# Critique of Pure Reason (Meiklejohn)/Volume 1/Division 1

TRANSCENDENTAL LOGIC:
FIRST DIVISION.
TRANSCENDENTAL ANALYTIC.
§ 1.
Transcendental analytic is the dissection of the whole of our a priori knowledge into the elements of the pure cognition of the understanding. In order to effect our purpose, it is necessary: (1) That the conceptions be pure and not empirical; (2) That they belong not to intuition and sensibility, but to thought and understanding; (3) That they be elementary conceptions, and as such, quite different from deduced or compound conceptions; (4) That our table of these elementary conceptions be complete, and fill up the whole sphere of the pure understanding. Now this completeness of a science cannot be accepted with confidence on the guarantee of a mere estimate of its existence in an ​aggregate formed only by means of repeated experiments and attempts. The completeness which we require is possible only by means of an idea of the totality of the a priori cognition of the understanding, and through the thereby determined division of the conceptions which form the said whole; consequently, only by means of their connection in a system. Pure understanding distinguishes itself not merely from everything empirical, but also completely from all sensibility. It is a unity self-subsistent, self-sufficient, and not to be enlarged by any additions from without. Hence the sum of its cognition constitutes a system to be determined by and comprised under an idea; and the completeness and articulation of this system can at the same time serve as a test of the correctness and genuineness of all the parts of cognition that belong to it. The whole of this part of transcendental logic consists of two books, of which the one contains the conceptions, and the other the principles of pure understanding.

### BOOK I.BOOK I.
##### Analytic of Conceptions. § 2.Analytic of Conceptions. § 2.

By the term Analytic of Conceptions, I do not understand the analysis of these, or the usual process in philosophical investigations of dissecting the conceptions which present themselves, according to their content, and so making them clear; but I mean the hitherto little attempted dissection of the faculty of understanding itself, in order to investigate the possibility of conceptions a priori, by looking for them in the understanding alone, as their birthplace, and analysing the pure use of this faculty. For this is the proper duty of a transcendental philosophy; what remains is the logical treatment of the conceptions in philosophy in general. We shall therefore follow up the pure conceptions even to their germs and beginnings in the human understanding, in which they lie, until they are developed on occasions presented by experience, and, freed by the same understanding from the empirical conditions attaching to them, are set forth in their unalloyed purity. ​

### CHAPTER I. Of the Transcendental Clue to the Discovery of all Pure Conceptions of the Understanding.CHAPTER I. Of the Transcendental Clue to the Discovery of all Pure Conceptions of the Understanding.
##### Introductory. § 3.Introductory. § 3.

When we call into play a faculty of cognition, different conceptions manifest themselves according to the different circumstances, and make known this faculty, and assemble themselves into a more or less extensive collection, according to the time or penetration that has been applied to the consideration of them. Where this process, conducted as it is mechanically, so to speak, will end, cannot be determined with certainty. Besides, the conceptions which we discover in this haphazard manner present themselves by no means in order and systematic unity, but are at last coupled together only according to resemblances to each other, and arranged in series, according to the quantity of their content, from the simpler to the more complex—series which are anything but systematic, though not altogether without a certain kind of method in their construction.
Transcendental philosophy has the advantage, and moreover the duty, of searching for its conceptions according to a principle; because these conceptions spring pure and unmixed out of the understanding as an absolute unity, and therefore must be connected with each other according to one conception or idea. A connection of this kind, however, furnishes us with a ready prepared rule, by which its proper place may be assigned to every pure conception of the understanding, and the completeness of the system of all be determined a priori—both which would otherwise have been dependent on mere choice or chance.

#### SECTION I. Of defined above Use of understanding in General.SECTION I. Of defined above Use of understanding in General.
##### § 4.§ 4.

The understanding was defined above only negatively, as a non-sensuous faculty of cognition. Now, independently of sensibility, we cannot possibly have any intuition; ​consequently, the understanding is no faculty of intuition. But besides intuition there is no other mode of cognition, except through conceptions; consequently, the cognition of every, at least of every human, understanding is a cognition through conceptions—not intuitive, but discursive. All intuitions, as sensuous, depend on affections; conceptions, therefore, upon functions. By the word function I understand the unity of the act of arranging diverse representations under one common representation. Conceptions, then, are based on the spontaneity of thought, as sensuous intuitions are on the receptivity of impressions. Now, the understanding cannot make any other use of these conceptions than to judge by means of them. As no representation, except an intuition, relates immediately to its object, a conception never relates immediately to an object, but only to some other representation thereof, be that an intuition or itself a conception. A judgement, therefore, is the mediate cognition of an object, consequently the representation of a representation of it. In every judgement there is a conception which applies to, and is valid for many other conceptions, and which among these comprehends also a given representation, this last being immediately connected with an object. For example, in the judgement—"All bodies are divisible," our conception of divisible applies to various other conceptions; among these, however, it is here particularly applied to the conception of body, and this conception of body relates to certain phenomena which occur to us. These objects, therefore, are mediately represented by the conception of divisibility. All judgements, accordingly, are functions of unity in our representations, inasmuch as, instead of an immediate, a higher representation, which comprises this and various others, is used for our cognition of the object, and thereby many possible cognitions are collected into one. But we can reduce all acts of the understanding to judgements, so that understanding may be represented as the faculty of judging. For it is, according to what has been said above, a faculty of thought. Now thought is cognition by means of conceptions. But conceptions, as predicates of possible judgements, relate to some representation of a yet undetermined object. Thus the conception of body indicates something—for example, metal—which can be cognized by means of that conception. It is therefore a conception, for the reason alone that other representations are contained under it, by means of which it can relate to objects. It is therefore the ​predicate to a possible judgement; for example: "Every metal is a body." All the functions of the understanding therefore can be discovered, when we can completely exhibit the functions of unity in judgements. And that this may be effected very easily, the following section will show.

#### SECTION II.—Of the Logical Function of the Understanding in Judgements.SECTION II.—Of the Logical Function of the Understanding in Judgements.
##### § 5.§ 5.

If we abstract all the content of a judgement, and consider only the intellectual form thereof, we find that the function of thought in a judgement can be brought under four heads, of which each contains three momenta. These may be conveniently represented in the following table:
| | 1 Quantity of judgements Universal Particular Singular | |
| 2 Quality Affirmative Negative Infinite | | 3 Relation Categorical Hypothetical Disjunctive |
| | 4 Modality Problematical Assertorical Apodeictical | |
As this division appears to differ in some, though not essential points, from the usual technique of logicians, the following observations, for the prevention of otherwise possible misunderstanding, will not be without their use.
1. Logicians say, with justice, that in the use of judgements in syllogisms, singular judgements may be treated like universal ones. For, precisely because a singular judgement has no extent at all, its predicate cannot refer to a part of that which is contained in the conception of the subject and be excluded from the rest. The predicate is valid for the whole conception just as if it were a general conception, and had extent, to the whole of which the predicate applied. On the other hand, let us compare ​a singular with a general judgement, merely as a cognition, in regard to quantity. The singular judgement relates to the general one, as unity to infinity, and is therefore in itself essentially different. Thus, if we estimate a singular judgement (judicium singulare) not merely according to its intrinsic validity as a judgement, but also as a cognition generally, according to its quantity in comparison with that of other cognitions, it is then entirely different from a general judgement (judicium commune), and in a complete table of the momenta of thought deserves a separate place—though, indeed, this would not be necessary in a logic limited merely to the consideration of the use of judgements in reference to each other.
2. In like manner, in transcendental logic, infinite must be distinguished from affirmative judgements, although in general logic they are rightly enough classed under affirmative. General logic abstracts all content of the predicate (though it be negative), and only considers whether the said predicate be affirmed or denied of the subject. But transcendental logic considers also the worth or content of this logical affirmation—an affirmation by means of a merely negative predicate, and inquires how much the sum total of our cognition gains by this affirmation. For example, if I say of the soul, "It is not mortal"—by this negative judgement I should at least ward off error. Now, by the proposition, "The soul is not mortal," I have, in respect of the logical form, really affirmed, inasmuch as I thereby place the soul in the unlimited sphere of immortal beings. Now, because of the whole sphere of possible existences, the mortal occupies one part, and the immortal the other, neither more nor less is affirmed by the proposition than that the soul is one among the infinite multitude of things which remain over, when I take away the whole mortal part. But by this proceeding we accomplish only this much, that the infinite sphere of all possible existences is in so far limited that the mortal is excluded from it, and the soul is placed in the remaining part of the extent of this sphere. But this part remains, notwithstanding this exception, infinite, and more and more parts may be taken away from the whole sphere, without in the slightest degree thereby augmenting or affirmatively determining our conception of the soul. These judgements, therefore, infinite in respect of their logical extent, are, in respect of the content of their cognition, merely limitative; and are consequently entitled to a place in our transcendental table of all the momenta of thought in judgements, because the ​function of the understanding exercised by them may perhaps be of importance in the field of its pure a priori cognition.
3. All relations of thought in judgements are those (a) of the predicate to the subject; (b) of the principle to its consequence; (c) of the divided cognition and all the members of the division to each other. In the first of these three classes, we consider only two conceptions; in the second, two judgements; in the third, several judgements in relation to each other. The hypothetical proposition, "If perfect justice exists, the obstinately wicked are punished," contains properly the relation to each other of two propositions, namely, "Perfect justice exists," and "The obstinately wicked are punished." Whether these propositions are in themselves true is a question not here decided. Nothing is cogitated by means of this judgement except a certain consequence. Finally, the disjunctive judgement contains a relation of two or more propositions to each other—a relation not of consequence, but of logical opposition, in so far as the sphere of the one proposition excludes that of the other. But it contains at the same time a relation of community, in so far as all the propositions taken together fill up the sphere of the cognition. The disjunctive judgement contains, therefore, the relation of the parts of the whole sphere of a cognition, since the sphere of each part is a complemental part of the sphere of the other, each contributing to form the sum total of the divided cognition. Take, for example, the proposition, "The world exists either through blind chance, or through internal necessity, or through an external cause." Each of these propositions embraces a part of the sphere of our possible cognition as to the existence of a world; all of them taken together, the whole sphere. To take the cognition out of one of these spheres, is equivalent to placing it in one of the others; and, on the other hand, to place it in one sphere is equivalent to taking it out of the rest. There is, therefore, in a disjunctive judgement a certain community of cognitions, which consists in this, that they mutually exclude each other, yet thereby determine, as a whole, the true cognition, inasmuch as, taken together, they make up the complete content of a particular given cognition. And this is all that I find necessary, for the sake of what follows, to remark in this place.
4. The modality of judgements is a quite peculiar function, with this distinguishing characteristic, that it contributes nothing to the content of a judgement (for besides quantity, quality, ​and relation, there is nothing more that constitutes the content of a judgement), but concerns itself only with the value of the copula in relation to thought in general. Problematical judgements are those in which the affirmation or negation is accepted as merely possible (ad libitum). In the assertorical, we regard the proposition as real (true); in the apodeictical, we look on it as necessary. Thus the two judgements (antecedens et consequens), the relation of which constitutes a hypothetical judgement, likewise those (the members of the division) in whose reciprocity the disjunctive consists, are only problematical. In the example above given the proposition, "There exists perfect justice," is not stated assertorically, but as an ad libitum judgement, which someone may choose to adopt, and the consequence alone is assertorical. Hence such judgements may be obviously false, and yet, taken problematically, be conditions of our cognition of the truth. Thus the proposition, "The world exists only by blind chance," is in the disjunctive judgement of problematical import only: that is to say, one may accept it for the moment, and it helps us (like the indication of the wrong road among all the roads that one can take) to find out the true proposition. The problematical proposition is, therefore, that which expresses only logical possibility (which is not objective); that is, it expresses a free choice to admit the validity of such a proposition—a merely arbitrary reception of it into the understanding. The assertorical speaks of logical reality or truth; as, for example, in a hypothetical syllogism, the antecedens presents itself in a problematical form in the major, in an assertorical form in the minor, and it shows that the proposition is in harmony with the laws of the understanding. The apodeictical proposition cogitates the assertorical as determined by these very laws of the understanding, consequently as affirming a priori, and in this manner it expresses logical necessity. Now because all is here gradually incorporated with the understanding,—inasmuch as in the first place we judge problematically; then accept assertorically our judgement as true; lastly, affirm it as inseparably united with the understanding, that is, as necessary and apodeictical,—we may safely reckon these three functions of modality as so many momenta of thought. ​

#### SECTION III.—Of the Pure Conceptions of the Understanding, or Categories.SECTION III.—Of the Pure Conceptions of the Understanding, or Categories.
##### § 6.§ 6.

General logic, as has been repeatedly said, makes abstraction of all content of cognition, and expects to receive representations from some other quarter, in order, by means of analysis, to convert them into conceptions. On the contrary, transcendental logic has lying before it the manifold content of a priori sensibility, which transcendental aesthetic presents to it in order to give matter to the pure conceptions of the understanding, without which transcendental logic would have no content, and be therefore utterly void. Now space and time contain an infinite diversity of determinations of pure a priori intuition, but are nevertheless the condition of the mind's receptivity, under which alone it can obtain representations of objects, and which, consequently, must always affect the conception of these objects. But the spontaneity of thought requires that this diversity be examined after a certain manner, received into the mind, and connected, in order afterwards to form a cognition out of it. This Process I call synthesis.
By the word synthesis, in its most general signification, I understand the process of joining different representations to each other and of comprehending their diversity in one cognition. This synthesis is pure when the diversity is not given empirically but a priori (as that in space and time). Our representations must be given previously to any analysis of them; and no conceptions can arise, quoad their content, analytically. But the synthesis of a diversity (be it given a priori or empirically) is the first requisite for the production of a cognition, which in its beginning, indeed, may be crude and confused, and therefore in need of analysis,—still, synthesis is that by which alone the elements of our cognitions are collected and united into a certain content, consequently it is the first thing on which we must fix our attention, if we wish to investigate the origin of our knowledge.
Synthesis, generally speaking, is, as we shall afterwards see, the mere operation of the imagination—a blind but indispensable ​function of the soul, without which we should have no cognition whatever, but of the working of which we are seldom even conscious. But to reduce this synthesis to conceptions is a function of the understanding, by means of which we attain to cognition, in the proper meaning of the term.
Pure synthesis, represented generally, gives us the pure conception of the understanding. But by this pure synthesis, I mean that which rests upon a basis of a priori synthetical unity. Thus, our numeration (and this is more observable in large numbers) is a synthesis according to conceptions, because it takes place according to a common basis of unity (for example, the decade). By means of this conception, therefore, the unity in the synthesis of the manifold becomes necessary.
By means of analysis different representations are brought under one conception—an operation of which general logic treats. On the other hand, the duty of transcendental logic is to reduce to conceptions, not representations, but the pure synthesis of representations. The first thing which must be given to us for the sake of the a priori cognition of all objects, is the diversity of the pure intuition; the synthesis of this diversity by means of the imagination is the second; but this gives, as yet, no cognition. The conceptions which give unity to this pure synthesis, and which consist solely in the representation of this necessary synthetical unity, furnish the third requisite for the cognition of an object, and these conceptions are given by the understanding.
The same function which gives unity to the different representation in a judgement, gives also unity to the mere synthesis of different representations in an intuition; and this unity we call the pure conception of the understanding. Thus, the same understanding, and by the same operations, whereby in conceptions, by means of analytical unity, it produced the logical form of a judgement, introduces, by means of the synthetical unity of the manifold in intuition, a transcendental content into its representations, on which account they are called pure conceptions of the understanding, and they apply a priori to objects, a result not within the power of general logic. ​
In this manner, there arise exactly so many pure conceptions of the understanding, applying a priori to objects of intuition in general, as there are logical functions in all possible judgements. For there is no other function or faculty existing in the understanding besides those enumerated in that table. These conceptions we shall, with Aristotle, call categories, our purpose being originally identical with his, notwithstanding the great difference in the execution.
| | TABLE OF THE CATEGORIES | |
| 1 Of Quantity Unity Plurality Totality | | 2 Of Quality Reality Negation Limitation |
| 3 Of Relation Of Inherence and Subsistence (substantia et accidens) Of Causality and Dependence (cause and effect) Of Community (reciprocity between the agent and patient) |||
| | 4 Of Modality Possibility —Impossibility Existence —Non-existence Necessity —Contingence | |
This, then, is a catalogue of all the originally pure conceptions of the synthesis which the understanding contains a priori, and these conceptions alone entitle it to be called a pure understanding; inasmuch as only by them it can render the manifold of intuition conceivable, in other words, think an object of intuition. This division is made systematically from a common principle, namely the faculty of judgement (which is just the same as the power of thought), and has not arisen rhapsodically from a search at haphazard after pure conceptions, respecting the full number of which we never could be certain, inasmuch as we employ induction alone in our search, without considering that in this way we can never understand ​wherefore precisely these conceptions, and none others, abide in the pure understanding. It was a design worthy of an acute thinker like Aristotle, to search for these fundamental conceptions. Destitute, however, of any guiding principle, he picked them up just as they occurred to him, and at first hunted out ten, which he called categories (predicaments). Afterwards be believed that he had discovered five others, which were added under the name of post predicaments. But his catalogue still remained defective. Besides, there are to be found among them some of the modes of pure sensibility (quando, ubi, situs, also prius, simul), and likewise an empirical conception (motus)—which can by no means belong to this genealogical register of the pure understanding. Moreover, there are deduced conceptions (actio, passio) enumerated among the original conceptions, and, of the latter, some are entirely wanting.
With regard to these, it is to be remarked, that the categories, as the true primitive conceptions of the pure understanding, have also their pure deduced conceptions, which, in a complete system of transcendental philosophy, must by no means be ​passed over; though in a merely critical essay we must be contented with the simple mention of the fact.
Let it be allowed me to call these pure, but deduced conceptions of the understanding, the predicables of the pure understanding, in contradistinction to predicaments. If we are in possession of the original and primitive, the deduced and subsidiary conceptions can easily be added, and the genealogical tree of the understanding completely delineated. As my present aim is not to set forth a complete system, but merely the principles of one, I reserve this task for another time. It may be easily executed by any one who will refer to the ontological manuals, and subordinate to the category of causality, for example, the predicables of force, action, passion; to that of community, those of presence and resistance; to the categories of modality, those of origination, extinction, change; and so with the rest. The categories combined with the modes of pure sensibility, or with one another, afford a great number of deduced à priori conceptions; a complete enumeration of which would be a useful and not unpleasant, but in this place a perfectly dispensable, occupation.
I purposely omit the definitions of the categories in this treatise. I shall analyse these conceptions only so far as is necessary for the doctrine of method, which is to form a part of this critique. In a system of pure reason, definitions of them would be with justice demanded of me, but to give them here would only bide from our view the main aim of our investigation, at the same time raising doubts and objections, the consideration of which, without injustice to our main purpose, may be very well postponed till another opportunity. Meanwhile, it ought to be sufficiently clear, from the little we have already said on this subject, that the formation of a complete vocabulary of pure conceptions, accompanied by all the requisite explanations, is not only a possible, but an easy undertaking. The compartments already exist; it is only necessary to fill them up; and a systematic topic like the ​present, indicates with perfect precision the proper place to which each conception belongs, while it readily points out any that have not yet been filled up.

##### § 7.§ 7.

Our table of the categories suggests considerations of some importance, which may perhaps have significant results in regard to the scientific form of all rational cognitions. For, that this table is useful in the theoretical part of philosophy, nay, indispensable for the sketching of the complete plan of a science, so far as that science rests upon conceptions a priori, and for dividing it mathematically, according to fixed principles, is most manifest from the fact that it contains all the elementary conceptions of the understanding, nay, even the form of a system of these in the understanding itself, and consequently indicates all the momenta, and also the internal arrangement of a projected speculative science, as I have elsewhere shown. Here follow some of these observations.
I. This table, which contains four classes of conceptions of the understanding, may, in the first instance, be divided into two classes, the first of which relates to objects of intuition—pure as well as empirical; the second, to the existence of these objects, either in relation to one another, or to the understanding.
The former of these classes of categories I would entitle the mathematical, and the latter the dynamical categories. The former, as we see, has no correlates; these are only to be found in the second class. This difference must have a ground in the nature of the human understanding.
II. The number of the categories in each class is always the same, namely, three;—a fact which also demands some consideration, because in all other cases division a priori through conceptions is necessarily dichotomy. It is to be added, that the third category in each triad always arises from the combination of the second with the first.
Thus totality is nothing else but plurality contemplated as unity; limitation is merely reality conjoined with negation; community is the causality of a substance, reciprocally determining, and determined by other substances; and ​finally, necessity is nothing but existence, which is given through the possibility itself. Let it not be supposed, however, that the third category is merely a deduced, and not a primitive conception of the pure understanding. For the conjunction of the first and second, in order to produce the third conception, requires a particular function of the understanding, which is by no means identical with those which are exercised in the first and second. Thus, the conception of a number (which belongs to the category of totality) is not always possible, where the conceptions of multitude and unity exist (for example, in the representation of the infinite). Or, if I conjoin the conception of a cause with that of a substance, it does not follow that the conception of influence, that is, how one substance can be the cause of something in another substance, will be understood from that. Thus it is evident that a particular act of the understanding is here necessary; and so in the other instances.
III. With respect to one category, namely, that of community, which is found in the third class, it is not so easy as with the others to detect its accordance with the form of the disjunctive judgement which corresponds to it in the table of the logical functions.
In order to assure ourselves of this accordance, we must observe that in every disjunctive judgement, the sphere of the judgement (that is, the complex of all that is contained in it) is represented as a whole divided into parts; and, since one part cannot be contained in the other, they are cogitated as co-ordinated with, not subordinated to each other, so that they do not determine each other unilaterally, as in a linear series, but reciprocally, as in an aggregate—(if one member of the division is posited, all the rest are excluded; and conversely).
Now a like connection is cogitated in a whole of things; for one thing is not subordinated, as effect, to another as cause of its existence, but, on the contrary, is co-ordinated contemporaneously and reciprocally, as a cause in relation to the determination of the others (for example, in a body—the parts of which mutually attract and repel each other). ​And this is an entirely different kind of connection from that which we find in the mere relation of the cause to the effect (the principle to the consequence), for in such a connection the consequence does not in its turn determine the principle, and therefore does not constitute, with the latter, a whole,—just as the Creator does not with the world make up a whole. The process of understanding by which it represents to itself the sphere of a divided conception, is employed also when we think of a thing as divisible; and in the same manner as the members of the division in the former exclude one another, and yet are connected in one sphere, so the understanding represents to itself the parts of the latter, as having—each of them—an existence (as substances), independently of the others, and yet as united in one whole.

