuition and
A perfectly different understanding from ours, both of which are
Consequently themselves problematical. The conception of a noumenon is
Therefore not the conception of an object, but merely a problematical
Conception inseparably connected with the limitation of our sensibility
That is to say, this conception contains the answer to the question:
"Are there objects quite unconnected with, and independent of, our
Intuition?"--a question to which only an indeterminate answer can be
Given. That answer is: "Inasmuch as sensuous intuition does not apply
To all things without distinction, there remains room for other and
Different objects." The existence of these problematical objects
Is therefore not absolutely denied, in the absence of a determinate
Conception of them, but, as no category is valid in respect of them
Neither must they be admitted as objects for our understanding

Understanding accordingly limits sensibility, without at the same time
Enlarging its own field. While, moreover, it forbids sensibility to
Apply its forms and modes to things in themselves and restricts it
To the sphere of phenomena, it cogitates an object in itself, only
However, as a transcendental object, which is the cause of a phenomenon
(consequently not itself a phenomenon), and which cannot be thought
Either as a quantity or as reality, or as substance (because these
Conceptions always require sensuous forms in which to determine an
Object)--an object, therefore, of which we are quite unable to say
Whether it can be met with in ourselves or out of us, whether it would
Be annihilated together with sensibility, or, if this were taken away
Would continue to exist. If we wish to call this object a noumenon
Because the representation of it is non-sensuous, we are at liberty
To do so. But as we can apply to it none of the conceptions of our
Understanding, the representation is for us quite void, and is available
Only for the indication of the limits of our sensuous intuition, thereby
Leaving at the same time an empty space, which we are competent to
Fill by the aid neither of possible experience, nor of the pure
Understanding

The critique of the pure understanding, accordingly, does not permit us
To create for ourselves a new field of objects beyond those which are
Presented to us as phenomena, and to stray into intelligible worlds;
Nay, it does not even allow us to endeavour to form so much as a
Conception of them. The specious error which leads to this--and which is
A perfectly excusable one--lies in the fact that the employment of the
Understanding, contrary to its proper purpose and destination, is made
Transcendental, and objects, that is, possible intuitions, are made to
Regulate themselves according to conceptions, instead of the conceptions
Arranging themselves according to the intuitions, on which alone their
Own objective validity rests. Now the reason of this again is that
Apperception, and with it thought, antecedes all possible determinate
Arrangement of representations. Accordingly we think something in
General and determine it on the one hand sensuously, but, on the other
Distinguish the general and in abstracto represented object from this
Particular mode of intuiting it. In this case there remains a mode of
Determining the object by mere thought, which is really but a logical
Form without content, which, however, seems to us to be a mode of
The existence of the object in itself (noumenon), without regard to
Intuition which is limited to our senses

Before ending this transcendental analytic, we must make an addition
Which, although in itself of no particular importance, seems to be
Necessary to the completeness of the system. The highest conception
With which a transcendental philosophy commonly begins, is the division
Into possible and impossible. But as all division presupposes a divided
Conception, a still higher one must exist, and this is the conception of
An object in general--problematically understood and without its being
Decided whether it is something or nothing. As the categories are the
Only conceptions which apply to objects in general, the distinguishing
Of an object, whether it is something or nothing, must proceed according
To the order and direction of the categories

1. To the categories of quantity, that is, the conceptions of all, many
And one, the conception which annihilates all, that is, the conception
Of none, is opposed. And thus the object of a conception, to which no
Intuition can be found to correspond, is = nothing. That is, it is a
Conception without an object (ens rationis), like noumena, which cannot
Be considered possible in the sphere of reality, though they must not
Therefore be held to be impossible--or like certain new fundamental
Forces in matter, the existence of which is cogitable without
Contradiction, though, as examples from experience are not forthcoming
They must not be regarded as possible

2. Reality is something; negation is nothing, that is, a conception of
The absence of an object, as cold, a shadow (nihil privativum)

3. The mere form of intuition, without substance, is in itself no
Object, but the merely formal condition of an object (as phenomenon)
As pure space and pure time. These are certainly something, as forms
Of intuition, but are not themselves objects which are intuited (ens
Imaginarium)

4. The object of a conception which is self-contradictory, is nothing
Because the conception is nothing--is impossible, as a figure composed
Of two straight lines (nihil negativum)

The table of this division of the conception of nothing (the
Corresponding division of the conception of something does not require
Special description) must therefore be arranged as follows:

NOTHING AS

1
As Empty Conception
Without object
Ens rationis

2
Empty object of
A conception
Nihil privativum

3
Empty intuition
Without object
Ens imaginarium

4
Empty object
Without conception
Nihil negativum

We see that the ens rationis is distinguished from the nihil negativum
Or pure nothing by the consideration that the former must not be
Reckoned among possibilities, because it is a mere fiction--though
Not self-contradictory, while the latter is completely opposed to
All possibility, inasmuch as the conception annihilates itself. Both
However, are empty conceptions. On the other hand, the nihil privativum
And ens imaginarium are empty data for conceptions. If light be not
Given to the senses, we cannot represent to ourselves darkness, and if
Extended objects are not perceived, we cannot represent space. Neither
The negation, nor the mere form of intuition can, without something
Real, be an object