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 P 277 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 P 278 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 P 279 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 P 280 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 P 281 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 P 282 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 P 283 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 P 284 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 P 285 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 P 286 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 P 287 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 P 288 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 P 289 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 P 290 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. P 291 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.