##### § 8.§ 8.

In the transcendental philosophy of the ancients there exists one more leading division, which contains pure conceptions of the understanding, and which, although not numbered among the categories, ought, according to them, as conceptions a priori, to be valid of objects. But in this case they would augment the number of the categories; which cannot be. These are set forth in the proposition, so renowned among the schoolmen,—"Quodlibet ens est UNUM, VERUM, BONUM." Now, though the inferences from this principle were mere tautological propositions, and though it is allowed only by courtesy to retain a place in modern metaphysics, yet a thought which maintained itself for such a length of time, however empty it seems to be, deserves an investigation of its origin, and justifies the conjecture that it must be grounded in some law of the understanding, which, as is often the case, has only been erroneously interpreted. These pretended transcendental predicates are, in fact, nothing but logical requisites and criteria of all cognition of objects, and they employ, as the basis for this cognition, the categories of Quantity, namely, Unity, Plurality, and Totality. But these, which must be taken as material conditions, that is, as belonging to the possibility of things themselves, they employed merely in a formal signification, as belonging to the logical requisites of all cognition, and yet most unguardedly changed these criteria of thought into properties of objects, as things in themselves. Now, ​in every cognition of an object, there is unity of conception, which may be called qualitative unity, so far as by this term we understand only the unity in our connection of the manifold; for example, unity of the theme in a play, an oration, or a story. Secondly, there is truth in respect of the deductions from it. The more true deductions we have from a given conception, the more criteria of its objective reality. This we might call the qualitative plurality of characteristic marks, which belong to a conception as to a common foundation, but are not cogitated as a quantity in it. Thirdly, there is perfection,—which consists in this, that the plurality falls back upon the unity of the conception, and accords completely with that conception and with no other. This we may denominate qualitative completeness. Hence it is evident that these logical criteria of the possibility of cognition are merely the three categories of quantity modified and transformed to suit an unauthorized manner of applying them. That is to say, the three categories, in which the unity in the production of the quantum must be homogeneous throughout, are transformed solely with a view to the connection of heterogeneous parts of cognition in one act of consciousness, by means of the quality of the cognition, which is the principle of that connection. Thus the criterion of the possibility of a conception (not of its object) is the definition of it, in which the unity of the conception, the truth of all that may be immediately deduced from it, and finally, the completeness of what has been thus deduced, constitute the requisites for the reproduction of the whole conception. Thus also, the criterion or test of an hypothesis is the intelligibility of the received principle of explanation, or its unity (without help from any subsidiary hypothesis),—the truth of our deductions from it (consistency with each other and with experience),—and lastly, the completeness of the principle of the explanation of these deductions, which refer to neither more nor less than what was admitted in the hypothesis, restoring analytically and a posteriori, what was cogitated synthetically and a priori. By the conceptions, therefore, of Unity, Truth, and Perfection, we have made no addition to the transcendental table of the categories, which is complete without them. We have, on the contrary, merely employed the three categories of quantity, setting aside their application to objects of experience, as ​general logical laws of the consistency of cognition with itself.

### CHAPTER II. Of the Deduction of the Pure Conceptions of the Understanding.CHAPTER II. Of the Deduction of the Pure Conceptions of the Understanding.
#### SECTION I.—Of the Principles of a Transcendental Deduction in general.SECTION I.—Of the Principles of a Transcendental Deduction in general.
##### § 9.§ 9.

Teachers of jurisprudence, when speaking of rights and claims, distinguish in a cause the question of right (quid juris) from the question of fact (quid facti), and while they demand proof of both, they give to the proof of the former, which goes to establish right or claim in law, the name of deduction. Now we make use of a great number of empirical conceptions, without opposition from any one; and consider ourselves, even without any attempt at deduction, justified in attaching to them a sense, and a supposititious signification, because we have always experience at hand to demonstrate their objective reality. There exist also, however, usurped conceptions, such as fortune, fate, which circulate with almost universal indulgence, and yet are occasionally challenged by the question, "quid juris?" In such cases, we have great difficulty in discovering any deduction for these terms, inasmuch as we cannot produce any manifest ground of right, either from experience or from reason, on which the claim to employ them can be founded. ​
Among the many conceptions, which make up the very variegated web of human cognition, some are destined for pure use a priori, independent of all experience; and their title to be so employed always requires a deduction, inasmuch as, to justify such use of them, proofs from experience are not sufficient; but it is necessary to know how these conceptions can apply to objects without being derived from experience. I term, therefore, an examination of the manner in which conceptions can apply a priori to objects, the transcendental deduction of conceptions, and I distinguish it from the empirical deduction, which indicates the mode in which conception is obtained through experience and reflection thereon; consequently, does not concern itself with the right, but only with the fact of our obtaining conceptions in such and such a manner. We have already seen that we are in possession of two perfectly different kinds of conceptions, which nevertheless agree with each other in this, that they both apply to objects completely a priori. These are the conceptions of space and time as forms of sensibility, and the categories as pure conceptions of the understanding. To attempt an empirical deduction of either of these classes would be labour in vain, because the distinguishing characteristic of their nature consists in this, that they apply to their objects, without having borrowed anything from experience towards the representation of them. Consequently, if a deduction of these conceptions is necessary, it must always be transcendental.
Meanwhile, with respect to these conceptions, as with respect to all our cognition, we certainly may discover in experience, if not the principle of their possibility, yet the occasioning causes of their production. It will be found that the impressions of sense give the first occasion for bringing into action the whole faculty of cognition, and for the production of experience, which contains two very dissimilar elements, namely, a matter for cognition, given by the senses, and a certain form for the arrangement of this matter, arising out of the inner fountain of pure intuition and thought; and these, on occasion given by sensuous impressions, are called into exercise and produce conceptions. Such ​an investigation into the first efforts of our faculty of cognition to mount from particular perceptions to general conceptions is undoubtedly of great utility; and we have to thank the celebrated Locke for having first opened the way for this inquiry. But a deduction of the pure a priori conceptions of course never can be made in this way, seeing that, in regard to their future employment, which must be entirely independent of experience, they must have a far different certificate of birth to show from that of a descent from experience. This attempted physiological derivation, which cannot properly be called deduction, because it relates merely to a quaestio facti, I shall entitle an explanation of the possession of a pure cognition. It is therefore manifest that there can only be a transcendental deduction of these conceptions and by no means an empirical one; also, that all attempts at an empirical deduction, in regard to pure a priori conceptions, are vain, and can only be made by one who does not understand the altogether peculiar nature of these cognitions.
But although it is admitted that the only possible deduction of pure a priori cognition is a transcendental deduction, it is not, for that reason, perfectly manifest that such a deduction is absolutely necessary. We have already traced to their sources the conceptions of space and time, by means of a transcendental deduction, and we have explained and determined their objective validity a priori. Geometry, nevertheless, advances steadily and securely in the province of pure a priori cognitions, without needing to ask from Philosophy any certificate as to the pure and legitimate origin of its fundamental conception of space. But the use of the conception in this science extends only to the external world of sense, the pure form of the intuition of which is space; and in this world, therefore, all geometrical cognition, because it is founded upon a priori intuition, possesses immediate evidence, and the objects of this cognition are given a priori (as regards their form) in intuition by and through the cognition itself. With the pure conceptions of Understanding, on the contrary, commences the ​absolute necessity of seeking a transcendental deduction, not only of these conceptions themselves, but likewise of space, because, inasmuch as they make affirmations concerning objects not by means of the predicates of intuition and sensibility, but of pure thought a priori, they apply to objects without any of the conditions of sensibility. Besides, not being founded on experience, they are not presented with any object in a priori intuition upon which, antecedently to experience, they might base their synthesis. Hence results, not only doubt as to the objective validity and proper limits of their use, but that even our conception of space is rendered equivocal; inasmuch as we are very ready with the aid of the categories, to carry the use of this conception beyond the conditions of sensuous intuition;—and for this reason, we have already found a transcendental deduction of it needful. The reader, then, must be quite convinced of the absolute necessity of a transcendental deduction, before taking a single step in the field of pure reason; because otherwise he goes to work blindly, and after he has wondered about in all directions, returns to the state of utter ignorance from which he started. He ought, moreover, clearly to recognize beforehand the ​unavoidable difficulties in his undertaking, so that he may not afterwards complain of the obscurity in which the subject itself is deeply involved, or become too soon impatient of the obstacles in his path;—because we have a choice of only two things—either at once to give up all pretensions to knowledge beyond the limits of possible experience, or to bring this critical investigation to completion.
We have been able, with very little trouble, to make it comprehensible how the conceptions of space and time, although à priori cognitions, must necessarily apply to external objects, and render a synthetical cognition of these possible, independently of all experience. For inasmuch as only by means of such pure form of sensibility an object can appear to us, that is, be an object of empirical intuition, space and time are pure intuitions, which contain a priori the condition of the possibility of objects as phenomena, and an à priori synthesis in these intuitions possesses objective validity.
On the other hand, the categories of the understanding do not represent the conditions under which objects are given to us in intuition; objects can consequently appear to us without necessarily connecting themselves with these, and consequently without any necessity binding on the understanding to contain à priori the conditions of these objects. Thus we find ourselves involved in a difficulty which did not present itself in the sphere of sensibility, that is to say, we cannot discover how the subjective conditions of thought can have objective validity, in other words, can become conditions of the possibility of all cognition of objects; —for phenomena may certainly be given to us in intuition without any help from the functions of the understanding. Let us take, for example, the conception of cause, which indicates a peculiar kind of synthesis, namely, that with something, A, something entirely different, B, is connected according to a law. It is not a priori manifest why phenomena should contain anything of this kind (we are of course debarred from appealing for proof to experience, for the objective validity of this conception must be demonstrated à priori), and it hence remains doubtful à priori, whether such a conception be not quite void and without any corresponding object among phenomena. For that objects of ​sensuous intuition must correspond to the formal conditions of sensibility existing a priori in the mind is quite evident, from the fact that without these they could not be objects for us; but that they must also correspond to the conditions which understanding requires for the synthetical unity of thought is an assertion, the grounds for which are not so easily to be discovered. For phenomena might be so constituted as not to correspond to the conditions of the unity of thought; and all things might lie in such confusion that, for example, nothing could be met with in the sphere of phenomena to suggest a law of synthesis, and so correspond to the conception of cause and effect; so that this conception would be quite void, null, and without significance. Phenomena would nevertheless continue to present objects to our intuition; for mere intuition does not in any respect stand in need of the functions of thought.
If we thought to free ourselves from the labour of these investigations by saying, "Experience is constantly offering us examples of the relation of cause and effect in phenomena, and presents us with abundant opportunity of abstracting the conception of cause, and so at the same time of corroborating the objective validity of this conception";—we should in this case be overlooking the fact, that the conception of cause cannot arise in this way at all; that, on the contrary, it must either have an a priori basis in the, understanding, or be rejected as a mere chimera. For this conception demands that something, A, should be of such a nature that something else, B, should follow from it necessarily, and according to an absolutely universal law. We may certainly collect from phenomena a law, according to which this or that usually happens, but the element of necessity is not to be found in it. Hence it is evident that to the synthesis of cause and effect belongs a dignity, which is utterly wanting in any empirical synthesis; for it is no mere mechanical synthesis, by means of addition, but a dynamical one; that is to say, the effect is not to be cogitated as merely annexed to the cause, but as posited by and through the cause, and resulting from it. The strict universality of this law never can be a characteristic of empirical laws, which obtain through induction only a comparative universality, that is, an extended range of practical application. But the pure conceptions of ​the understanding would entirely lose all their peculiar character, if we treated them merely as the productions of experience.

##### Transition to the Transcendental Deduction of the Categories. § 10Transition to the Transcendental Deduction of the Categories. § 10

There are only two possible ways in which synthetical representation and its objects can coincide with and relate necessarily to each other, and, as it were, meet together. Either the object alone makes the representation possible, or the representation alone makes the object possible. In the former case, the relation between them is only empirical, and an a priori representation is impossible. And this is the case with phenomena, as regards that in them which is referable to mere sensation. In the latter case—although representation alone (for of its causality, by means of the will, we do not here speak) does not produce the object as to its existence, it must nevertheless be a priori determinative in regard to the object, if it is only by means of the representation that we can cognize anything as an object. Now there are only two conditions of the possibility of a cognition of objects; firstly, Intuition, by means of which the object, though only as phenomenon, is given; secondly, Conception, by means of which the object which corresponds to this intuition is thought. But it is evident from what has been said on aesthetic that the first condition, under which alone objects can be intuited, must in fact exist, as a formal basis for them, a priori in the mind. With this formal condition of sensibility, therefore, all phenomena necessarily correspond, because it is only through it that they can be phenomena at all; that is, can be empirically intuited and given. Now the question is whether there do not exist, a priori in the mind, conceptions of understanding also, as conditions under which alone something, if not intuited, is yet thought as object. If this question be answered in the affirmative, it follows that all empirical cognition of objects is necessarily conformable to such conceptions, since, if they are not presupposed, it is impossible that anything can be an object of experience. Now all experience contains, besides the intuition of the senses through which an object is ​given, a conception also of an object that is given in intuition. Accordingly, conceptions of objects in general must lie as a priori conditions at the foundation of all empirical cognition; and consequently, the objective validity of the categories, as a priori conceptions, will rest upon this, that experience (as far as regards the form of thought) is possible only by their means. For in that case they apply necessarily and a priori to objects of experience, because only through them can an object of experience be thought.
The whole aim of the transcendental deduction of all a priori conceptions is to show that these conceptions are a priori conditions of the possibility of all experience. Conceptions which afford us the objective foundation of the possibility of experience are for that very reason necessary. But the analysis of the experiences in which they are met with is not deduction, but only an illustration of them, because from experience they could never derive the attribute of necessity. Without their original applicability and relation to all possible experience, in which all objects of cognition present themselves, the relation of the categories to objects, of whatever nature, would be quite incomprehensible.
The celebrated Locke, for want of due reflection on these points, and because he met with pure conceptions of the understanding in experience, sought also to deduce them from experience, and yet proceeded so inconsequently as to attempt, with their aid, to arrive it cognitions which lie far beyond the limits of all experience. David Hume perceived that, to render this possible, it was necessary that the conceptions should have an a priori origin. But as he could not explain how it was possible that conceptions which are not connected with each other in the understanding must nevertheless be thought as necessarily connected in the object,—and it never occurred to him that the understanding itself might, perhaps, by means of these conceptions, be the author of the experience in which its objects were presented to it,—he was forced to drive these conceptions from experience, that is, from a subjective necessity arising from repeated association of experiences erroneously considered to be objective,—in one word, from "habit." But he proceeded with perfect consequence and declared it to be impossible with ​such conceptions and the principles arising from them, to overstep the limits of experience. The empirical derivation, however, which both of these philosophers attributed to these conceptions, cannot possibly be reconciled with the fact that we do possess scientific a priori cognitions, namely, those of pure mathematics and general physics.
The former of these two celebrated men opened a wide door to extravagance—(for if reason has once undoubted right on its side, it will not allow itself to be confined to set limits, by vague recommendations of moderation); the latter gave himself up entirely to scepticism,—a natural consequence, after having discovered, as he thought, that the faculty of cognition was not trustworthy. We now intend to make a trial whether it be not possible safely to conduct reason between these two rocks, to assign her determinate limits, and yet leave open for her the entire sphere of her legitimate activity.
I shall merely premise an explanation of what the categories are. They are conceptions of an object in general, by means of which its intuition is contemplated as determined in relation to one of the logical functions of judgement. The following will make this plain. The function of the categorical judgement is that of the relation of subject to predicate; for example, in the proposition, "All bodies are divisible." But in regard to the merely logical use of the understanding, it still remains undetermined to which of these two conceptions belongs the function Of subject and to which that of predicate. For we could also say, "Some divisible is a body." But the category of substance, when the conception of a body is brought under it, determines that; and its empirical intuition in experience must be contemplated always as subject and never as mere predicate. And so with all the other categories. ​

#### SECTION II. Transcendental Deduction of the pure Conceptions of the Understanding.SECTION II. Transcendental Deduction of the pure Conceptions of the Understanding.
##### § 11. Of the Possibility of a Conjunction of the manifold representations given by Sense.§ 11. Of the Possibility of a Conjunction of the manifold representations given by Sense.

The manifold content in our representations can be given in an intuition which is merely sensuous—in other words, is nothing but susceptibility; and the form of this intuition can exist a priori in our faculty of representation, without being anything else but the mode in which the subject is affected. But the conjunction (conjunctio) of a manifold in intuition never can be given us by the senses; it cannot therefore be contained in the pure form of sensuous intuition, for it is a spontaneous act of the faculty of representation. And as we must, to distinguish it from sensibility, entitle this faculty understanding; so all conjunction—whether conscious or unconscious, be it of the manifold in intuition, sensuous or non-sensuous, or of several conceptions—is an act of the understanding. To this act we shall give the general appellation of synthesis, thereby to indicate, at the same time, that we cannot represent anything as conjoined in the object without having previously conjoined it ourselves. Of all mental notions, that of conjunction is the only one which cannot be given through objects, but can be originated only by the subject itself, because it is an act of its purely spontaneous activity. The reader will easily enough perceive that the possibility of conjunction must be grounded in the very nature of this act, and that it must be equally valid for all conjunction, and that analysis, which appears to be its contrary, must, nevertheless, always presuppose it; for where the understanding has not previously conjoined, it cannot dissect or analyse, because only as conjoined by it, must that which is to be analysed have been given to our faculty of representation.
But the conception of conjunction includes, besides the conception of the manifold and of the synthesis of it, that of the ​unity of it also. Conjunction is the representation of the synthetical unity of the manifold. This idea of unity, therefore, cannot arise out of that of conjunction; much rather does that idea, by combining itself with the representation of the manifold, render the conception of conjunction possible. This unity, which a priori precedes all conceptions of conjunction, is not the category of unity (§ 6); for all the categories are based upon logical functions of judgement, and in these functions we already have conjunction, and consequently unity of given conceptions. It is therefore evident that the category of unity presupposes conjunction. We must therefore look still higher for this unity (as qualitative, § 8), in that, namely, which contains the ground of the unity of diverse conceptions in judgements, the ground, consequently, of the possibility of the existence of the understanding, even in regard to its logical use.

##### Of the Originally Synthetical Unity of Apperception. § 12Of the Originally Synthetical Unity of Apperception. § 12

The "I think" must accompany all my representations, for otherwise something would be represented in me which could not be thought; in other words, the representation would either be impossible, or at least be, in relation to me, nothing. That representation which can be given previously to all thought is called intuition. All the diversity or manifold content of intuition, has, therefore, a necessary relation to the "I think," in the subject in which this diversity is found. But this representation, "I think," is an act of spontaneity; that is to say, it cannot be regarded as belonging to mere sensibility. I call it pure apperception, in order to distinguish ​it from empirical; or primitive apperception, because it is self-consciousness which, whilst it gives birth to the representation" I think," must necessarily be capable of accompanying all our representations. It is in all acts of consciousness one and the same, and unaccompanied by it, no representation can exist for me. The unity of this apperception I call the transcendental unity of self-consciousness, in order to indicate the possibility of a priori cognition arising from it. For the manifold representations which are given in an intuition would not all of them be my representations, if they did not all belong to one self-consciousness, that is, as my representations (even although I am not conscious of them as such), they must conform to the condition under which alone they can exist together in a common self-consciousness, because otherwise they would not all without exception belong to me. From this primitive conjunction follow many important results.
For example, this universal identity of the apperception of the manifold given in intuition contains a synthesis of representations and is possible only by means of the consciousness of this synthesis. For the empirical consciousness which accompanies different representations is in itself fragmentary and disunited, and without relation to the identity of the subject. This relation, then, does not exist because I accompany every representation with consciousness, but because I join one representation to another, and am conscious of the synthesis of them. Consequently, only because I can connect a variety of given representations in one consciousness, is it possible that I can represent to myself the identity of consciousness in these representations; in other words, the analytical unity of apperception is possible only under the presupposition of a synthetical unity. The thought, "These representations ​given in intuition belong all of them to me," is accordingly just the same as, "I unite them in one self-consciousness, or can at least so unite them"; and although this thought is not itself the consciousness of the synthesis of representations, it presupposes the possibility of it; that is to say, for the reason alone that I can comprehend the variety of my representations in one consciousness, do I call them my representations, for otherwise I must have as many-coloured and various a self as are the representations of which I am conscious. Synthetical unity of the manifold in intuitions, as given a priori, is therefore the foundation of the identity of apperception itself, which antecedes a priori all determinate thought. But the conjunction of representations into a conception is not to be found in objects themselves, nor can it be, as it were, borrowed from them and taken up into the understanding by perception, but it is on the contrary an operation of the understanding itself, which is nothing more than the faculty of conjoining a priori and of bringing the variety of given representations under the unity of apperception. This principle is the highest in all human cognition.
This fundamental principle of the necessary unity of apperception is indeed an identical, and therefore analytical, proposition; but it nevertheless explains the necessity for a synthesis of the manifold given in an intuition, without which the identity of self-consciousness would be incogitable. For the ego, as a simple representation, presents us with no manifold content; only in intuition, which is quite different from the representation ego, can it be given us, and by means of conjunction it is cogitated in one self-consciousness. An understanding, in which all the manifold should be given by means of consciousness itself, would be intuitive; our understanding can only think and must look for its intuition to sense. I am, therefore, conscious of my identical self, in relation to all the variety of representations given to me in an intuition, because I call all of them my representations. In other ​words, I am conscious myself of a necessary a priori synthesis of my representations, which is called the original synthetical unity of apperception, under which rank all the representations presented to me, but that only by means of a synthesis.

##### The Principle of the Synthetical Unity of Apperception is the highest Principle of all exercise of the Understanding. § 13The Principle of the Synthetical Unity of Apperception is the highest Principle of all exercise of the Understanding. § 13

The supreme principle of the possibility of all intuition in relation to sensibility was, according to our transcendental aesthetic, that all the manifold in intuition be subject to the formal conditions of space and time. The supreme principle of the possibility of it in relation to the understanding is that all the manifold in it be subject to conditions of the originally synthetical unity or apperception. To the former of these two principles are subject all the various representations of intuition, in so far as they are given to us; to the latter, in so far as they must be capable of conjunction in one consciousness; for without this nothing can be thought or cognized, because the given representations would not have in common the act Of the apperception "I think" and therefore could not be connected in one self-consciousness.
Understanding is, to speak generally, the faculty Of cognitions. These consist in the determined relation of given representation to an object. But an object is that, in the conception of which the manifold in a given intuition is united. Now all union of representations requires unity of consciousness in the synthesis of them. Consequently, it is the unity of consciousness alone that constitutes the possibility of representations relating to an object, and therefore of their objective validity, and of their becoming cognitions, and consequently, ​the possibility of the existence of the understanding itself.
The first pure cognition of understanding, then, upon which is founded all its other exercise, and which is at the same time perfectly independent of all conditions of mere sensuous intuition, is the principle of the original synthetical unity of apperception. Thus the mere form of external sensuous intuition, namely, space, affords us, per se, no cognition; it merely contributes the manifold in a priori intuition to a possible cognition. But, in order to cognize something in space (for example, a line), I must draw it, and thus produce synthetically a determined conjunction of the given manifold, so that the unity of this act is at the same time the unity of consciousness (in the conception of a line), and by this means alone is an object (a determinate space) cognized. The synthetical unity of consciousness is, therefore, an objective condition of all cognition, which I do not merely require in order to cognize an object, but to which every intuition must necessarily be subject, in order to become an object for me; because in any other way, and without this synthesis, the manifold in intuition could not be united in one consciousness.
This proposition is, as already said, itself analytical, although it constitutes the synthetical unity, the condition of all thought; for it states nothing more than that all my representations in any given intuition must be subject to the condition which alone enables me to connect them, as my representation with the identical self, and so to unite them synthetically in one apperception, by means of the general expression, "I think."
But this principle is not to be regarded as a principle for every possible understanding, but only for the understanding by means of whose pure apperception in the thought I am, no manifold content is given. The understanding or mind which contained the manifold in intuition, in and through the act itself of its own self-consciousness, in other words, an understanding by and in the representation of which the objects of the representation should at the same time exist, would not require a special act of synthesis of the manifold as the condition of the unity of its consciousness, an act of which the human understanding, which thinks only and cannot intuite, has absolute need. But this principle is the first ​principle of all the operations of our understanding, so that we cannot form the least conception of any other possible understanding, either of one such as should be itself intuition, or possess a sensuous intuition, but with forms different from those of space and time.

##### What Objective Unity of Self-consciousness is. § 14What Objective Unity of Self-consciousness is. § 14

It is by means of the transcendental unity of apperception that all the manifold, given in an intuition is united into a conception of the object. On this account it is called objective, and must be distinguished from the subjective unity of consciousness, which is a determination of the internal sense, by means of which the said manifold in intuition is given empirically to be so united. Whether I can be empirically conscious of the manifold as coexistent or as successive, depends upon circumstances, or empirical conditions. Hence the empirical unity of consciousness by means of association of representations, itself relates to a phenomenal world and is wholly contingent. On the contrary, the pure form of intuition in time, merely as an intuition, which contains a given manifold, is subject to the original unity of consciousness, and that solely by means of the necessary relation of the manifold in intuition to the "I think," consequently by means of the pure synthesis of the understanding, which lies a priori at the foundation of all empirical synthesis. The transcendental unity of apperception is alone objectively valid; the empirical which we do not consider in this essay, and which is merely a unity deduced from the former under given conditions in concreto, possesses only subjective validity. One person connects the notion conveyed in a word with one thing, another with another thing; and the unity of consciousness in that which is empirical, is, in relation to that which is given by experience, not necessarily and universally valid.

##### The Logical Form of all Judgements consists in the Objective Unity of Apperception of the Conceptions contained therein. § 15The Logical Form of all Judgements consists in the Objective Unity of Apperception of the Conceptions contained therein. § 15

I could never satisfy myself with the definition which logicians give of a judgement. It is, according to them, the representation ​of a relation between two conceptions. I shall not dwell here on the faultiness of this definition, in that it suits only for categorical and not for hypothetical or disjunctive judgements, these latter containing a relation not of conceptions but of judgements themselves;—a blunder from which many evil results have followed. It is more important for our present purpose to observe, that this definition does not determine in what the said relation consists.
But if I investigate more closely the relation of given cognitions in every judgement, and distinguish it, as belonging to the understanding, from the relation which is produced according to laws of the reproductive imagination (which has only subjective validity), I find that judgement is nothing but the mode of bringing given cognitions under the objective unit of apperception. This is plain from our use of the term of relation is in judgements, in order to distinguish the objective unity of given representations from the subjective unity. For this term indicates the relation of these representations to the original apperception, and also their necessary unity, even although the judgement is empirical, therefore contingent, as in the judgement: "All bodies are heavy." I do not mean by this, that these representations do necessarily belong to each other in empirical intuition, but that by means of the necessary unity of appreciation they belong to each other in the synthesis of intuitions, that is to say, they belong to each other according to principles of the objective determination of all our representations, in so far as cognition can arise from them, these principles being all deduced from the main principle of the transcendental unity of apperception. In this way alone can there arise from this relation a judgement, that is, a relation which has objective validity, and is perfectly distinct from that relation of the very same representations which ​has only subjective validity—a relation, to wit, which is produced according to laws of association. According to these laws, I could only say: "When I hold in my hand or carry a body, I feel an impression of weight"; but I could not say: "It, the body, is heavy"; for this is tantamount to saying both these representations are conjoined in the object, that is, without distinction as to the condition of the subject, and do not merely stand together in my perception, however frequently the perceptive act may be repeated.

##### All Sensuous Intuitions are subject to the Categories, as Conditions under which alone the manifold Content of them can be united in one Consciousness. § 16All Sensuous Intuitions are subject to the Categories, as Conditions under which alone the manifold Content of them can be united in one Consciousness. § 16

The manifold content given in a sensuous intuition comes necessarily under the original synthetical unity of apperception, because thereby alone is the unity of intuition possible (§ 13). But that act of the understanding, by which the manifold content of given representations (whether intuitions or conceptions) is brought under one apperception, is the logical function of judgements (§ 15). All the manifold, therefore, in so far as it is given in one empirical intuition, is determined in relation to one of the logical functions of judgement, by means of which it is brought into union in one consciousness. Now the categories are nothing else than these functions of judgement so far as the manifold in a given intuition is determined in relation to them (§ 9). Consequently, the manifold in a given intuition is necessarily subject to the categories of the understanding.

##### Observation. § 17Observation. § 17

The manifold in an intuition, which I call mine, is represented by means of the synthesis of the understanding, as belonging to the necessary unity of self-consciousness, and this takes place by means of the category. ​The category indicates accordingly that the empirical consciousness of a given manifold in an intuition is subject to a pure self-consciousness a priori, in the same manner as an empirical intuition is subject to a pure sensuous intuition, which is also a priori.—In the above proposition, then, lies the beginning of a deduction of the pure conceptions of the understanding. Now, as the categories have their origin in the understanding alone, independently of sensibility, I must in my deduction make abstraction of the mode in which the manifold of an empirical intuition is given, in order to fix my attention exclusively on the unity which is brought by the understanding into the intuition by means of the category. In what follows (§ 22), it will be shown, from the mode in which the empirical intuition is given in the faculty of sensibility, that the unity which belongs to it is no other than that which the category (according to § 16) imposes on the manifold in a given intuition, and thus, its a priori validity in regard to all objects of sense being established, the purpose of our deduction will be fully attained.
But there is one thing in the above demonstration of which I could not make abstraction, namely, that the manifold to be intuited must be given previously to the synthesis of the understanding, and independently of it. How this takes place remains here undetermined. For if I cogitate an understanding which was itself intuitive (as, for example, a divine understanding which should not represent given objects, but by whose representation the objects themselves should be given or produced), the categories would possess no significance in relation to such a faculty of cognition. They are merely rules for an understanding, whose whole power consists in thought, that is, in the act of submitting the synthesis of the manifold which is presented to it in intuition from a very different quarter, to the unity of apperception; a faculty, therefore, which cognizes nothing per se, but only connects and arranges the material of cognition, the intuition, namely, which must be presented to it by means of the object. But to show reasons for this peculiar character of our understandings, that it produces unity of apperception a priori only by means of categories, and a certain kind and number thereof, is as impossible as to explain why we are endowed with precisely so many functions of judgement and no more, or why time and space are the only forms of our intuition. ​

##### § 18. In Cognition, its Application to Objects of Experience is the only legitimate use of the Category.§ 18. In Cognition, its Application to Objects of Experience is the only legitimate use of the Category.

To think an object and to cognize an object are by no means the same thing. In cognition there are two elements: firstly, the conception, whereby an object is cogitated (the category); and, secondly, the intuition, whereby the object is given. For supposing that to the conception a corresponding intuition could not be given, it would still be a thought as regards its form, but without any object, and no cognition of anything would be possible by means of it, inasmuch as, so far as I knew, there existed and could exist nothing to which my thought could be applied. Now all intuition possible to us is sensuous; consequently, our thought of an object by means of a pure conception of the understanding, can become cognition for us only in so far as this conception is applied to objects of the senses. Sensuous intuition is either pure intuition (space and time) or empirical intuition—of that which is immediately represented in space and time by means of sensation as real. Through the determination of pure intuition we obtain a priori cognitions of objects, as in mathematics, but only as regards their form as phenomena; whether there can exist things which must be intuited in this form is not thereby established. All mathematical conceptions, therefore, are not per se cognition, except in so far as we presuppose that there exist things which can only be represented conformably to the form of our pure sensuous intuition. But things in space and time are given only in so far as they are perceptions (representations accompanied with sensation), therefore only by empirical representation. Consequently the pure conceptions of the understanding, even when they are applied to intuitions a priori (as in mathematics), produce cognition only in so far as these (and therefore the conceptions of the understanding by means of them) can be applied to empirical intuitions. Consequently the categories do not, even by means of pure intuition afford us any cognition of things; they can only do so in so far as they can be applied to empirical intuition. That is to say, the categories serve only to render empirical cognition possible. But this is what we call experience. Consequently, ​in cognition, their application to objects of experience is the only legitimate use of the categories.

##### § 19.§ 19.

The foregoing proposition is of the utmost importance, for it determines the limits of the exercise of the pure conceptions of the understanding in regard to objects, just as transcendental aesthetic determined the limits of the exercise of the pure form of our sensuous intuition. Space and time, as conditions of the possibility of the presentation of objects to us, are valid no further than for objects of sense, consequently, only for experience. Beyond these limits they represent to us nothing, for they belong only to sense, and have no reality apart from it. The pure conceptions of the understanding are free from this limitation, and extend to objects of intuition in general, be the intuition like or unlike to ours, provided only it be sensuous, and not intellectual. But this extension of conceptions beyond the range of our intuition is of no advantage; for they are then mere empty conceptions of objects, as to the possibility or impossibility of the existence of which they furnish us with no means of discovery. They are mere forms of thought, without objective reality, because we have no intuition to which the synthetical unity of apperception, which alone the categories contain, could be applied, for the purpose of determining an object. Our sensuous and empirical intuition can alone give them significance and meaning.
If, then, we suppose an object of a non-sensuous intuition to be given we can in that case represent it by all those predicates which are implied in the presupposition that nothing appertaining to sensuous intuition belongs to it; for example, that it is not extended, or in space; that its duration is not time; that in it no change (the effect of the determinations in time) is to be met with, and so on. But it is no proper knowledge if I merely indicate what the intuition of the object is not, without being able to say what is contained in it, for I have not shown the possibility of an object to which my pure conception of understanding could be applicable, because I have not been able to furnish any intuition corresponding to it, but am only able to say that our intuition is not valid for it. But the most important point is this, that to a something of ​this kind not one category can be found applicable. Take, for example, the conception of substance, that is, something that can exist as subject, but never as mere predicate; in regard to this conception I am quite ignorant whether there can really be anything to correspond to such a determination of thought, if empirical intuition did not afford me the occasion for its application. But of this more in the sequel.

##### § 20. Of the Application of the Categories to Objects of the Senses in general.§ 20. Of the Application of the Categories to Objects of the Senses in general.

The pure conceptions of the understanding apply to objects of intuition in general, through the understanding alone, whether the intuition be our own or some other, provided only it be sensuous, but are, for this very reason, mere forms of thought, by means of which alone no determined object can be cognized. The synthesis or conjunction of the manifold in these conceptions relates, we have said, only to the unity of apperception, and is for this reason the ground of the possibility of a priori cognition, in so far as this cognition is dependent on the understanding. This synthesis is, therefore, not merely transcendental, but also purely intellectual. But because a certain form of sensuous intuition exists in the mind a priori which rests on the receptivity of the representative faculty (sensibility), the understanding, as a spontaneity, is able to determine the internal sense by means of the diversity of given representations, conformably to the synthetical unity of apperception, and thus to cogitate the synthetical unity of the apperception of the manifold of sensuous intuition a priori, as the condition to which must necessarily be submitted all objects of human intuition. And in this manner the categories as mere forms of thought receive objective reality, that is, application to objects which are given to us in intuition, but that only as phenomena, for it is only of phenomena that we are capable of a priori intuition.
This synthesis of the manifold of sensuous intuition, which is possible and necessary a priori, may be called figurative (synthesis speciosa), in contradistinction to that which is cogitated in the mere category in regard to the manifold of an intuition in general, and is called connection or conjunction of the understanding (synthesis intellectualis). Both are transcendental, ​not merely because they themselves precede a priori all experience, but also because they form the basis for the possibility of other cognition a priori.
But the figurative synthesis, when it has relation only to the originally synthetical unity of apperception, that is to the transcendental unity cogitated in the categories, must, to be distinguished from the purely intellectual conjunction, be entitled the transcendental synthesis of imagination. Imagination is the faculty of representing an object even without its presence in intuition. Now, as all our intuition is sensuous, imagination, by reason of the subjective condition under which alone it can give a corresponding intuition to the conceptions of the understanding, belongs to sensibility. But in so far as the synthesis of the imagination is an act of spontaneity, which is determinative, and not, like sense, merely determinable, and which is consequently able to determine sense a priori, according to its form, conformably to the unity of apperception, in so far is the imagination a faculty of determining sensibility a priori, and its synthesis of intuitions according to the categories must be the transcendental synthesis of the imagination. It is an operation of the understanding on sensibility, and the first application of the understanding to objects of possible intuition, and at the same time the basis for the exercise of the other functions of that faculty. As figurative, it is distinguished from the merely intellectual synthesis, which is produced by the understanding alone, without the aid of imagination. Now, in so far as imagination is spontaneity, I sometimes call it also the productive imagination, and distinguish it from the reproductive, the synthesis of which is subject entirely to empirical laws, those of association, namely, and which, therefore, contributes nothing to the explanation of the possibility of a priori cognition, and for this reason belongs not to transcendental philosophy, but to psychology.
We have now arrived at the proper place for explaining the paradox which must have struck every one in our exposition of the internal sense (SS 6), namely—how this sense represents us to our own consciousness, only as we appear to ourselves, not as we are in ourselves, because, to wit, we intuite ourselves ​only as we are inwardly affected. Now this appears to be contradictory, inasmuch as we thus stand in a passive relation to ourselves; and therefore in the systems of psychology, the internal sense is commonly held to be one with the faculty of apperception, while we, on the contrary, carefully distinguish them.
That which determines the internal sense is the understanding, and its original power of conjoining the manifold of intuition, that is, of bringing this under an apperception (upon which rests the possibility of the understanding itself). Now, as the human understanding is not in itself a faculty of intuition, and is unable to exercise such a power, in order to conjoin, as it were, the manifold of its own intuition, the synthesis of understanding is, considered per se, nothing but the unity of action, of which, as such, it is self-conscious, even apart from sensibility, by which, moreover, it is able to determine our internal sense in respect of the manifold which may be presented to it according to the form of sensuous intuition. Thus, under the name of a transcendental synthesis of imagination, the understanding exercises an activity upon the passive subject, whose faculty it is; and so we are right in saying that the internal sense is affected thereby. Apperception and its synthetical unity are by no means one and the same with the internal sense. The former, as the source of all our synthetical conjunction, applies, under the name of the categories, to the manifold of intuition in general, prior to all sensuous intuition of objects. The internal sense, on the contrary, contains merely the form of intuition, but without any synthetical conjunction of the manifold therein, and consequently does not contain any determined intuition, which is possible only through consciousness of the determination of the manifold by the transcendental act of the imagination (synthetical influence of the understanding on the internal sense), which I have named figurative synthesis.
This we can indeed always perceive in ourselves. We cannot cogitate a geometrical line without drawing it in thought, nor a circle without describing it, nor represent the three dimensions of space without drawing three lines from the same point perpendicular to one another. We cannot even cogitate time, unless, in drawing a straight line (which is to serve ​as the external figurative representation of time), we fix our attention on the act of the synthesis of the manifold, whereby we determine successively the internal sense, and thus attend also to the succession of this determination. Motion as an act of the subject (not as a determination of an object), consequently the synthesis of the manifold in space, if we make abstraction of space and attend merely to the act by which we determine the internal sense according to its form, is that which produces the conception of succession. The understanding, therefore, does by no means find in the internal sense any such synthesis of the manifold, but produces it, in that it affects this sense. At the same time, how "I who think" is distinct from the "I" which intuites itself (other modes of intuition being cogitable as at least possible), and yet one and the same with this latter as the same subject; how, therefore, I am able to say: "I, as an intelligence and thinking subject, cognize myself as an object thought, so far as I am, moreover, given to myself in intuition,—only, like other phenomena, not as I am in myself, and as considered by the understanding, but merely as I appear,"—is a question that has in it neither more nor less difficulty than the question—"How can I be an object to myself," or this,—"How I can be an object of my own intuition and internal perceptions." But that such must be the fact, if we admit that space is merely a pure form of the phenomena of external sense, can be clearly proved by the consideration that we cannot represent time, which is not an object of external intuition, in any other way than under the image of a line, which we draw in thought, a mode of representation without which we could not cognize the unity of its dimension, and also that we are necessitated to take our determination of periods of time, or of points of time, for all our internal perceptions from the changes which we perceive in outward things. It follows that we must arrange the determinations of the internal sense, as phenomena in time, exactly in the same manner as we arrange those of the external senses in space. ​And consequently, if we grant, respecting this latter, that by means of them we know objects only in so far as we are affected externally, we must also confess, with regard to the internal sense, that by means of it we intuite ourselves only as we are internally affected by ourselves; in other words, as regards internal intuition, we cognize our own subject only as phenomenon, and not as it is in itself.

##### § 21§ 21

On the other hand, in the transcendental synthesis of the manifold content of representations, consequently in the synthetical unity of apperception, I am conscious of myself, not as I appear to myself, nor as I am in myself, but only that "I am." This representation is a Thought, not an Intuition. Now, as in order to cognize ourselves, in addition to the act of thinking, which subjects the manifold of every possible intuition to the unity of apperception, there is necessary a determinate mode of intuition, whereby this manifold is given; although my own existence is certainly not mere phenomenon (much less mere illusion), the determination of my existence. Can ​only take place conformably to the form of the internal sense, according to the particular mode in which the manifold which I conjoin is given in internal intuition, and I have therefore no knowledge of myself as I am, but merely as I appear to myself. The consciousness of self is thus very far from a knowledge of self, in which I do not use the categories, whereby I cogitate an object, by means of the conjunction of the manifold in one apperception. In the same way as I require, for the sake of the cognition of an object distinct from myself, not only the thought of an object in general (in the category), but also an intuition by which to determine that general conception, in the same way do I require, in order to the cognition of myself, not only the consciousness of myself or the thought that I think myself, but in addition an intuition of the manifold in myself, by which to determine this thought. It is true that I exist as an intelligence which is conscious only of its faculty of conjunction or synthesis, but subjected in relation to the manifold which this intelligence has to conjoin to a limitative conjunction called the internal sense. My intelligence (that is, I) can render that conjunction or synthesis perceptible only according to the relations of time, which are quite beyond the proper sphere of the conceptions of the understanding and consequently cognize itself in respect to an intuition (which cannot possibly be intellectual, nor given by the understanding), only as it appears to itself, and not as it would cognize itself, if its intuition were intellectual.

##### § 22. Transcendental Deduction of the universally possible employment in experience of the Pure Conceptions of the Understanding.§ 22. Transcendental Deduction of the universally possible employment in experience of the Pure Conceptions of the Understanding.

In the metaphysical deduction, the a priori origin of categories was proved by their complete accordance with the general logical of thought; in the transcendental deduction was exhibited the possibility of the categories as a priori cognitions of objects of an intuition in general (§ 16 and 17). At present we are about to explain the possibility of cognizing, a priori, by means of the categories, all objects which can possibly be presented to our senses, not, indeed, according to the form of their intuition, but according to the ​laws of their conjunction or synthesis, and thus, as it were, of prescribing laws to nature and even of rendering nature possible. For if the categories were inadequate to this task, it would not be evident to us why everything that is presented to our senses must be subject to those laws which have an a priori origin in the understanding itself.
I premise that by the term synthesis of apprehension I understand the combination of the manifold in an empirical intuition, whereby perception, that is, empirical consciousness of the intuition (as phenomenon), is possible.
We have a priori forms of the external and internal sensuous intuition in the representations of space and time, and to these must the synthesis of apprehension of the manifold in a phenomenon be always comformable, because the synthesis itself can only take place according to these forms. But space and time are not merely forms of sensuous intuition, but intuitions themselves (which contain a manifold), and therefore contain a priori the determination of the unity of this manifold (See the Transcendent Aesthetic.) Therefore is unity of the synthesis of the manifold without or within us, consequently also a conjunction to which all that is to be represented as determined in space or time must correspond, given a priori along with (not in) these intuitions, as the condition of the synthesis of all apprehension of them. But this synthetical unity can be no other than that of the conjunction of the manifold of a given intuition in general, in a primitive act of consciousness, according to the categories, but applied to our sensuous intuition. Consequently all synthesis, whereby alone is even perception possible, is subject to the categories. And, as ​experience is cognition by means of conjoined perceptions, the categories are conditions of the possibility of experience and are therefore valid a priori for all objects of experience.
When, then, for example, I make the empirical intuition of a house by apprehension of the manifold contained therein into a perception, the necessary unity of space and of my external sensuous intuition lies at the foundation of this act, and I, as it were, draw the form of the house conformably to this synthetical unity of the manifold in space. But this very synthetical unity remains, even when I abstract the form of space, and has its seat in the understanding, and is in fact the category of the synthesis of the homogeneous in an intuition; that is to say, the category of quantity, to which the aforesaid synthesis of apprehension, that is, the perception, must be completely conformable.
To take another example, when I perceive the freezing of water, I apprehend two states (fluidity and solidity), which, as such, stand toward each other mutually in a relation of time. But in the time, which I place as an internal intuition, at the foundation of this phenomenon, I represent to myself synthetical unity of the manifold, without which the aforesaid relation could not be given in an intuition as determined (in regard to the succession of time). Now this synthetical unity, as the a priori condition under which I conjoin the manifold of an intuition, is, if I make abstraction of the permanent form of my internal intuition (that is to say, of time), the category of cause, by means of which, when applied to my sensibility, I determine everything that occurs according to relations of time. Consequently apprehension in such an event, and the event itself, as far as regards the possibility of its perception, stands under the conception of the relation of cause and effect: and so in all other cases.
Categories are conceptions which prescribe laws a priori to ​phenomena, consequently to nature as the complex of all phenomena (natura materialiter spectata). And now the question arises—inasmuch as these categories are not derived from nature, and do not regulate themselves according to her as their model (for in that case they would be empirical)—how it is conceivable that nature must regulate herself according to them, in other words, how the categories can determine a priori the synthesis of the manifold of nature, and yet not derive their origin from her. The following is the solution of this enigma.
It is not in the least more difficult to conceive how the laws of the phenomena of nature must harmonize with the understanding and with its a priori form—that is, its faculty of conjoining the manifold—than it is to understand how the phenomena themselves must correspond with the a priori form of our sensuous intuition. For laws do not exist in the phenomena any more than the phenomena exist as things in themselves. Laws do not exist except by relation to the subject in which the phenomena inhere, in so far as it possesses understanding, just as phenomena have no existence except by relation to the same existing subject in so far as it has senses. To things as things in themselves, conformability to law must necessarily belong independently of an understanding to cognize them. But phenomena are only representations of things which are utterly unknown in respect to what they are in themselves. But as mere representations, they stand under no law of conjunction except that which the conjoining faculty prescribes. Now that which conjoins the manifold of sensuous intuition is imagination, a mental act to which understanding contributes unity of intellectual synthesis, and sensibility, manifoldness of apprehension. Now as all possible perception depends on the synthesis of apprehension, and this empirical synthesis itself on the transcendental, consequently on the categories, it is evident that all possible perceptions, and therefore everything that can attain to empirical consciousness, that is, all phenomena of nature, must, as regards their conjunction, be subject to the categories. And nature (considered merely as nature in general) is dependent on them as the original ground of her necessary conformability to law (as natura formaliter spectata). But the pure faculty (of the understanding) of prescribing laws ​priori to phenomena by means of mere categories, is not competent to enounce other or more laws than those on which a nature in general, as a conformability to law of phenomena of space and time, depends. Particular laws, inasmuch as they concern empirically determined phenomena, cannot be entirely deduced from pure laws, although they all stand under them. Experience must be superadded in order to know these particular laws; but in regard to experience in general, and everything that can be cognized as an object thereof, these a priori laws are our only rule and guide.

##### § 23. Result of this Deduction of the Conceptions of the Understanding.§ 23. Result of this Deduction of the Conceptions of the Understanding.

We cannot think any object except by means of the categories; we cannot cognize any thought except by means of intuitions corresponding to these conceptions. Now all our intuitions are sensuous, and our cognition, in so far as the object of it is given, is empirical. But empirical cognition is experience; consequently no a priori cognition is possible for us, except of objects of possible experience.
But this cognition, which is limited to objects of experience, is not for that reason derived entirely, from, experience, but—and this is asserted of the pure intuitions and the pure conceptions of the understanding—there are, unquestionably, elements of cognition, which exist in the mind a priori. Now there are only two ways in which a necessary harmony of experience with the conceptions of its objects can be cogitated. Either experience makes these conceptions possible, or the conceptions make experience possible. The former of ​these statements will not bold good with respect to the categories (nor in regard to pure sensuous intuition), for they are a priori conceptions, and therefore independent of experience. The assertion of an empirical origin would attribute to them a sort of generatio aequivoca. Consequently, nothing remains but to adopt the second alternative (which presents us with a system, as it were, of the epigenesis of pure reason), namely, that on the part of the understanding the categories do contain the grounds of the possibility of all experience. But with respect to the questions how they make experience possible, and what are the principles of the possibility thereof with which they present us in their application to phenomena, the following section on the transcendental exercise of the faculty of judgement will inform the reader.
It is quite possible that someone may propose a species of preformation-system of pure reason—a middle way between the two—to wit, that the categories are neither innate and first a priori principles of cognition, nor derived from experience, but are merely subjective aptitudes for thought implanted in us contemporaneously with our existence, which were so ordered and disposed by our Creator, that their exercise perfectly harmonizes with the laws of nature which regulate experience. Now, not to mention that with such an hypothesis it is impossible to say at what point we must stop in the employment of predetermined aptitudes, the fact that the categories would in this case entirely lose that character of necessity which is essentially involved in the very conception of them, is a conclusive objection to it. The conception of cause, for example, which expresses the necessity of an effect under a presupposed condition, would be false, if it rested only upon such an arbitrary subjective necessity of uniting certain empirical representations according to such a rule of relation. I could not then say—"The effect is connected with its cause in the object (that is, necessarily)," but only, "I am so constituted that I can think this representation as so connected, and not otherwise." Now this is just what the sceptic wants. For in this case, all our knowledge, depending on the supposed objective validity of our judgement, is nothing but mere illusion; nor would there be wanting people who would deny any such subjective necessity in respect to themselves, though they must feel it. At all events, we ​could not dispute with any one on that which merely depends on the manner in which his subject is organized.

##### Short view of the above Deduction.Short view of the above Deduction.

The foregoing deduction is an exposition of the pure conceptions of the understanding (and with them of all theoretical a priori cognition), as principles of the possibility of experience, but of experience as the determination of all phenomena in space and time in general—of experience, finally, from the principle of the original synthetical unity of apperception, as the form of the understanding in relation to time and space as original forms of sensibility.
I consider the division by paragraphs to be necessary only up to this point, because we had to treat of the elementary conceptions. As we now proceed to the exposition of the employment of these, I shall not designate the chapters in this manner any further.

### BOOK II. Analytic of Principles.BOOK II. Analytic of Principles.

General logic is constructed upon a plan which coincides exactly with the division of the higher faculties of cognition. These are, Understanding, Judgement, and Reason. This science, accordingly, treats in its analytic of Conceptions, Judgements, and Conclusions in exact correspondence with the functions and order of those mental powers which we include generally under the generic denomination of understanding.
As this merely formal logic makes abstraction of all content of cognition, whether pure or empirical, and occupies itself with the mere form of thought (discursive cognition), it must contain in its analytic a canon for reason. For the form of reason has its law, which, without taking into consideration the particular nature of the cognition about which it is employed, can be discovered a priori, by the simple analysis of the action of reason into its momenta.
Transcendental logic, limited as it is to a determinate content, that of pure a priori cognitions, to wit, cannot imitate general logic in this division. For it is evident ​that the transcendental employment of reason is not objectively valid, and therefore does not belong to the logic of truth (that is, to analytic), but as a logic of illusion, occupies a particular department in the scholastic system under the name of transcendental dialectic.
Understanding and judgement accordingly possess in transcendental logic a canon of objectively valid, and therefore true exercise, and are comprehended in the analytical department of that logic. But reason, in her endeavours to arrive by a priori means at some true statement concerning objects and to extend cognition beyond the bounds of possible experience, is altogether dialectic, and her illusory assertions cannot be constructed into a canon such as an analytic ought to contain.
Accordingly, the analytic of principles will be merely a canon for the faculty of judgement, for the instruction of this faculty in its application to phenomena of the pure conceptions of the understanding, which contain the necessary condition for the establishment of a priori laws. On this account, although the subject of the following chapters is the especial principles of understanding, I shall make use of the term Doctrine of the faculty of judgement, in order to define more particularly my present purpose.

#### INTRODUCTION. Of the Transcendental Faculty of judgement in General.INTRODUCTION. Of the Transcendental Faculty of judgement in General.

If understanding in general be defined as the faculty of laws or rules, the faculty of judgement may be termed the faculty of subsumption under these rules; that is, of distinguishing whether this or that does or does not stand under a given rule (casus datae legis). General logic contains no directions or precepts for the faculty of judgement, nor can it contain any such. For as it makes abstraction of all content of cognition, no duty is left for it, except that of exposing analytically the mere form of cognition in conceptions, judgements, and conclusions, and of thereby establishing formal rules for all exercise of the understanding. Now if this logic wished to give some general direction how we should subsume under these rules, that is, how we should distinguish ​whether this or that did or did not stand under them, this again could not be done otherwise than by means of a rule. But this rule, precisely because it is a rule, requires for itself direction from the faculty of judgement. Thus, it is evident that the understanding is capable of being instructed by rules, but that the judgement is a peculiar talent, which does not, and cannot require tuition, but only exercise. This faculty is therefore the specific quality of the so-called mother wit, the want of which no scholastic discipline can compensate.
For although education may furnish, and, as it were, engraft upon a limited understanding rules borrowed from other minds, yet the power of employing these rules correctly must belong to the pupil himself; and no rule which we can prescribe to him with this purpose is, in the absence or deficiency of this gift of nature, secure from misuse. A physician therefore, a judge or a statesman, may have in his head many admirable pathological, juridical, or political rules, in a degree that may enable him to be a profound teacher in his particular science, and yet in the application of these rules he may very possibly blunder—either because he is wanting in natural judgement (though not in understanding) and, whilst he can comprehend the general in abstracto, cannot distinguish whether a particular case in concreto ought to rank under the former; or because his faculty of judgement bas not been sufficiently exercised by examples and real practice. Indeed, the grand and only use of examples, is to sharpen the judgement. For as regards the correctness and precision of the insight of the understanding, examples are commonly injurious rather than otherwise, because, as casus in terminis they seldom adequately fulfil the conditions of the rule. Besides, they often weaken the power of our understanding to apprehend rules or laws in their universality, independently of particular circumstances of experience; and hence, accustom us to employ them ​more as formulae than as principles. Examples are thus the go-cart of the judgement, which he who is naturally deficient in that faculty cannot afford to dispense with.
But although general logic cannot give directions to the faculty of judgement, the case is very different as regards transcendental logic, insomuch that it appears to be the especial duty of the latter to secure and direct, by means of determinate rules, the faculty of judgement in the employment of the pure understanding. For, as a doctrine, that is, as an endeavour to enlarge the sphere of the understanding in regard to pure a priori cognitions, philosophy is worse than useless, since from all the attempts hitherto made, little or no ground has been gained. But, as a critique, in order to guard against the mistakes of the faculty of judgement (lapsus judicii) in the employment of the few pure conceptions of the understanding which we possess, although its use is in this case purely negative, philosophy is called upon to apply all its acuteness and penetration.
But transcendental philosophy has this peculiarity, that besides indicating the rule, or rather the general condition for rules, which is given in the pure conception of the understanding, it can, at the same time, indicate a priori the case to which the rule must be applied. The cause of the superiority which, in this respect, transcendental philosophy possesses above all other sciences except mathematics, lies in this:—it treats of conceptions which must relate a priori to their objects, whose objective validity consequently cannot be demonstrated a posteriori, and is, at the same time, under the obligation of presenting in general but sufficient tests, the conditions under which objects can be given in harmony with those conceptions; otherwise they would be mere logical forms, without content, and not pure conceptions of the understanding.
Our transcendental doctrine of the faculty of judgement will contain two chapters. The first will treat of the sensuous condition under which alone pure conceptions of the understanding can be employed,—that is, of the schematism of the pure understanding. The second will treat of those synthetical judgements which are derived a priori from pure conceptions of the understanding under those conditions, and which lie a priori at the foundation of all other cognitions, that is to say, it will treat of the principles of the pure understanding. ​

#### CHAPTER I. Of the Schematism of the Pure Conceptions of the Understanding.CHAPTER I. Of the Schematism of the Pure Conceptions of the Understanding.

In all subsumptions of an object under a conception, the representation of the object must be homogeneous with the conception; in other words, the conception must contain that which is represented in the object to be subsumed under it. For this is the meaning of the expression: "An object is contained under a conception." Thus the empirical conception of a plate is homogeneous with the pure geometrical conception of a circle, inasmuch as the roundness which is cogitated in the former is intuited in the latter.
But pure conceptions of the understanding, when compared with empirical intuitions, or even with sensuous intuitions in general, are quite heterogeneous, and never can be discovered in any intuition. How then is the subsumption of the latter under the former, and consequently the application of the categories to phenomena, possible?—For it is impossible to say, for example, Causality can be intuited through the senses and is contained in the phenomenon.—This natural and important question forms the real cause of the necessity of a transcendental doctrine of the faculty of judgement, with the purpose, to wit, of showing how pure conceptions of the understanding can be applied to phenomena. In all other sciences, where the conceptions by which the object is thought in the general are not so different and heterogeneous from those which represent the object in concreto—as it is given, it is quite unnecessary to institute any special inquiries concerning the application of the former to the latter.
Now it is quite clear that there must be some third thing, which on the one side is homogeneous with the category, and with the phenomenon on the other, and so makes the application of the former to the latter possible. This mediating representation ​must be pure (without any empirical content), and yet must on the one side be intellectual, on the other sensuous. Such a representation is the transcendental schema.
The conception of the understanding contains pure synthetical unity of the manifold in general. Time, as the formal condition of the manifold of the internal sense, consequently of the conjunction of all representations, contains a priori a manifold in the pure intuition. Now a transcendental determination of time is so far homogeneous with the category, which constitutes the unity thereof, that it is universal and rests upon a rule a priori. On the other hand, it is so far homogeneous with the phenomenon, inasmuch as time is contained in every empirical representation of the manifold. Thus an application of the category to phenomena becomes possible, by means of the transcendental determination of time, which, as the schema of the conceptions of the understanding, mediates the subsumption of the latter under the former.
After what has been proved in our deduction of the categories, no one, it is to be hoped, can hesitate as to the proper decision of the question, whether the employment of these pure conceptions of the understanding ought to be merely empirical or also transcendental; in other words, whether the categories, as conditions of a possible experience, relate a priori solely to phenomena, or whether, as conditions of the possibility of things in general, their application can be extended to objects as things in themselves. For we have there seen that conceptions are quite impossible, and utterly without signification, unless either to them, or at least to the elements of which they consist, an object be given; and that, consequently, they cannot possibly apply to objects as things in themselves without regard to the question whether and how these may be given to us; and, further, that the only manner in which objects can be given to us is by means of the modification of our sensibility; and, finally, that pure a priori conceptions, in addition to the function of the understanding in the category, must contain a priori formal conditions of sensibility (of the internal sense, namely), which again contain the general condition under which alone the category can be applied to any object. This formal and pure condition of sensibility, to which the conception of the understanding is restricted in its employment, we shall name the schema of the conception of the understanding, and the ​procedure of the understanding with these schemata we shall call the schematism of the pure understanding.
The schema is, in itself, always a mere product of the imagination. But, as the synthesis of imagination has for its aim no single intuition, but merely unity in the determination of sensibility, the schema is clearly distinguishable from the image. Thus, if I place five points one after another.... this is an image of the number five. On the other hand, if I only think a number in general, which may be either five or a hundred, this thought is rather the representation of a method of representing in an image a sum (e.g., a thousand) in conformity with a conception, than the image itself, an image which I should find some little difficulty in reviewing, and comparing with the conception. Now this representation of a general procedure of the imagination to present its image to a conception, I call the schema of this conception.
In truth, it is not images of objects, but schemata, which lie at the foundation of our pure sensuous conceptions. No image could ever be adequate to our conception of a triangle in general. For the generalness of the conception it never could attain to, as this includes under itself all triangles, whether right-angled, acute-angled, etc., whilst the image would always be limited to a single part of this sphere. The schema of the triangle can exist nowhere else than in thought, and it indicates a rule of the synthesis of the imagination in regard to pure figures in space. Still less is an object of experience, or an image of the object, ever to the empirical conception. On the contrary, the conception always relates immediately to the schema of the imagination, as a rule for the determination of our intuition, in conformity with a certain general conception. The conception of a dog indicates a rule, according to which my imagination can delineate the figure of a four-footed animal in general, without being limited to any particular individual form which experience presents to me, or indeed to any possible image that I can represent to myself in concreto. This schematism of our understanding in regard to phenomena and their mere form, is an art, hidden in the depths of the human soul, whose true modes of action we shall only with difficulty discover and unveil. Thus much only can ​we say:—The image is a product of the empirical faculty of the productive imagination—the schema of sensuous conceptions (of figures in space, for example) is a product, and, as it were, a monogram of the pure imagination à priori, whereby and according to which images first become possible, which, however, can be connected with the conception only mediately by means of the schema which they indicate, and are in themselves never fully adequate to it. On the other hand, the schema of a pure conception of the understanding is something that cannot be reduced into any image—it is nothing else than the pure synthesis expressed by the category, conformably to a rule of unity according to conceptions. It is a transcendental product of the imagination, a product which concerns the determination of the internal sense, according to conditions of its form (time) in respect to all representations, in so far as these representations must be conjoined à priori in one conception, conformably to the unity of apperception.
Without entering upon a dry and tedious analysis of the essential requisites of transcendental schemata of the pure conceptions of the understanding, we shall rather proceed at once to give an explanation of them according to the order of the categories, and in connection therewith.
For the external sense the pure image of all quantities (quantorum) is space; the pure image of all objects of sense in general, is time. But the pure schema of quantity (quantitatis) as a conception of the understanding, is number, a representation which comprehends the successive addition of one to one (homogeneous quantities). Thus, number is nothing else than the unity of the synthesis of the manifold in a homogeneous intuition, by means of my generating time itself in my apprehension of the intuition.
Reality, in the pure conception of the understanding, is that which corresponds to a sensation in general; that, consequently, the conception of which indicates a being (in time). Negation is that the conception of which represents a not-being (in time). The opposition of these two consists therefore in the difference of one and the same time, as a time filled or a time empty. Now as time is only the form of intuition, ​of intuition, consequently of objects as phenomena, that which in objects corresponds to sensation is the transcendental matter of all objects as things in themselves (Sachheit, reality). Now every sensation has a degree or quantity by which it can fill time, that is to say, the internal sense in respect of the representation of an object, more or less, until it vanishes into nothing (= 0 = negatio). Thus there is a relation and connection between reality and negation, or rather a transition from the former to the latter, which makes every reality representable to us as a quantum; and the schema of a reality as the quantity of something in so far as it fills time, is exactly this continuous and uniform generation of the reality in time, as we descend in time from the sensation which has a certain degree, down to the vanishing thereof, or gradually ascend from negation to the quantity thereof.
The schema of substance is the permanence of the real in time; that is, the representation of it as a substratum of the empirical determination of time; a substratum which therefore remains, whilst all else changes. (Time passes not, but in it passes the existence of the changeable. To time, therefore, which is itself unchangeable and permanent, corresponds that which in the phenomenon is unchangeable in existence, that is, substance, and it is only by it that the succession and coexistence of phenomena can be determined in regard to time.)
The schema of cause and of the causality of a thing is the real which, when posited, is always followed by something else. It consists, therefore, in the succession of the manifold, in so far as that succession is subjected to a rule.
The schema of community (reciprocity of action and reaction), or the reciprocal causality of substances in respect of their accidents, is the coexistence of the determinations of the one with those of the other, according to a general rule.
The schema of possibility is the accordance of the synthesis of different representations with the conditions of time in general (as, for example, opposites cannot exist together at the same time in the same thing, but only after each other), and is therefore the determination of the representation of a thing at any time.
The schema of reality is existence in a determined time. ​
The schema of necessity is the existence of an object in all time.
It is clear, from all this, that the schema of the category of quantity contains and represents the generation (synthesis) of time itself, in the successive apprehension of an object; the schema of quality the synthesis of sensation with the representation of time, or the filling up of time; the schema of relation the relation of perceptions to each other in all time (that is, according to a rule of the determination of time): and finally, the schema of modality and its categories, time itself, as the correlative of the determination of an object—whether it does belong to time, and how. The schemata, therefore, are nothing but a priori determinations of time according to rules, and these, in regard to all possible objects, following the arrangement of the categories, relate to the series in time, the content in time, the order in time, and finally, to the complex or totality in time.
Hence it is apparent that the schematism of the understanding, by means of the transcendental synthesis of the imagination, amounts to nothing else than the unity of the manifold of intuition in the internal sense, and thus indirectly to the unity of apperception, as a function corresponding to the internal sense (a receptivity). Thus, the schemata of the pure conceptions of the understanding are the true and only conditions whereby our understanding receives an application to objects, and consequently significance. Finally, therefore, the categories are only capable of empirical use, inasmuch as they serve merely to subject phenomena to the universal rules of synthesis, by means of an a priori necessary unity (on account of the necessary union of all consciousness in one original apperception); and so to render them susceptible of a complete connection in one experience. But within this whole of possible experience lie all our cognitions, and in the universal relation to this experience consists transcendental truth, which antecedes all empirical truth, and renders the latter possible.
It is, however, evident at first sight, that although the schemata of sensibility are the sole agents in realizing the categories, they do, nevertheless, also restrict them, that is, they limit the categories by conditions which lie beyond the sphere of understanding—namely, in sensibility. Hence the schema is properly only the phenomenon, ​or the sensuous conception of an object in harmony with the category. (Numerus est quantitas phaenomenon,—sensatio realitas phaenomenon; constans et perdurabile rerum substantia phaenomenon—aeternitas, necessitas, phaenomena, etc.) Now, if we remove a restrictive condition, we thereby amplify, it appears, the formerly limited conception. In this way, the categories in their pure signification, free from all conditions of sensibility, ought to be valid of things as they are, and not, as the schemata represent them, merely as they appear; and consequently the categories must have a significance far more extended, and wholly independent of all schemata. In truth, there does always remain to the pure conceptions of the understanding, after abstracting every sensuous condition, a value and significance, which is, however, merely logical. But in this case, no object is given them, and therefore they have no meaning sufficient to afford us a conception of an object. The notion of substance, for example, if we leave out the sensuous determination of permanence, would mean nothing more than a something which can be cogitated as subject, without the possibility of becoming a predicate to anything else. Of this representation I can make nothing, inasmuch as it does not indicate to me what determinations the thing possesses which must thus be valid as premier subject. Consequently, the categories, without schemata are merely functions of the understanding for the production of conceptions, but do not represent any object. This significance they derive from sensibility, which at the same time realizes the understanding and restricts it.

#### CHAPTER II. System of all Principles of the Pure Understanding.CHAPTER II. System of all Principles of the Pure Understanding.

In the foregoing chapter we have merely considered the general conditions under which alone the transcendental faculty of judgement is justified in using the pure conceptions of the understanding for synthetical judgements. Our duty at present is ​to exhibit in systematic connection those judgements which the understanding really produces a priori. For this purpose, our table of the categories will certainly afford us the natural and safe guidance. For it is precisely the categories whose application to possible experience must constitute all pure a priori cognition of the understanding; and the relation of which to sensibility will, on that very account, present us with a complete and systematic catalogue of all the transcendental principles of the use of the understanding.
Principles a priori are so called, not merely because they contain in themselves the grounds of other judgements, but also because they themselves are not grounded in higher and more general cognitions. This peculiarity, however, does not raise them altogether above the need of a proof. For although there could be found no higher cognition, and therefore no objective proof, and although such a principle rather serves as the foundation for all cognition of the object, this by no means hinders us from drawing a proof from the subjective sources of the possibility of the cognition of an object. Such a proof is necessary, moreover, because without it the principle might be liable to the imputation of being a mere gratuitous assertion.
In the second place, we shall limit our investigations to those principles which relate to the categories. For as to the principles of transcendental aesthetic, according to which space and time are the conditions of the possibility of things as phenomena, as also the restriction of these principles, namely, that they cannot be applied to objects as things in themselves—these, of course, do not fall within the scope of our present inquiry. In like manner, the principles of mathematical science form no part of this system, because they are all drawn from intuition, and not from the pure conception of the understanding. The possibility of these principles, however, will necessarily be considered here, inasmuch as they are synthetical judgements a priori, not indeed for the purpose of proving their accuracy and apodeictic certainty, which is unnecessary, but merely to render conceivable and deduce the possibility of such evident a priori cognitions.
But we shall have also to speak of the principle of analytical judgements, in opposition to synthetical judgements, which is the proper subject of our inquiries, because this very ​opposition will free the theory of the latter from all ambiguity, and place it clearly before our eyes in its true nature.

##### SECTION I. Of the Supreme Principle of all Analytical Judgements.SECTION I. Of the Supreme Principle of all Analytical Judgements.

Whatever may be the content of our cognition, and in whatever manner our cognition may be related to its object, the universal, although only negative conditions of all our judgements is that they do not contradict themselves; otherwise these judgements are in themselves (even without respect to the object) nothing. But although there may exist no contradiction in our judgement, it may nevertheless connect conceptions in such a manner that they do not correspond to the object, or without any grounds either a priori or a posteriori for arriving at such a judgement, and thus, without being self-contradictory, a judgement may nevertheless be either false or groundless.
Now, the proposition, "No subject can have a predicate that contradicts it," is called the principle of contradiction, and is a universal but purely negative criterion of all truth. But it belongs to logic alone, because it is valid of cognitions, merely as cognitions and without respect to their content, and declares that the contradiction entirely nullifies them. We can also, however, make a positive use of this principle, that is, not merely to banish falsehood and error (in so far as it rests upon contradiction), but also for the cognition of truth. For if the judgement is analytical, be it affirmative or negative, its truth must always be recognizable by means of the principle of contradiction. For the contrary of that which lies and is cogitated as conception in the cognition of the object will be always properly negatived, but the conception itself must always be affirmed of the object, inasmuch as the contrary thereof would be in contradiction to the object.
We must therefore hold the principle of contradiction to be the universal and fully sufficient principle of all analytical cognition. But as a sufficient criterion of truth, it has no further utility or authority. ​For the fact that no cognition can be at variance with this principle without nullifying itself, constitutes this principle the sine qua non, but not the determining ground of the truth of our cognition. As our business at present is properly with the synthetical part of our knowledge only, we shall always be on our guard not to transgress this inviolable principle; but at the same time not to expect from it any direct assistance in the establishment of the truth of any synthetical proposition.
There exists, however, a formula of this celebrated principle—a principle merely formal and entirely without content—which contains a synthesis that has been inadvertently and quite unnecessarily mixed up with it. It is this:—"It is impossible for a thing to be and not to be at the same time." Not to mention the superfluousness of the addition of the word impossible to indicate the apodeictic certainty, which ought to be self-evident from the proposition itself, the proposition is affected by the condition of time, and as it were says: "A thing = A, which is something = B, cannot at the same time be non-B." But both, B as well as non-B, may quite well exist in succession. For example, a man who is young cannot at the same time be old; but the same man can very well be at one time young, and at another not young, that is, old. Now the principle of contradiction as a merely logical proposition must not by any means limit its application merely to relations of time, and consequently a formula like the preceding is quite foreign to its true purpose. The misunderstanding arises in this way. We first of all separate a predicate of a thing from the conception of the thing, and afterwards connect with this predicate its opposite, and hence do not establish any contradiction with the subject, but only with its predicate, which has been conjoined with the subject synthetically,—a contradiction, moreover, which obtains only when the first and second predicate are affirmed in the same time. If I say: "A man who is ignorant is not learned," the condition "at the same time" must be added, for he who is at one time ignorant, may at another be learned. But if I say: "No ignorant man is a learned man," the proposition is analytical, because the characteristic ignorance is now a constituent part of the conception of the subject; and in this case the negative proposition is evident immediately ​from the proposition of contradiction, without the necessity of adding the condition "the same time." This is the reason why I have altered the formula of this principle—an alteration which shows very clearly the nature of an analytical proposition.

##### SECTION II. Of the Supreme Principle of all Synthetical Judgements.SECTION II. Of the Supreme Principle of all Synthetical Judgements.

The explanation of the possibility of synthetical judgements is a task with which general logic has nothing to do; indeed she needs not even be acquainted with its name. But in transcendental logic it is the most important matter to be dealt with—indeed the only one, if the question is of the possibility of synthetical judgements a priori, the conditions and extent of their validity. For when this question is fully decided, it can reach its aim with perfect ease, the determination, to wit, of the extent and limits of the pure understanding.
In an analytical judgement I do not go beyond the given conception, in order to arrive at some decision respecting it. If the judgement is affirmative, I predicate of the conception only that which was already cogitated in it; if negative, I merely exclude from the conception its contrary. But in synthetical judgements, I must go beyond the given conception, in order to cogitate, in relation with it, something quite different from that which was cogitated in it, a relation which is consequently never one either of identity or contradiction, and by means of which the truth or error of the judgement cannot be discerned merely from the judgement itself.
Granted, then, that we must go out beyond a given conception, in order to compare it synthetically with another, a third thing is necessary, in which alone the synthesis of two conceptions can originate. Now what is this tertium quid that is to be the medium of all synthetical judgements? It is only a complex in which all our representations are contained, the internal sense to wit, and its form a priori, time.
The synthesis of our representations rests upon the imagination; their synthetical unity (which is requisite to a judgement), upon the unity of apperception. In this ​, therefore, is to be sought the possibility of synthetical judgements, and as all three contain the sources of a priori representations, the possibility of pure synthetical judgements also; nay, they are necessary upon these grounds, if we are to possess a knowledge of objects, which rests solely upon the synthesis of representations.
If a cognition is to have objective reality, that is, to relate to an object, and possess sense and meaning in respect to it, it is necessary that the object be given in some way or another. Without this, our conceptions are empty, and we may indeed have thought by means of them, but by such thinking we have not, in fact, cognized anything, we have merely played with representation. To give an object, if this expression be understood in the sense of "to present" the object, not mediately but immediately in intuition, means nothing else than to apply the representation of it to experience, be that experience real or only possible. Space and time themselves, pure as these conceptions are from all that is empirical, and certain as it is that they are represented fully a priori in the mind, would be completely without objective validity, and without sense and significance, if their necessary use in the objects of experience were not shown. Nay, the representation of them is a mere schema, that always relates to the reproductive imagination, which calls up the objects of experience, without which they have no meaning. And so it is with all conceptions without distinction.
The possibility of experience is, then, that which gives objective reality to all our a priori cognitions. Now experience depends upon the synthetical unity of phenomena, that is, upon a synthesis according to conceptions of the object of phenomena in general, a synthesis without which experience never could become knowledge, but would be merely a rhapsody of perceptions, never fitting together into any connected text, according to rules of a thoroughly united (possible) consciousness, and therefore never subjected to the transcendental and necessary unity of apperception. Experience has therefore for a foundation, a priori principles of its form, that is to say, general rules of unity in the synthesis of phenomena, the objective reality of which rules, as necessary conditions even of the possibility of experience can which rules, as necessary conditions—even of the possibility of experience—can always be shown in experience. But apart from this relation, a priori synthetical ​propositions are absolutely impossible, because they have no third term, that is, no pure object, in which the synthetical unity can exhibit the objective reality of its conceptions.
Although, then, respecting space, or the forms which productive imagination describes therein, we do cognize much à priori in synthetical judgements, and are really in no need of experience for this purpose, such knowledge would nevertheless amount to nothing but a busy trifling with a mere chimera, were not space to be considered as the condition of the phenomena which constitute the material of external experience. Hence those pure synthetical judgements do relate, though but mediately, to possible experience, or rather to the possibility of experience, and upon that alone is founded the objective validity of their synthesis.
While then, on the one hand, experience, as empirical synthesis, is the only possible mode of cognition which gives reality to all other synthesis; on the other hand, this latter synthesis, as cognition à priori, possesses truth, that is, accordance with its object, only in so far as it contains nothing more than what is necessary to the synthetical unity of experience.
Accordingly, the supreme principle of all synthetical judgements is: Every object is subject to the necessary conditions of the synthetical unity of the manifold of intuition in a possible experience.
A priori synthetical judgements are possible when we apply the formal conditions of the à priori intuition, the synthesis of the imagination, and the necessary unity of that synthesis in a transcendental apperception, to a possible cognition of experience, and say: The conditions of the possibility of experience in general are at the same time conditions of the possibility of the objects of experience, and have, for that reason, objective validity in an à priori synthetical judgement.

##### SECTION III. Systematic Representation of all Synthetical Principles of the Pure Understanding.SECTION III. Systematic Representation of all Synthetical Principles of the Pure Understanding.

That principles exist at all is to be ascribed solely to the pure understanding, which is not only the faculty of rules in regard to that which happens, but is even the source of principles according to which everything that can be presented to us as an object is necessarily subject to rules, because without such rules we never could attain to cognition of an object. Even the laws of nature, if they are contemplated as principles of the empirical use of the understanding, possess also a characteristic of necessity, and we may therefore at least expect them to be determined upon grounds which are valid a priori and antecedent to all experience. But all laws of nature, without distinction, are subject to higher principles of the understanding, inasmuch as the former are merely applications of the latter to particular cases of experience. These higher principles alone therefore give the conception, which contains the necessary condition, and, as it were, the exponent of a rule; experience, on the other hand, gives the case which comes under the rule.
There is no danger of our mistaking merely empirical principles for principles of the pure understanding, or conversely; for the character of necessity, according to conceptions which distinguish the latter, and the absence of this in every empirical proposition, how extensively valid soever it may be, is a perfect safeguard against confounding them. There are, however, pure principles a priori, which nevertheless I should not ascribe to the pure understanding—for this reason, that they are not derived from pure conceptions, but (although by the mediation of the understanding) from pure intuitions. But understanding is the faculty of conceptions. Such principles mathematical science possesses, but their application to experience, consequently their objective validity, nay the possibility of such a priori synthetical cognitions (the deduction thereof) rests entirely upon the pure understanding.
On this account, I shall not reckon among my principles ​those of mathematics; though I shall include those upon the possibility and objective validity a priori, of principles of the mathematical science, which, consequently, are to be looked upon as the principle of these, and which proceed from conceptions to intuition, and not from intuition to conceptions.
In the application of the pure conceptions of the understanding to possible experience, the employment of their synthesis is either mathematical or dynamical, for it is directed partly on the intuition alone, partly on the existence of a phenomenon. But the a priori conditions of intuition are in relation to a possible experience absolutely necessary, those of the existence of objects of a possible empirical intuition are in themselves contingent. Hence the principles of the mathematical use of the categories will possess a character of absolute necessity, that is, will be apodeictic; those, on the other hand, of the dynamical use, the character of an a priori necessity indeed, but only under the condition of empirical thought in an experience, therefore only mediately and indirectly. Consequently they will not possess that immediate evidence which is peculiar to the former, although their application to experience does not, for that reason, lose its truth and certitude. But of this point we shall be better able to judge at the conclusion of this system of principles.
The table of the categories is naturally our guide to the table of principles, because these are nothing else than rules for the objective employment of the former. Accordingly, all principles of the pure understanding are:
| | 1 Axioms of Intuition | |
| 2 Anticipations of Perception | | 3 Analogies of Experience |
| | 4 Postulates of Empirical Thought in general | |
These appellations I have chosen advisedly, in order that we might not lose sight of the distinctions in respect of the ​evidence and the employment of these principles. It will, however, soon appear that—a fact which concerns both the evidence of these principles, and the a priori determination of phenomena—according to the categories of quantity and quality (if we attend merely to the form of these), the principles of these categories are distinguishable from those of the two others, in as much as the former are possessed of an intuitive, but the latter of a merely discursive, though in both instances a complete, certitude. I shall therefore call the former mathematical, and the latter dynamical principles. It must be observed, however, that by these terms I mean just as little in the one case the principles of mathematics as those of general (physical) dynamics in the other. I have here in view merely the principles of the pure understanding, in their application to the internal sense (without distinction of the representations given therein), by means of which the sciences of mathematics and dynamics become possible. Accordingly, I have named these principles rather with reference to their application than their content; and I shall now proceed to consider them in the order in which they stand in the table.

##### 1. AXIOMS OF INTUITION. The principle of these is: All Intuitions are Extensive Quantities.1. AXIOMS OF INTUITION. The principle of these is: All Intuitions are Extensive Quantities.

PROOF.
All phenomena c ​ontain, as regards their form, an intuition in space and time, which lies a priori at the foundation of all without exception. Phenomena, therefore, cannot be apprehended, that is, received into empirical consciousness otherwise than through the synthesis of a manifold, through which the representations of a determinate space or time are generated; that is to say, through the composition of the homogeneous and the consciousness of the synthetical unity of this manifold (homogeneous). Now the consciousness of a homogeneous manifold in intuition, in so far as thereby the representation of an object is rendered possible, is the conception of a quantity (quanti). Consequently, even the perception of an object as phenomenon is possible only through the same synthetical unity of the manifold of the given sensuous intuition, through which the unity of the composition of the homogeneous manifold in the conception of a quantity is cogitated; that is to say, all phenomena are quantities, and extensive quantities, because as intuitions in space or time they must be represented by means of the same synthesis through which space and time themselves are determined.
An extensive quantity I call that wherein the representation of the parts renders possible (and therefore necessarily antecedes) the representation of the whole. I cannot represent to myself any line, however small, without drawing it in thought, that is, without generating from a point all its parts one after another, and in this way alone producing this intuition. Precisely the same is the case with every, even the smallest, portion of time. I cogitate therein only the successive progress from one moment to another, and hence, by means of the different portions of time and the addition of them, a determinate quantity of time is produced. As the pure intuition in all phenomena is either time or space, so is every phenomenon in its character of intuition an extensive quantity, inasmuch as it can only be cognized in our apprehension by successive synthesis (from part to part). All phenomena are, accordingly, to be considered as aggregates, that is, as a collection of previously given parts; which is not the case with every sort of quantities, but only with those which are represented and apprehended by us as extensive. ​
On this successive synthesis of the productive imagination, in the generation of figures, is founded the mathematics of extension, or geometry, with its axioms, which express the conditions of sensuous intuition a priori, under which alone the schema of a pure conception of external intuition can exist; for example, "be tween two points only one straight line is possible," "two straight lines cannot enclose a space," etc. These are the axioms which properly relate only to quantities (quanta) as such.
But, as regards the quantity of a thing (quantitas), that is to say, the answer to the question: "How large is this or that object?" although, in respect to this question, we have various propositions synthetical and immediately certain (indemonstrabilia); we have, in the proper sense of the term, no axioms. For example, the propositions: "If equals be added to equals, the wholes are equal"; "If equals be taken from equals, the remainders are equal"; are analytical, because I am immediately conscious of the identity of the production of the one quantity with the production of the other; whereas axioms must be a priori synthetical propositions. On the other hand, the self-evident propositions as to the relation of numbers, are certainly synthetical but not universal, like those of geometry, and for this reason cannot be called axioms, but numerical formulae. That 7 + 5 = 12 is not an analytical proposition. For neither in the representation of seven, nor of five, nor of the composition of the two numbers, do I cogitate the number twelve. (Whether I cogitate the number in the addition of both, is not at present the question; for in the case of an analytical proposition, the only point is whether I really cogitate the predicate in the representation of the subject.) But although the proposition is synthetical, it is nevertheless only a singular proposition. In so far as regard is here had merely to the synthesis of the homogeneous (the units), it cannot take place except in one manner, although our use of these numbers is afterwards general. If I say: "A triangle can be constructed with three lines, any two of which taken together are greater than the third," I exercise merely the pure function of the productive imagination, which may draw the lines longer or shorter and construct the angles at its pleasure. On the contrary, the number seven is possible only in one manner, and so is likewise ​the number twelve, which results from the synthesis of seven and five. Such propositions, then, cannot be termed axioms (for in that case we should have an infinity of these), but numerical formulae.
This transcendental principle of the mathematics of phenomena greatly enlarges our a priori cognition. For it is by this principle alone that pure mathematics is rendered applicable in all its precision to objects of experience, and without it the validity of this application would not be so self-evident; on the contrary, contradictions and confusions have often arisen on this very point. Phenomena are not things in themselves. Empirical intuition is possible only through pure intuition (of space and time); consequently, what geometry affirms of the latter, is indisputably valid of the former. All evasions, such as the statement that objects of sense do not conform to the rules of construction in space (for example, to the rule of the infinite divisibility of lines or angles), must fall to the ground. For, if these objections hold good, we deny to space, and with it to all mathematics, objective validity, and no longer know wherefore, and how far, mathematics can be applied to phenomena. The synthesis of spaces and times as the essential form of all intuition, is that which renders possible the apprehension of a phenomenon, and therefore every external experience, consequently all cognition of the objects of experience; and whatever mathematics in its pure use proves of the former, must necessarily hold good of the latter. All objections are but the chicaneries of an ill-instructed reason, which erroneously thinks to liberate the objects of sense from the formal conditions of our sensibility, and represents these, although mere phenomena, as things in themselves, presented as such to our understanding. But in this case, no a priori synthetical cognition of them could be possible, consequently not through pure conceptions of space and the science which determines these conceptions, that is to say, geometry, would itself be impossible.

##### 2. ANTICIPATIONS OF PERCEPTION. The principle of these is: In all phenomena the Real, that which is an object of sensation, has Intensive Quantity, that is, has a Degree.2. ANTICIPATIONS OF PERCEPTION. The principle of these is: In all phenomena the Real, that which is an object of sensation, has Intensive Quantity, that is, has a Degree.

PROOF. ​
Perception is empirical consciousness, that is to say, a consciousness which contains an element of sensation. Phenomena as objects of perception are not pure, that is, merely formal intuitions, like space and time, for they cannot be perceived in themselves. They contain, then, over and above the intuition, the materials for an object (through which is represented something existing in space or time), that is to say, they contain the real of sensation, as a representation merely subjective, which gives us merely the consciousness that the subject is affected, and which we refer to some external object. Now, a gradual transition from empirical consciousness to pure consciousness is possible, inasmuch as the real in this consciousness entirely vanishes, and there remains a merely formal consciousness (a priori) of the manifold in time and space; consequently there is possible a synthesis also of the production of the quantity of a sensation from its commencement, that is, from the pure intuition = 0 onwards up to a certain quantity of the sensation. Now as sensation in itself is not an objective representation, and in it is to be found neither the intuition of space nor of time, it cannot possess any extensive quantity, and yet there does belong to it a quantity (and that by means of its apprehension, in which empirical consciousness can within a certain time rise from nothing = 0 up to its given amount), consequently an intensive quantity. And thus we must ascribe intensive quantity, that is, a degree of influence on sense to all objects of perception, in so far as this perception contains sensation.
All cognition, by means of which I am enabled to cognize and determine a priori what belongs to empirical cognition, may be called an anticipation; and without doubt this is the sense in which Epicurus employed his expression prholepsis. But as there is in phenomena something which is never cognized a priori, which on this account constitutes the proper difference between pure and empirical cognition, that is to say, sensation (as the matter of perception), it follows, that sensation is just that element in cognition which cannot be at ​all anticipated. On the other hand, we might very well term the pure determinations in space and time, as well in regard to figure as to quantity, anticipations of phenomena, because they represent a priori that which may always be given a posteriori in experience. But suppose that in every sensation, as sensation in general, without any particular sensation being thought of, there existed something which could be cognized a priori, this would deserve to be called anticipation in a special sense—special, because it may seem surprising to forestall experience, in that which concerns the matter of experience, and which we can only derive from itself. Yet such really is the case here.
Apprehension, by means of sensation alone, fills only one moment, that is, if I do not take into consideration a succession of many sensations. As that in the phenomenon, the apprehension of which is not a successive synthesis advancing from parts to an entire representation, sensation has therefore no extensive quantity; the want of sensation in a moment of time would represent it as empty, consequently = O. That which in the empirical intuition corresponds to sensation is reality (realitas phaenomenon); that which corresponds to the absence of it, negation = O. Now every sensation is capable of a diminution, so that it can decrease, and thus gradually disappear. Therefore, between reality in a phenomenon and negation, there exists a continuous concatenation of many possible intermediate sensations, the difference of which from each other is always smaller than that between the given sensation and zero, or complete negation. That is to say, the real in a phenomenon has always a quantity, which however is not discoverable in apprehension, inasmuch as apprehension take place by means of mere sensation in one instant, and not by the successive synthesis of many sensations, and therefore does not progress from parts to the whole. Consequently, it has a quantity, but not an extensive quantity.
Now that quantity which is apprehended only as unity, and in which plurality can be represented only by approximation to negation = O, I term intensive quantity. Consequently, reality in a phenomenon has intensive quantity, that is, a degree. if we consider ​this reality as cause (be it of sensation or of another reality in the phenomenon, for example, a change), we call the degree of reality in its character of cause a momentum, for example, the momentum of weight; and for this reason, that the degree only indicates that quantity the apprehension of which is not successive, but instantaneous. This, however, I touch upon only in passing, for with causality I have at present nothing to do.
Accordingly, every sensation, consequently every reality in phenomena, however small it may be, has a degree, that is, an intensive quantity, which may always be lessened, and between reality and negation there exists a continuous connection of possible realities, and possible smaller perceptions. Every colour- for example, red—has a degree, which, be it ever so small, is never the smallest, and so is it always with heat, the momentum of weight, etc.
This property of quantities, according to which no part of them is the smallest possible (no part simple), is called their continuity. Space and time are quanta continua, because no part of them can be given, without enclosing it within boundaries (points and moments), consequently, this given part is itself a space or a time. Space, therefore, consists only of spaces, and time of times. Points and moments are only boundaries, that is, the mere places or positions of their limitation. But places always presuppose intuitions which are to limit or determine them; and we cannot conceive either space or time composed of constituent parts which are given before space or time. Such quantities may also be called flowing, because synthesis (of the productive imagination) in the production of these quantities is a progression in time, the continuity of which we are accustomed to indicate by the expression flowing.
All phenomena, then, are continuous quantities, in respect both to intuition and mere perception (sensation, and with it reality). In the former case they are extensive quantities; in the latter, intensive. When the synthesis of the manifold of a phenomenon is interrupted, there results merely an aggregate of several phenomena, and not properly a phenomenon as a quantity, which is not produced by the mere continuation of the productive synthesis of a certain kind ​, but by the repetition of a synthesis always ceasing. For example, if I call thirteen dollars a sum or quantity of money, I employ the term quite correctly, inasmuch as I understand by thirteen dollars the value of a mark in standard silver, which is, to be sure, a continuous quantity, in which no part is the smallest, but every part might constitute a piece of money, which would contain material for still smaller pieces. If, however, by the words thirteen dollars I understand so many coins (be their value in silver what it may), it would be quite erroneous to use the expression a quantity of dollars; on the contrary, I must call them aggregate, that is, a number of coins. And as in every number we must have unity as the foundation, so a phenomenon taken as unity is a quantity, and as such always a continuous quantity (quantum continuum).
Now, seeing all phenomena, whether considered as extensive or intensive, are continuous quantities, the proposition: "All change (transition of a thing from one state into another) is continuous," might be proved here easily, and with mathematical evidence, were it not that the causality of a change lies, entirely beyond the bounds of a transcendental philosophy, and presupposes empirical principles. For of the possibility of a cause which changes the condition of things, that is, which determines them to the contrary to a certain given state, the understanding gives us a priori no knowledge; not merely because it has no insight into the possibility of it (for such insight is absent in several a priori cognitions), but because the notion of change concerns only certain determinations of phenomena, which experience alone can acquaint us with, while their cause lies in the unchangeable. But seeing that we have nothing which we could here employ but the pure fundamental conceptions of all possible experience, among which of course nothing empirical can be admitted, we dare not, without injuring the unity of our system, anticipate general physical science, which is built upon certain fundamental experiences.
Nevertheless, we are in no want of proofs of the great influence which the principle above developed exercises in the anticipation of perceptions, and even in supplying the want of them, so far as to shield us against the false conclusions which otherwise we might rashly draw.
If all reality in perception has a degree, betw ​een which and negation there is an endless sequence of ever smaller degrees, and if, nevertheless, every sense must have a determinate degree of receptivity for sensations; no perception, and consequently no experience is possible, which can prove, either immediately or mediately, an entire absence of all reality in a phenomenon; in other words, it is impossible ever to draw from experience a proof of the existence of empty space or of empty time. For in the first place, an entire absence of reality in a sensuous intuition cannot of course be an object of perception; secondly, such absence cannot be deduced from the contemplation of any single phenomenon, and the difference of the degrees in its reality; nor ought it ever to be admitted in explanation of any phenomenon. For if even the complete intuition of a determinate space or time is thoroughly real, that is, if no part thereof is empty, yet because every reality has its degree, which, with the extensive quantity of the phenomenon unchanged, can diminish through endless gradations down to nothing (the void), there must be infinitely graduated degrees, with which space or time is filled, and the intensive quantity in different phenomena may be smaller or greater, although the extensive quantity of the intuition remains equal and unaltered.
We shall give an example of this. Almost all natural philosophers, remarking a great difference in the quantity of the matter of different kinds in bodies with the same volume (partly on account of the momentum of gravity or weight, partly on account of the momentum of resistance to other bodies in motion), conclude unanimously that this volume (extensive quantity of the phenomenon) must be void in all bodies, although in different proportion. But who would suspect that these for the most part mathematical and mechanical inquirers into nature should ground this conclusion solely on a metaphysical hypothesis—a sort of hypothesis which they profess to disparage and avoid? Yet this they do, in assuming that the real in space (I must not here call it impenetrability or weight, because these are empirical conceptions) is always identical, and can only be distinguished according to its extensive quantity, that is, multiplicity. Now to this presupposition, for which they can have no ground in experience, and which consequently is merely metaphysical, I oppose a transcendental demonstration, ​which it is true will not explain the difference in the filling up of spaces, but which nevertheless completely does away with the supposed necessity of the above-mentioned presupposition that we cannot explain the said difference otherwise than by the hypothesis of empty spaces. This demonstration, moreover, has the merit of setting the understanding at liberty to conceive this distinction in a different manner, if the explanation of the fact requires any such hypothesis. For we perceive that although two equal spaces may be completely filled by matters altogether different, so that in neither of them is there left a single point wherein matter is not present, nevertheless, every reality has its degree (of resistance or of weight), which, without diminution of the extensive quantity, can become less and less ad infinitum, before it passes into nothingness and disappears. Thus an expansion which fills a space—for example, caloric, or any other reality in the phenomenal world—can decrease in its degrees to infinity, yet without leaving the smallest part of the space empty; on the contrary, filling it with those lesser degrees as completely as another phenomenon could with greater. My intention here is by no means to maintain that this is really the case with the difference of matters, in regard to their specific gravity; I wish only to prove, from a principle of the pure understanding, that the nature of our perceptions makes such a mode of explanation possible, and that it is erroneous to regard the real in a phenomenon as equal quoad its degree, and different only quoad its aggregation and extensive quantity, and this, too, on the pretended authority of an a priori principle of the understanding.
Nevertheless, this principle of the anticipation of perception must somewhat startle an inquirer whom initiation into transcendental philosophy has rendered cautious. We must naturally entertain some doubt whether or not the understanding can enounce any such synthetical proposition as that respecting the degree of all reality in phenomena, and consequently the possibility of the internal difference of sensation itself—abstraction being made of its empirical quality. Thus it is a question not unworthy of solution: "How the understanding can pronounce synthetically and a priori respecting phenomena, and thus anticipate these, even in that which is peculiarly and merely empirical, that, namely, which concerns sensation itself?" ​
The quality of sensation is in all cases merely empirical, and cannot be represented a priori (for example, colours, taste, etc.). But the real—that which corresponds to sensation—in opposition to negation = O, only represents something the conception of which in itself contains a being (ein seyn), and signifies nothing but the synthesis in an empirical consciousness. That is to say, the empirical consciousness in the internal sense can be raised from 0 to every higher degree, so that the very same extensive quantity of intuition, an illuminated surface, for example, excites as great a sensation as an aggregate of many other surfaces less illuminated. We can therefore make complete abstraction of the extensive quantity of a phenomenon, and represent to ourselves in the mere sensation in a certain momentum, a synthesis of homogeneous ascension from 0 up to the given empirical consciousness, All sensations therefore as such are given only a posteriori, but this property thereof, namely, that they have a degree, can be known a priori. It is worthy of remark, that in respect to quantities in general, we can cognize a priori only a single quality, namely, continuity; but in respect to all quality (the real in phenomena), we cannot cognize a priori anything more than the intensive quantity thereof, namely, that they have a degree. All else is left to experience.

##### 3. ANALOGIES OF EXPERIENCE. The principle of these is: Experience is possible only through the representation of a necessary connection of Perceptions.3. ANALOGIES OF EXPERIENCE. The principle of these is: Experience is possible only through the representation of a necessary connection of Perceptions.

PROOF.
Experience is an empirical cognition; that is to say, a cognition which determines an object by means of perceptions. It is therefore a synthesis of perceptions, a synthesis which is not itself contained in perception, but which contains the synthetical unity of the manifold of perception in a consciousness; ​and this unity constitutes the essential of our cognition of objects of the senses, that is, of experience (not merely of intuition or sensation). Now in experience our perceptions come together contingently, so that no character of necessity in their connection appears, or can appear from the perceptions themselves, because apprehension is only a placing together of the manifold of empirical intuition, and no representation of a necessity in the connected existence of the phenomena which apprehension brings together, is to be discovered therein. But as experience is a cognition of objects by means of perceptions, it follows that the relation of the existence of the existence of the manifold must be represented in experience not as it is put together in time, but as it is objectively in time. And as time itself cannot be perceived, the determination of the existence of objects in time can only take place by means of their connection in time in general, consequently only by means of a priori connecting conceptions. Now as these conceptions always possess the character of necessity, experience is possible only by means of a representation of the necessary connection of perception.
The three modi of time are permanence, succession, and coexistence. Accordingly, there are three rules of all relations of time in phenomena, according to which the existence of every phenomenon is determined in respect of the unity of all time, and these antecede all experience and render it possible.
The general principle of all three analogies rests on the necessary unity of apperception in relation to all possible empirical consciousness (perception) at every time, consequently, as this unity lies a priori at the foundation of all mental operations, the principle rests on the synthetical unity of all phenomena according to their relation in time. For the original apperception relates to our internal sense (the complex of all representations), and indeed relates a priori to its form, that is to say, the relation of the manifold empirical consciousness in time. Now this manifold must be combined in original apperception according to relations of time—a necessity imposed by the a priori transcendental unity of apperception, to which is subjected all that can belong to my (i.e., my own) cognition, and therefore all that can become an object for me. This synthetical and a priori ​determined unity in relation of perceptions in time is therefore the rule: "All empirical determinations of time must be subject to rules of the general determination of time"; and the analogies of experience, of which we are now about to treat, must be rules of this nature.
These principles have this peculiarity, that they do not concern phenomena, and the synthesis of the empirical intuition thereof, but merely the existence of phenomena and their relation to each other in regard to this existence. Now the mode in which we apprehend a thing in a phenomenon can be determined a priori in such a manner that the rule of its synthesis can give, that is to say, can produce this a priori intuition in every empirical example. But the existence of phenomena cannot be known a priori, and although we could arrive by this path at a conclusion of the fact of some existence, we could not cognize that existence determinately, that is to say, we should be incapable of anticipating in what respect the empirical intuition of it would be distinguishable from that of others.
The two principles above mentioned, which I called mathematical, in consideration of the fact of their authorizing the application of mathematic phenomena, relate to these phenomena only in regard to their possibility, and instruct us how phenomena, as far as regards their intuition or the real in their perception, can be generated according to the rules of a mathematical synthesis. Consequently, numerical quantities, and with them the determination of a phenomenon as a quantity, can be employed in the one case as well as in the other. Thus, for example, out of 200,000 illuminations by the moon, I might compose and give a priori, that is construct, the degree of our sensations of the sunlight. We may therefore entitle these two principles constitutive.
The case is very different with those principles whose province it is to subject the existence of phenomena to rules a priori. For as existence does not admit of being constructed, ​it is clear that they must only concern the relations of existence and be merely regulative principles. In this case, therefore, neither axioms nor anticipations are to be thought of. Thus, if a perception is given us, in a certain relation of time to other (although undetermined) perceptions, we cannot then say a priori, what and how great (in quantity) the other perception necessarily connected with the former is, but only how it is connected, quoad its existence, in this given modus of time. Analogies in philosophy mean something very different from that which they represent in mathematics. In the latter they are formulae, which enounce the equality of two relations of quantity, and are always constitutive, so that if two terms of the proportion are given, the third is also given, that is, can be constructed by the aid of these formulae. But in philosophy, analogy is not the equality of two quantitative but of two qualitative relations. In this case, from three given terms, I can give a priori and cognize the relation to a fourth member, but not this fourth term itself, although I certainly possess a rule to guide me in the search for this fourth term in experience, and a mark to assist me in discovering it. An analogy of experience is therefore only a rule according to which unity of experience must arise out of perceptions in respect to objects (phenomena) not as a constitutive, but merely as a regulative principle. The same holds good also of the postulates of empirical thought in general, which relate to the synthesis of mere intuition (which concerns the form of phenomena), the synthesis of perception (which concerns the matter of phenomena), and the synthesis of experience (which concerns the relation of these perceptions). For they are only regulative principles, and clearly distinguishable from the mathematical, which are constitutive, not indeed in regard to the certainty which both ​possess a priori, but in the mode of evidence thereof, consequently also in the manner of demonstration.
But what has been observed of all synthetical propositions, and must be particularly remarked in this place, is this, that these analogies possess significance and validity, not as principles of the transcendental, but only as principles of the empirical use of the understanding, and their truth can therefore be proved only as such, and that consequently the phenomena must not be subjoined directly under the categories, but only under their schemata. For if the objects to which those principles must be applied were things in themselves, it would be quite impossible to cognize aught concerning them synthetically a priori. But they are nothing but phenomena; a complete knowledge of which—a knowledge to which all principles a priori must at last relate—is the only possible experience. It follows that these principles can have nothing else for their aim than the conditions of the empirical cognition in the unity of synthesis of phenomena. But this synthesis is cogitated only in the schema of the pure conception of the understanding, of whose unity, as that of a synthesis in general, the category contains the function unrestricted by any sensuous condition. These principles will therefore authorize us to connect phenomena according to an analogy, with the logical and universal unity of conceptions, and consequently to employ the categories in the principles themselves; but in the application of them to experience, we shall use only their schemata, as the key to their proper application, instead of the categories, or rather the latter as restricting conditions, under the title of "formulae" of the former.

##### A. FIRST ANALOGY. Principle of the Permanence of Substance. In all changes of phenomena, substance is permanent, and the quantum thereof in nature is neither increased nor diminished.A. FIRST ANALOGY. Principle of the Permanence of Substance. In all changes of phenomena, substance is permanent, and the quantum thereof in nature is neither increased nor diminished.

PROOF.
All phenomena exist in time, wherein alone as substratum, that is, as the permanent form of the internal intuition, coexistence and succession can be represented. Consequently ​time, in which all changes of phenomena must be cogitated, remains and changes not, because it is that in which succession and coexistence can be represented only as determinations thereof. Now, time in itself cannot be an object of perception. It follows that in objects of perception, that is, in phenomena, there must be found a substratum which represents time in general, and in which all change or coexistence can be perceived by means of the relation of phenomena to it. But the substratum of all reality, that is, of all that pertains to the existence of things, is substance; all that pertains to existence can be cogitated only as a determination of substance. Consequently, the permanent, in relation to which alone can all relations of time in phenomena be determined, is substance in the world of phenomena, that is, the real in phenomena, that which, as the substratum of all change, remains ever the same. Accordingly, as this cannot change in existence, its quantity in nature can neither be increased nor diminished.
Our apprehension of the manifold in a phenomenon is always successive, is Consequently always changing. By it alone we could, therefore, never determine whether this manifold, as an object of experience, is coexistent or successive, unless it had for a foundation something fixed and permanent, of the existence of which all succession and coexistence are nothing but so many modes (modi of time). Only in the permanent, then, are relations of time possible (for simultaneity and succession are the only relations in time); that is to say, the permanent is the substratum of our empirical representation of time itself, in which alone all determination of time is possible. Permanence is, in fact, just another expression for time, as the abiding correlate of all existence of phenomena, and of all change, and of all coexistence. For change does not affect time itself, but only the phenomena in time (just as coexistence cannot be regarded as a modus of time itself, seeing that in time no parts are coexistent, but all successive). If we were to attribute succession to time itself, we should be obliged to cogitate another time, in which this succession would be possible. It is only by means of the permanent th ​at existence in different parts of the successive series of time receives a quantity, which we entitle duration. For in mere succession, existence is perpetually vanishing and recommencing, and therefore never has even the least quantity. Without the permanent, then, no relation in time is possible. Now, time in itself is not an object of perception; consequently the permanent in phenomena must be regarded as the substratum of all determination of time, and consequently also as the condition of the possibility of all synthetical unity of perceptions, that is, of experience; and all existence and all change in time can only be regarded as a mode in the existence of that which abides unchangeably. Therefore, in all phenomena, the permanent is the object in itself, that is, the substance (phenomenon); but all that changes or can change belongs only to the mode of the existence of this substance or substances, consequently to its determinations.
I find that in all ages not only the philosopher, but even the common understanding, has preposited this permanence as a substratum of all change in phenomena; indeed, I am compelled to believe that they will always accept this as an indubitable fact. Only the philosopher expresses himself in a more precise and definite manner, when he says: "In all changes in the world, the substance remains, and the accidents alone are changeable." But of this decidedly synthetical proposition, I nowhere meet with even an attempt at proof; nay, it very rarely has the good fortune to stand, as it deserves to do, at the head of the pure and entirely a priori laws of nature. In truth, the statement that substance is permanent, is tautological. For this very permanence is the ground on which we apply the category of substance to the phenomenon; and we should have been obliged to prove that in all phenomena there is something permanent, of the existence of which the changeable is nothing but a determination. But because a proof of this nature cannot be dogmatical, that is, cannot be drawn from conceptions, inasmuch as it concerns a synthetical proposition a priori, and as philosophers never reflected that such propositions are valid only in relation to possible experience, and therefore cannot be proved except by means of a deduction of the possibility of experience, it is no wonder that while it has served as the foundation of all experience ( ​for we feel the need of it in empirical cognition), it has never been supported by proof.
A philosopher was asked: "What is the weight of smoke?" He answered: "Subtract from the weight of the burnt wood the weight of the remaining ashes, and you will have the weight of the smoke." Thus he presumed it to be incontrovertible that even in fire the matter (substance) does not perish, but that only the form of it undergoes a change. In like manner was the saying: "From nothing comes nothing," only another inference from the principle or permanence, or rather of the ever-abiding existence of the true subject in phenomena. For if that in the phenomenon which we call substance is to be the proper substratum of all determination of time, it follows that all existence in past as well as in future time, must be determinable by means of it alone. Hence we are entitled to apply the term substance to a phenomenon, only because we suppose its existence in all time, a notion which the word permanence does not fully express, as it seems rather to be referable to future time. However, the internal necessity perpetually to be, is inseparably connected with the necessity always to have been, and so the expression may stand as it is. "Gigni de nihilo nihil; in nihilum nil posse reverti, are two propositions which the ancients never parted, and which people nowadays sometimes mistakenly disjoin, because they imagine that the propositions apply to objects as things in themselves, and that the former might be inimical to the dependence (even in respect of its substance also) of the world upon a supreme cause. But this apprehension is entirely needless, for the question in this case is only of phenomena in the sphere of experience, the unity of which never could be possible, if we admitted the possibility that new things (in respect of their substance) should arise. For in that case, we should lose altogether that which alone can represent the unity of time, to wit, the identity of the substratum, as that through which alone all change possesses complete and thorough unity. This permanence is, however, nothing but the manner in which we represent to ourselves the existence of things in the phenomenal world.
The determinations of a substance, which are only particular modes of its existence, are called accidents. They are always real, because they concern the existence of subs ​tance (negations are only determinations, which express the non-existence of something in the substance). Now, if to this real in the substance we ascribe a particular existence (for example, to motion as an accident of matter), this existence is called inherence, in contradistinction to the existence of substance, which we call subsistence. But hence arise many misconceptions, and it would be a more accurate and just mode of expression to designate the accident only as the mode in which the existence of a substance is positively determined. Meanwhile, by reason of the conditions of the logical exercise of our understanding, it is impossible to avoid separating, as it were, that which in the existence of a substance is subject to change, whilst the substance remains, and regarding it in relation to that which is properly permanent and radical. On this account, this category of substance stands under the title of relation, rather because it is the condition thereof than because it contains in itself any relation.
Now, upon this notion of permanence rests the proper notion of the conception change. Origin and extinction are not changes of that which originates or becomes extinct. Change is but a mode of existence, which follows on another mode of existence of the same object; hence all that changes is permanent, and only the condition thereof changes. Now since this mutation affects only determinations, which can have a beginning or an end, we may say, employing an expression which seems somewhat paradoxical: "Only the permanent (substance) is subject to change; the mutable suffers no change, but rather alternation, that is, when certain determinations cease, others begin."
Change, then, cannot be perceived by us except in substances, and origin or extinction in an absolute sense, that does not concern merely a determination of the permanent, cannot be a possible perception, for it is this very notion of the permanent which renders possible the representation of a transition from one state into another, and from non-being to being, which, consequently, can be empirically cognized only as alternating determinations of that which is permanent. Grant that a thing absolutely begins to be; we must then have a point of time in which it was not. But how and by what can we fix and determine this point of time, unless by that which already exists? For a void time—preceding—is ​not an object of perception; but if we connect this beginning with objects which existed previously, and which continue to exist till the object in question in question begins to be, then the latter can only be a determination of the former as the permanent. The same holds good of the notion of extinction, for this presupposes the empirical representation of a time, in which a phenomenon no longer exists.
Substances (in the world of phenomena) are the substratum of all determinations of time. The beginning of some, and the ceasing to be of other substances, would utterly do away with the only condition of the empirical unity of time; and in that case phenomena would relate to two different times, in which, side by side, existence would pass; which is absurd. For there is only one time in which all different times must be placed, not as coexistent, but as successive.
Accordingly, permanence is a necessary condition under which alone phenomena, as things or objects, are determinable in a possible experience. But as regards the empirical criterion of this necessary permanence, and with it of the substantiality of phenomena, we shall find sufficient opportunity to speak in the sequel.

##### B. SECOND ANALOGY. Principle of the Succession of Time According to the Law of Causality. All changes take place according to the law of the connection of Cause and Effect.B. SECOND ANALOGY. Principle of the Succession of Time According to the Law of Causality. All changes take place according to the law of the connection of Cause and Effect.

PROOF.
(That all phenomena in the succession of time are only changes, that is, a successive being and non-being of the determinations of substance, which is permanent; consequently that a being of substance itself which follows on the non-being thereof, or a non-being of substance which follows on the being thereof, in other words, that the origin or extinction of substance itself, is impossible—all this has been fully established in treating of the foregoing principle. This principle might have been expressed as follows: "All alteration (succession) of phenomena is merely change"; for the changes of substance ​are not origin or extinction, because the conception of change presupposes the same subject as existing with two opposite determinations, and consequently as permanent. After this premonition, we shall proceed to the proof.)
I perceive that phenomena succeed one another, that is to say, a state of things exists at one time, the opposite of which existed in a former state. In this case, then, I really connect together two perceptions in time. Now connection is not an operation of mere sense and intuition, but is the product of a synthetical faculty of imagination, which determines the internal sense in respect of a relation of time. But imagination can connect these two states in two ways, so that either the one or the other may antecede in time; for time in itself cannot be an object of perception, and what in an object precedes and what follows cannot be empirically determined in relation to it. I am only conscious, then, that my imagination places one state before and the other after; not that the one state antecedes the other in the object. In other words, the objective relation of the successive phenomena remains quite undetermined by means of mere perception. Now in order that this relation may be cognized as determined, the relation between the two states must be so cogitated that it is thereby determined as necessary, which of them must be placed before and which after, and not conversely. But the conception which carries with it a necessity of synthetical unity, can be none other than a pure conception of the understanding which does not lie in mere perception; and in this case it is the conception of "the relation of cause and effect," the former of which determines the latter in time, as its necessary consequence, and not as something which might possibly antecede (or which might in some cases not be perceived to follow). It follows that it is only because we subject the sequence of phenomena, and consequently all change, to the law of causality, that experience itself, that is, empirical cognition of phenomena, becomes possible; and consequently, that phenomena themselves, as objects of experience, are possible only by virtue of this law.
Our apprehension of the manifold of phenomena is always successive. The representations of parts succeed one another. Whether they succeed one another in the object also, is a second point for reflection, which was not contained in the former. ​Now we may certainly give the name of object to everything, even to every representation, so far as we are conscious thereof; but what this word may mean in the case of phenomena, not merely in so far as they (as representations) are objects, but only in so far as they indicate an object, is a question requiring deeper consideration. In so far as they, regarded merely as representations, are at the same time objects of consciousness, they are not to be distinguished from apprehension, that is, reception into the synthesis of imagination, and we must therefore say: "The manifold of phenomena is always produced successively in the mind." If phenomena were things in themselves, no man would be able to conjecture from the succession of our representations how this manifold is connected in the object; for we have to do only with our representations. How things may be in themselves, without regard to the representations through which they affect us, is utterly beyond the sphere of our cognition. Now although phenomena are not things in themselves, and are nevertheless the only thing given to us to be cognized, it is my duty to show what sort of connection in time belongs to the manifold in phenomena themselves, while the representation of this manifold in apprehension is always successive. For example, the apprehension of the manifold in the phenomenon of a house which stands before me, is successive. Now comes the question whether the manifold of this house is in itself successive—which no one will be at all willing to grant. But, so soon as I raise my conception of an object to the transcendental signification thereof, I find that the house is not a thing in itself, but only a phenomenon, that is, a representation, the transcendental object of which remains utterly unknown. What then am I to understand by the question: "How can the manifold be connected in the phenomenon itself—not considered as a thing in itself, but merely as a phenomenon?" Here that which lies in my successive apprehension is regarded as representation, whilst the phenomenon which is given me, notwithstanding that it is nothing more than a complex of these representations, is regarded as the object thereof, with which my conception, drawn from the representations of apprehension, must harmonize. It is very soon seen that, as accordance of the cognition with its object constitutes truth, the question now before us can only relate to the formal conditions of empirical truth; and that the phenomenon, in ​opposition to the representations of apprehension, can only be distinguished therefrom as the object of them, if it is subject to a rule which distinguishes it from every other apprehension, and which renders necessary a mode of connection of the manifold. That in the phenomenon which contains the condition of this necessary rule of apprehension, is the object.
Let us now proceed to our task. That something happens, that is to say, that something or some state exists which before was not, cannot be empirically perceived, unless a phenomenon precedes, which does not contain in itself this state. For a reality which should follow upon a void time, in other words, a beginning, which no state of things precedes, can just as little be apprehended as the void time itself. Every apprehension of an event is therefore a perception which follows upon another perception. But as this is the case with all synthesis of apprehension, as I have shown above in the example of a house, my apprehension of an event is not yet sufficiently distinguished from other apprehensions. But I remark also that if in a phenomenon which contains an occurrence, I call the antecedent state of my perception, A, and the following state, B, the perception B can only follow A in apprehension, and the perception A cannot follow B, but only precede it. For example, I see a ship float down the stream of a river. My perception of its place lower down follows upon my perception of its place higher up the course of the river, and it is impossible that, in the apprehension of this phenomenon, the vessel should be perceived first below and afterwards higher up the stream. Here, therefore, the order in the sequence of perceptions in apprehension is determined; and by this order apprehension is regulated. In the former example, my perceptions in the apprehension of a house might begin at the roof and end at the foundation, or vice versa; or I might apprehend the manifold in this empirical intuition, by going from left to right, and from right to left. Accordingly, in the series of these perceptions, there was no determined order, which necessitated my beginning at a certain point, in order empirically to connect the manifold. But this rule is always to be met with in the perception of that which happens, and it makes the order of the successive perceptions in the apprehension of such a phenomenon necessary. ​
I must, therefore, in the present case, deduce the subjective sequence of apprehension from the objective sequence of phenomena, for otherwise the former is quite undetermined, and one phenomenon is not distinguishable from another. The former alone proves nothing as to the connection of the manifold in an object, for it is quite arbitrary. The latter must consist in the order of the manifold in a phenomenon, according to which order the apprehension of one thing (that which happens) follows that of another thing (which precedes), in conformity with a rule. In this way alone can I be authorized to say of the phenomenon itself, and not merely of my own apprehension, that a certain order or sequence is to be found therein. That is, in other words, I cannot arrange my apprehension otherwise than in this order.
In conformity with this rule, then, it is necessary that in that which antecedes an event there be found the condition of a rule, according to which in this event follows always and necessarily; but I cannot reverse this and go back from the event, and determine (by apprehension) that which antecedes it. For no phenomenon goes back from the succeeding point of time to the preceding point, although it does certainly relate to a preceding point of time; from a given time, on the other hand, there is always a necessary progression to the determined succeeding time. Therefore, because there certainly is something that follows, I must of necessity connect it with something else, which antecedes, and upon which it follows, in conformity with a rule, that is necessarily, so that the event, as conditioned, affords certain indication of a condition, and this condition determines the event.
Let us suppose that nothing precedes an event, upon which this event must follow in conformity with a rule. All sequence of perception would then exist only in apprehension, that is to say, would be merely subjective, and it could not thereby be objectively determined what thing ought to precede, and what ought to follow in perception. In such a case, we should have nothing but a play of representations, which would possess no application to any object. That is to say, it would not be possible through perception to distinguish one phenomenon from another, as regards relations of time; because the succession in the act of apprehension would always be of the sam ​e sort, and therefore there would be nothing in the phenomenon to determine the succession, and to render a certain sequence objectively necessary. And, in this case, I cannot say that two states in a phenomenon follow one upon the other, but only that one apprehension follows upon another. But this is merely subjective, and does not determine an object, and consequently cannot be held to be cognition of an object—not even in the phenomenal world.
Accordingly, when we know in experience that something happens, we always presuppose that something precedes, whereupon it follows in conformity with a rule. For otherwise I could not say of the object that it follows; because the mere succession in my apprehension, if it be not determined by a rule in relation to something preceding, does not authorize succession in the object. Only, therefore, in reference to a rule, according to which phenomena are determined in their sequence, that is, as they happen, by the preceding state, can I make my subjective synthesis (of apprehension) objective, and it is only under this presupposition that even the experience of an event is possible.
No doubt it appears as if this were in thorough contradiction to all the notions which people have hitherto entertained in regard to the procedure of the human understanding. According to these opinions, it is by means of the perception and comparison of similar consequences following upon certain antecedent phenomena that the understanding is led to the discovery of a rule, according to which certain events always follow certain phenomena, and it is only by this process that we attain to the conception of cause. Upon such a basis, it is clear that this conception must be merely empirical, and the rule which it furnishes us with—"Everything that happens must have a cause"—would be just as contingent as experience itself. The universality and necessity of the rule or law would be perfectly spurious attributes of it. Indeed, it could not possess universal validity, inasmuch as it would not in this case be a priori, but founded on deduction. But the same is the case with this law as with other pure a priori representations (e.g., space and time), which we can draw in perfect clearness and completeness from experience, only because we had already placed them therein, and by that means, and by that alone, had rendered experience ​possible. Indeed, the logical clearness of this representation of a rule, determining the series of events, is possible only when we have made use thereof in experience. Nevertheless, the recognition of this rule, as a condition of the synthetical unity of phenomena in time, was the ground of experience itself and consequently preceded it a priori.
It is now our duty to show by an example that we never, even in experience, attribute to an object the notion of succession or effect (of an event—that is, the happening of something that did not exist before), and distinguish it from the subjective succession of apprehension, unless when a rule lies at the foundation, which compels us to observe this order of perception in preference to any other, and that, indeed, it is this necessity which first renders possible the representation of a succession in the object.
We have representations within us, of which also we can be conscious. But, however widely extended, however accurate and thoroughgoing this consciousness may be, these representations are still nothing more than representations, that is, internal determinations of the mind in this or that relation of time. Now how happens it that to these representations we should set an object, or that, in addition to their subjective reality, as modifications, we should still further attribute to them a certain unknown objective reality? It is clear that objective significancy cannot consist in a relation to another representation (of that which we desire to term object), for in that case the question again arises: "How does this other representation go out of itself, and obtain objective significancy over and above the subjective, which is proper to it, as a determination of a state of mind?" If we try to discover what sort of new property the relation to an object gives to our subjective representations, and what new importance they thereby receive, we shall find that this relation has no other effect than that of rendering necessary the connection of our representations in a certain manner, and of subjecting them to a rule; and that conversely, it is only because a certain order is necessary in the relations of time of our representations, that objective significancy is ascribed to them.
In the synthesis of phenomena, the manifold of our representations is always successive. Now hereby is not represented an object, for by means of this succession, wh ​ich is common to all apprehension, no one thing is distinguished from another. But so soon as I perceive or assume that in this succession there is a relation to a state antecedent, from which the representation follows in accordance with a rule, so soon do I represent something as an event, or as a thing that happens; in other words, I cognize an object to which I must assign a certain determinate position in time, which cannot be altered, because of the preceding state in the object. When, therefore, I perceive that something happens, there is contained in this representation, in the first place, the fact, that something antecedes; because, it. is only in relation to this that the phenomenon obtains its proper relation of time, in other words, exists after an antecedent time, in which it did not exist. But it can receive its determined place in time only by the presupposition that something existed in the foregoing state, upon which it follows inevitably and always, that is, in conformity with a rule. From all this it is evident that, in the first place, I cannot reverse the order of succession, and make that which happens precede that upon which it follows; and that, in the second place, if the antecedent state be posited, a certain determinate event inevitably and necessarily follows. Hence it follows that there exists a certain order in our representations, whereby the present gives a sure indication of some previously existing state, as a correlate, though still undetermined, of the existing event which is given—a correlate which itself relates to the event as its consequence, conditions it, and connects it necessarily with itself in the series of time.
If then it be admitted as a necessary law of sensibility, and consequently a formal condition of all perception, that the preceding necessarily determines the succeeding time (inasmuch as I cannot arrive at the succeeding except through the preceding), it must likewise be an indispensable law of empirical representation of the series of time that the phenomena of the past determine all phenomena in the succeeding time, and that the latter, as events, cannot take place, except in so far as the former determine their existence in time, that is to say, establish it according to a rule. For it is of course only in phenomena that we can empirically cognize this continuity in the connection of times.
For all experience and for the possibility of experience, understanding is indispensable, ​and the first step which it takes in this sphere is not to render the representation of objects clear, but to render the representation of an object in general, possible. It does this by applying the order of time to phenomena, and their existence. In other words, it assigns to each phenomenon, as a consequence, a place in relation to preceding phenomena, determined a priori in time, without which it could not harmonize with time itself, which determines a place a priori to all its parts. This determination of place cannot be derived from the relation of phenomena to absolute time (for it is not an object of perception); but, on the contrary, phenomena must reciprocally determine the places in time of one another, and render these necessary in the order of time. In other words, whatever follows or happens, must follow in conformity with a universal rule upon that which was contained in the foregoing state. Hence arises a series of phenomena, which, by means of the understanding, produces and renders necessary exactly the same order and continuous connection in the series of our possible perceptions, as is found a priori in the form of internal intuition (time), in which all our perceptions must have place.
That something happens, then, is a perception which belongs to a possible experience, which becomes real only because I look upon the phenomenon as determined in regard to its place in time, consequently as an object, which can always be found by means of a rule in the connected series of my perceptions. But this rule of the determination of a thing according to succession in time is as follows: "In what precedes may be found the condition, under which an event always (that is, necessarily) follows." From all this it is obvious that the principle of cause and effect is the principle of possible experience, that is, of objective cognition of phenomena, in regard to their relations in the succession of time.
The proof of this fundamental proposition rests entirely on the following momenta of argument. To all empirical cognition belongs the synthesis of the manifold by the imagination, a synthesis which is always successive, that is, in which the representations therein always follow one another. But the order of succession in imagination is not determined, and the series of successive representations may be taken retrogressively ​as well as progressively. But if this synthesis is a synthesis of apprehension (of the manifold of a given phenomenon),then the order is determined in the object, or to speak more accurately, there is therein an order of successive synthesis which determines an object, and according to which something necessarily precedes, and when this is posited, something else necessarily follows. If, then, my perception is to contain the cognition of an event, that is, of something which really happens, it must be an empirical judgement, wherein we think that the succession is determined; that is, it presupposes another phenomenon, upon which this event follows necessarily, or in conformity with a rule. If, on the contrary, when I posited the antecedent, the event did not necessarily follow, I should be obliged to consider it merely as a subjective play of my imagination, and if in this I represented to myself anything as objective, I must look upon it as a mere dream. Thus, the relation of phenomena (as possible perceptions), according to which that which happens is, as to its existence, necessarily determined in time by something which antecedes, in conformity with a rule—in other words, the relation of cause and effect—is the condition of the objective validity of our empirical judgements in regard to the sequence of perceptions, consequently of their empirical truth, and therefore of experience. The principle of the relation of causality in the succession of phenomena is therefore valid for all objects of experience, because it is itself the ground of the possibility of experience.
Here, however, a difficulty arises, which must be resolved. The principle of the connection of causality among phenomena is limited in our formula to the succession thereof, although in practice we find that the principle applies also when the phenomena exist together in the same time, and that cause and effect may be simultaneous. For example, there is heat in a room, which does not exist in the open air. I look about for the cause, and find it to be the fire, Now the fire as the cause is simultaneous with its effect, the heat of the room. In this case, then, there is no succession as regards time, between cause and effect, but they are simultaneous; and still the law holds good. The greater part of operating causes in nature are simultaneous with their effects, and the succession in time of the latter is produced only becau ​se the cause cannot achieve the total of its effect in one moment. But at the moment when the effect first arises, it is always simultaneous with the causality of its cause, because, if the cause had but a moment before ceased to be, the effect could not have arisen. Here it must be specially remembered that we must consider the order of time and not the lapse thereof. The relation remains, even though no time has elapsed. The time between the causality of the cause and its immediate effect may entirely vanish, and the cause and effect be thus simultaneous, but the relation of the one to the other remains always determinable according to time. If, for example, I consider a leaden ball, which lies upon a cushion and makes a hollow in it, as a cause, then it is simultaneous with the effect. But I distinguish the two through the relation of time of the dynamical connection of both. For if I lay the ball upon the cushion, then the hollow follows upon the before smooth surface; but supposing the cushion has, from some cause or another, a hollow, there does not thereupon follow a leaden ball.
Thus, the law of succession of time is in all instances the only empirical criterion of effect in relation to the causality of the antecedent cause. The glass is the cause of the rising of the water above its horizontal surface, although the two phenomena are contemporaneous. For, as soon as I draw some water with the glass from a larger vessel, an effect follows thereupon, namely, the change of the horizontal state which the water had in the large vessel into a concave, which it assumes in the glass.
This conception of causality leads us to the conception of action; that of action, to the conception of force; and through it, to the conception of substance. As I do not wish this critical essay, the sole purpose of which is to treat of the sources of our synthetical cognition a priori, to be crowded with analyses which merely explain, but do not enlarge the sphere of our conceptions, I reserve the detailed explanation of the above conceptions for a future system of pure reason. Such an analysis, indeed, executed with great particularity, may already be found in well-known works on this subject. But I cannot at present refrain from making a few remarks on the empirical criterion of a substance, in so far as it seems to be more evident and more easily recognized through the conception of ​action than through that of the permanence of a phenomenon.
Where action (consequently activity and force) exists, substance also must exist, and in it alone must be sought the seat of that fruitful source of phenomena. Very well. But if we are called upon to explain what we mean by substance, and wish to avoid the vice of reasoning in a circle, the answer is by no means so easy. How shall we conclude immediately from the action to the permanence of that which acts, this being nevertheless an essential and peculiar criterion of substance (phenomenon)? But after what has been said above, the solution of this question becomes easy enough, although by the common mode of procedure—merely analysing our conceptions—it would be quite impossible. The conception of action indicates the relation of the subject of causality to the effect. Now because all effect consists in that which happens, therefore in the changeable, the last subject thereof is the permanent, as the substratum of all that changes, that is, substance. For according to the principle of causality, actions are always the first ground of all change in phenomena and, consequently, cannot be a property of a subject which itself changes, because if this were the case, other actions and another subject would be necessary to determine this change. From all this it results that action alone, as an empirical criterion, is a sufficient proof of the presence of substantiality, without any necessity on my part of endeavouring to discover the permanence of substance by a comparison. Besides, by this mode of induction we could not attain to the completeness which the magnitude and strict universality of the conception requires. For that the primary subject of the causality of all arising and passing away, all origin and extinction, cannot itself (in the sphere of phenomena) arise and pass away, is a sound and safe conclusion, a conclusion which leads us to the conception of empirical necessity and permanence in existence, and consequently to the conception of a substance as phenomenon.
When something happens, the mere fact of the occurrence, without regard to that which occurs, is an object requiring investigation. The transition from the non-being of a state into the existence of it, supposing that this state contains no quality which previously existed in the phenomenon, is a fact of itse ​lf demanding inquiry. Such an event, as has been shown in No. A, does not concern substance (for substance does not thus originate), but its condition or state. It is therefore only change, and not origin from nothing. If this origin be regarded as the effect of a foreign cause, it is termed creation, which cannot be admitted as an event among phenomena, because the very possibility of it would annihilate the unity of experience. If, however, I regard all things not as phenomena, but as things in themselves and objects of understanding alone, they, although substances, may be considered as dependent, in respect of their existence, on a foreign cause. But this would require a very different meaning in the words, a meaning which could not apply to phenomena as objects of possible experience.
How a thing can be changed, how it is possible that upon one state existing in one point of time, an opposite state should follow in another point of time—of this we have not the smallest conception a priori. There is requisite for this the knowledge of real powers, which can only be given empirically; for example, knowledge of moving forces, or, in other words, of certain successive phenomena (as movements) which indicate the presence of such forces. But the form of every change, the condition under which alone it can take place as the coming into existence of another state (be the content of the change, that is, the state which is changed, what it may), and consequently the succession of the states themselves can very well be considered a priori, in relation to the law of causality and the conditions of time.
When a substance passes from one state, a, into another state, b, the point of time in which the latter exists is different from, and subsequent to that in which the former existed. In like manner, the second state, as reality (in the phenomenon), differs from the first, in which the reality of the second did not exist, as b from zero. That is to say, if the state, b, differs from the state, a, only in respect to quantity, the change is a coming into existence of b - a, which in the former state did not exist, and in relation to which that state is = O. ​
Now the question arises how a thing passes from one state = a, into another state = b. Between two moments there is always a certain time, and between two states existing in these moments there is always a difference having a certain quantity (for all parts of phenomena are in their turn quantities). Consequently, every transition from one state into another is always effected in a time contained between two moments, of which the first determines the state which leaves, and the second determines the state into the thing passes. the thing leaves, and the second determines the state into which the thing Both moments, then, are limitations of the time of a change, consequently of the intermediate state between both, and as such they belong to the total of the change. Now every change has a cause, which evidences its causality in the whole time during which the charge takes place. The cause, therefore, does not produce the change all at once or in one moment, but in a time, so that, as the time gradually increases from the commencing instant, a, to its completion at b, in like manner also, the quantity of the reality (b —a) is generated through the lesser degrees which are contained between the first and last. All change is therefore possible only through a continuous action of the causality, which, in so far as it is uniform, we call a momentum. The change does not consist of these momenta, but is generated or produced by them as their effect.
Such is the law of the continuity of all change, the ground of which is that neither time itself nor any phenomenon in time consists of parts which are the smallest possible, but that, notwithstanding, the state of a thing passes in the process of a change through all these parts, as elements, to its second state. There is no smallest degree of reality in a phenomenon, just as there is no smallest degree in the quantity of time; and so the new state of reality grows up out of the former state, through all the infinite degrees thereof, the differences of which one from another, taken all together, are less than the difference between o and a.
It is not our business to inquire here into the utility of this principle in the investigation of nature. But how such a proposition, which appears so greatly to extend our knowledge of nature, is possible completely a priori, is indeed a question which deserves investigation, although the first view seems to demonstrate the truth and reality of the principle, and the question, ​how it is possible, may be considered superfluous. For there are so many groundless pretensions to the enlargement of our knowledge by pure reason that we must take it as a general rule to be mistrustful of all such, and without a thoroughgoing and radical deduction, to believe nothing of the sort even on the clearest dogmatical evidence.
Every addition to our empirical knowledge, and every advance made in the exercise of our perception, is nothing more than an extension of the determination of the internal sense, that is to say, a progression in time, be objects themselves what they may, phenomena, or pure intuitions. This progression in time determines everything, and is itself determined by nothing else. That is to say, the parts of the progression exist only in time, and by means of the synthesis thereof, and are not given antecedently to it. For this reason, every transition in perception to anything which follows upon another in time, is a determination of time by means of the production of this perception. And as this determination of time is, always and in all its parts, a quantity, the perception produced is to be considered as a quantity which proceeds through all its degrees—no one of which is the smallest possible—from zero up to its determined degree. From this we perceive the possibility of cognizing a priori a law of changes—a law, however, which concerns their form merely. We merely anticipate our own apprehension, the formal condition of which, inasmuch as it is itself to be found in the mind antecedently to all given phenomena, must certainly be capable of being cognized a priori.
Thus, as time contains the sensuous condition a priori of the possibility of a continuous progression of that which exists to that which follows it, the understanding, by virtue of the unity of apperception, contains the condition a priori of the possibility of a continuous determination of the position in time of all phenomena, and this by means of the series of causes and effects, the former of which necessitate the sequence of the latter, and thereby render universally and for all time, and by consequence, objectively, valid the empirical cognition of the relations of time. ​

##### C. THIRD ANALOGY. Principle of Coexistence, According to the Law of Reciprocity or Community. All substances, in so far as they can be perceived in space at the same time, exist in a state of complete reciprocity of action.C. THIRD ANALOGY. Principle of Coexistence, According to the Law of Reciprocity or Community. All substances, in so far as they can be perceived in space at the same time, exist in a state of complete reciprocity of action.

PROOF.
Things are coexistent, when in empirical intuition the perception of the one can follow upon the perception of the other, and vice versa- which cannot occur in the succession of phenomena, as we have shown in the explanation of the second principle. Thus I can perceive the moon and then the earth, or conversely, first the earth and then the moon; and for the reason that my perceptions of these objects can reciprocally follow each other, I say, they exist contemporaneously. Now coexistence is the existence of the manifold in the same time. But time itself is not an object of perception; and therefore we cannot conclude from the fact that things are placed in the same time, the other fact, that the perception of these things can follow each other reciprocally. The synthesis of the imagination in apprehension would only present to us each of these perceptions as present in the subject when the other is not present, and contrariwise; but would not show that the objects are coexistent, that is to say, that, if the one exists, the other also exists in the same time, and that this is necessarily so, in order that the perceptions may be capable of following each other reciprocally. It follows that a conception of the understanding or category of the reciprocal sequence of the determinations of phenomena (existing, as they do, apart from each other, and yet contemporaneously), is requisite to justify us in saying that the reciprocal succession of perceptions has its foundation in the object, and to enable us to represent coexistence as objective. But that relation of substances in which the one contains determinations the ground of which is in the other substance, is the relation of influence. And, when this influence is reciprocal, it is the relation of community or reciprocity. Consequently the coexistence of substances in space cannot be cognized in experience otherwise ​than under the precondition of their reciprocal action. This is therefore the condition of the possibility of things themselves as objects of experience.
Things are coexistent, in so far as they exist in one and the same time. But how can we know that they exist in one and the same time? Only by observing that the order in the synthesis of apprehension of the manifold is arbitrary and a matter of indifference, that is to say, that it can proceed from A, through B, C, D, to E, or contrariwise from E to A. For if they were successive in time (and in the order, let us suppose, which begins with A), it is quite impossible for the apprehension in perception to begin with E and go backwards to A, inasmuch as A belongs to past time and, therefore, cannot be an object of apprehension.
Let us assume that in a number of substances considered as phenomena each is completely isolated, that is, that no one acts upon another. Then I say that the coexistence of these cannot be an object of possible perception and that the existence of one cannot, by any mode of empirical synthesis, lead us to the existence of another. For we imagine them in this case to be separated by a completely void space, and thus perception, which proceeds from the one to the other in time, would indeed determine their existence by means of a following perception, but would be quite unable to distinguish whether the one phenomenon follows objectively upon the first, or is coexistent with it.
Besides the mere fact of existence, then, there must be something by means of which A determines the position of B in time and, conversely, B the position of A; because only under this condition can substances be empirically represented as existing contemporaneously. Now that alone determines the position of another thing in time which is the cause of it or of its determinations. Consequently every substance (inasmuch as it can have succession predicated of it only in respect of its determinations) must contain the causality of certain determinations in another substance, and at the same time the effects of the causality of the other in itself. That is to say, substances must stand (mediately or immediately) in dynamical community with each other, if coexistence is to be cognized in any possible experience. But, in regard to objects of experience, that is absolutely necessary witho ​ut which the experience of these objects would itself be impossible. Consequently it is absolutely necessary that all substances in the world of phenomena, in so far as they are coexistent, stand in a relation of complete community of reciprocal action to each other.
The word community has in our languagetwo meanings, and contains the two notions conveyed in the Latin communio and commercium. We employ it in this place in the latter sense—that of a dynamical community, without which even the community of place (communio spatii) could not be empirically cognized. In our experiences it is easy to observe that it is only the continuous influences in all parts of space that can conduct our senses from one object to another; that the light which plays between our eyes and the heavenly bodies produces a mediating community between them and us, and thereby evidences their coexistence with us; that we cannot empirically change our position (perceive this change), unless the existence of matter throughout the whole of space rendered possible the perception of the positions we occupy; and that this perception can prove the contemporaneous existence of these places only through their reciprocal influence, and thereby also the coexistence of even the most remote objects—although in this case the proof is only mediate. Without community, every perception (of a phenomenon in space) is separated from every other and isolated, and the chain of empirical representations, that is, of experience, must, with the appearance of a new object, begin entirely de novo, without the least connection with preceding representations, and without standing towards these even in the relation of time. My intention here is by no means to combat the notion of empty space; for it may exist where our perceptions cannot exist, inasmuch as they cannot reach thereto, and where, therefore, no empirical perception of coexistence takes place. But in this case it is not an object of possible experience.
The following remarks may be useful in the way of explanation. In the mind, all phenomena, as contents of a possible experience, must exist in community (communio) of apperception or consciousness, and in so far as it is requisite that objects be represented as coexistent and connected, in so far must they reciprocally determine the position in time of each other ​and thereby constitute a whole. If this subjective community is to rest upon an objective basis, or to be applied to substances as phenomena, the perception of one substance must render possible the perception of another, and conversely. For otherwise succession, which is always found in perceptions as apprehensions, would be predicated of external objects, and their representation of their coexistence be thus impossible. But this is a reciprocal influence, that is to say, a real community (commercium) of substances, without which therefore the empirical relation of coexistence would be a notion beyond the reach of our minds. By virtue of this commercium, phenomena, in so far as they are apart from, and nevertheless in connection with each other, constitute a compositum reale. Such composita are possible in many different ways. The three dynamical relations then, from which all others spring, are those of inherence, consequence, and composition.
These, then, are the three analogies of experience. They are nothing more than principles of the determination of the existence of phenomena in time, according to the three modi of this determination; to wit, the relation to time itself as a quantity (the quantity of existence, that is, duration), the relation in time as a series or succession, finally, the relation in time as the complex of all existence (simultaneity). This unity of determination in regard to time is thoroughly dynamical; that is to say, time is not considered as that in which experience determines immediately to every existence its position; for this is impossible, inasmuch as absolute time is not an object of perception, by means of which phenomena can be connected with each other. On the contrary, the rule of the understanding, through which alone the existence of phenomena can receive synthetical unity as regards relations of time, determines for every phenomenon its position in time, and consequently a priori, and with validity for all and every time.
By nature, in the empirical sense of the word, we understand the totality of phenomena connected, in respect of their existence, according to necessary rules, that is, laws. There are therefore certain laws (which are moreover a priori) which make nature ​possible; and all empirical laws can exist only by means of experience, and by virtue of those primitive laws through which experience itself becomes possible. The purpose of the analogies is therefore to represent to us the unity of nature in the connection of all phenomena under certain exponents, the only business of which is to express the relation of time (in so far as it contains all existence in itself) to the unity of apperception, which can exist in synthesis only according to rules. The combined expression of all is this: "All phenomena exist in one nature, and must so exist, inasmuch as without this a priori unity, no unity of experience, and consequently no determination of objects in experience, is possible."
As regards the mode of proof which we have employed in treating of these transcendental laws of nature, and the peculiar character of it, we must make one remark, which will at the same time be important as a guide in every other attempt to demonstrate the truth of intellectual and likewise synthetical propositions a priori. Had we endeavoured to prove these analogies dogmatically, that is, from conceptions; that is to say, had we employed this method in attempting to show that everything which exists, exists only in that which is permanent—that every thing or event presupposes the existence of something in a preceding state, upon which it follows in conformity with a rule—lastly, that in the manifold, which is coexistent, the states coexist in connection with each other according to a rule- all our labour would have been utterly in vain. For more conceptions of things, analyse them as we may, cannot enable us to conclude from the existence of one object to the existence of another. What other course was left for us to pursue? This only, to demonstrate the possibility of experience as a cognition in which at last all objects must be capable of being presented to us, if the representation of them is to possess any objective reality. Now in this third, this mediating term, the essential form of which consists in the synthetical unity of the apperception of all phenomena, we found a priori conditions of the universal and necessary determination as to time of all existences in the world of phenomena, without which the empirical determination thereof as to time would itself be impossible, and we also discovered rules of synthetical unity a priori, by means of which we could anticipate ​experience. For want of this method, and from the fancy that it was possible to discover a dogmatical proof of the synthetical propositions which are requisite in the empirical employment of the understanding, has it happened that a proof of the principle of sufficient reason has been so often attempted, and always in vain. The other two analogies nobody has ever thought of, although they have always been silently employed by the mind, because the guiding thread furnished by the categories was wanting, the guide which alone can enable us to discover every hiatus, both in the system of conceptions and of principles.

##### 4. THE POSTULATES OF EMPIRICAL THOUGHT.4. THE POSTULATES OF EMPIRICAL THOUGHT.

* That which agrees with the formal conditions (intuition and conception) of experience, is possible.
* That which coheres with the material conditions of experience (sensation), is real.
* That whose coherence with the real is determined according to universal conditions of experience is (exists) necessary.
Explanation.
The categories of modality possess this peculiarity, that they do not in the least determine the object, or enlarge the conception to which they are annexed as predicates, but only express its relation to the faculty of cognition. Though my conception of a thing is in itself complete, I am still entitled to ask whether the object of it is merely possible, or whether it is also real, or, if the latter, whether it is also necessary. But hereby the object itself is not more definitely determined ​in thought, but the question is only in what relation it, including all its determinations, stands to the understanding and its employment in experience, to the empirical faculty of judgement, and to the reason of its application to experience.
For this very reason, too, the categories of modality are nothing more than explanations of the conceptions of possibility, reality, and necessity, as employed in experience, and at the same time, restrictions of all the categories to empirical use alone, not authorizing the transcendental employment of them. For if they are to have something more than a merely logical significance, and to be something more than a mere analytical expression of the form of thought, and to have a relation to things and their possibility, reality, or necessity, they must concern possible experience and its synthetical unity, in which alone objects of cognition can be given.
The postulate of the possibility of things requires also, that the conception of the things agree with the formal conditions of our experience in general. But this, that is to say, the objective form of experience, contains all the kinds of synthesis which are requisite for the cognition of objects. A conception which contains a synthesis must be regarded as empty and, without reference to an object, if its synthesis does not belong to experience—either as borrowed from it, and in this case it is called an empirical conception, or such as is the ground and a priori condition of experience (its form), and in this case it is a pure conception, a conception which nevertheless belongs to experience, inasmuch as its object can be found in this alone. For where shall we find the criterion or character of the possibility of an object which is cogitated by means of an a priori synthetical conception, if not in the synthesis which constitutes the form of empirical cognition of objects? That in such a conception no contradiction exists is indeed a necessary logical condition, but very far from being sufficient to establish the objective reality of the conception, that is, the possibility of such an object as is thought in the conception. Thus, in the conception of a figure which is contained within two straight lines, there is no contradiction, for the conceptions of two straight lines and of their junction contain no negation of a figure. The impossibility in such a case does not rest upon the conception in itself, but upon the ​construction of it in space, that is to say, upon the conditions of space and its determinations. But these have themselves objective reality, that is, they apply to possible things, because they contain a priori the form of experience in general.
And now we shall proceed to point out the extensive utility and influence of this postulate of possibility. When I represent to myself a thing that is permanent, so that everything in it which changes belongs merely to its state or condition, from such a conception alone I never can cognize that such a thing is possible. Or, if I represent to myself something which is so constituted that, when it is posited, something else follows always and infallibly, my thought contains no self-contradiction; but whether such a property as causality is to be found in any possible thing, my thought alone affords no means of judging. Finally, I can represent to myself different things (substances) which are so constituted that the state or condition of one causes a change in the state of the other, and reciprocally; but whether such a relation is a property of things cannot be perceived from these conceptions, which contain a merely arbitrary synthesis. Only from the fact, therefore, that these conceptions express a priori the relations of perceptions in every experience, do we know that they possess objective reality, that is, transcendental truth; and that independent of experience, though not independent of all relation to form of an experience in general and its synthetical unity, in which alone objects can be empirically cognized.
But when we fashion to ourselves new conceptions of substances, forces, action, and reaction, from the material presented to us by perception, without following the example of experience in their connection, we create mere chimeras, of the possibility of which we cannot discover any criterion, because we have not taken experience for our instructress, though we have borrowed the conceptions from her. Such fictitious conceptions derive their character of possibility not, like the categories, a priori, as conceptions on which all experience depends, but only, a posteriori, as conceptions given by means of experience itself, and their possibility must either be cognized a posteriori and empirically, or it cannot be cognized at all. A substance which is permanently present in space, yet without filling it (like that tertium quid between matter and the thinking subject which some have tried to intr ​oduce into metaphysics), or a peculiar fundamental power of the mind of intuiting the future by anticipation (instead of merely inferring from past and present events), or, finally, a power of the mind to place itself in community of thought with other men, however distant they may be—these are conceptions the possibility of which has no ground to rest upon. For they are not based upon experience and its known laws; and, without experience, they are a merely arbitrary conjunction of thoughts, which, though containing no internal contradiction, has no claim to objective reality, neither, consequently, to the possibility of such an object as is thought in these conceptions. As far as concerns reality, it is self-evident that we cannot cogitate such a possibility in concreto without the aid of experience; because reality is concerned only with sensation, as the matter of experience, and not with the form of thought, with which we can no doubt indulge in shaping fancies.
But I pass by everything which derives its possibility from reality in experience, and I purpose treating here merely of the possibility of things by means of a priori conceptions. I maintain, then, that the possibility of things is not derived from such conceptions per se, but only when considered as formal and objective conditions of an experience in general.
It seems, indeed, as if the possibility of a triangle could be cognized from the conception of it alone (which is certainly independent of experience); for we can certainly give to the conception a corresponding object completely a priori, that is to say, we can construct it. But as a triangle is only the form of an object, it must remain a mere product of the imagination, and the possibility of the existence of an object corresponding to it must remain doubtful, unless we can discover some other ground, unless we know that the figure can be cogitated under the conditions upon which all objects of experience rest. Now, the facts that space is a formal condition a priori of external experience, that the formative synthesis, by which we construct a triangle in imagination, is the very same as that we employ in the apprehension of a phenomenon for the purpose of making an empirical conception of it, are what alone connect the notion of the possibility of such a thing, with the conception of it. In the same manner, the possibility of continuous quantities, indeed of quantities in general, for the conceptions ​of them are without exception synthetical, is never evident from the conceptions in themselves, but only when they are considered as the formal conditions of the determination of objects in experience. And where, indeed, should we look for objects to correspond to our conceptions, if not in experience, by which alone objects are presented to us? It is, however, true that without antecedent experience we can cognize and characterize the possibility of things, relatively to the formal conditions, under which something is determined in experience as an object, consequently, completely a priori. But still this is possible only in relation to experience and within its limits.
The postulate concerning the cognition of the reality of things requires perception, consequently conscious sensation, not indeed immediately, that is, of the object itself, whose existence is to be cognized, but still that the object have some connection with a real perception, in accordance with the analogies of experience, which exhibit all kinds of real connection in experience.
From the mere conception of a thing it is impossible to conclude its existence. For, let the conception be ever so complete, and containing a statement of all the determinations of the thing, the existence of it has nothing to do with all this, but only with thew question whether such a thing is given, so that the perception of it can in every case precede the conception. For the fact that the conception of it precedes the perception, merely indicates the possibility of its existence; it is perception which presents matter to the conception, that is the sole criterion of reality. Prior to the perception of the thing, however, and therefore comparatively a priori, we are able to cognize its existence, provided it stands in connection with some perceptions according to the principles of the empirical conjunction of these, that is, in conformity with the analogies of perception. For, in this case, the existence of the supposed thing is connected with our perception in a possible experience, and we are able, with the guidance of these analogies, to reason in the series of possible perceptions from a thing which we do really perceive to the thing we do not perceive. Thus, we cognize the existence of a magnetic matter penetrating all bodies from the perception of the attraction of the steel-filings by the magnet, although the constitution of our ​organs renders an immediate perception of this matter impossible for us. For, according to the laws of sensibility and the connected context of our perceptions, we should in an experience come also on an immediate empirical intuition of this matter, if our senses were more acute—but this obtuseness has no influence upon and cannot alter the form of possible experience in general. Our knowledge of the existence of things reaches as far as our perceptions, and what may be inferred from them according to empirical laws, extend. If we do not set out from experience, or do not proceed according to the laws of the empirical connection of phenomena, our pretensions to discover the existence of a thing which we do not immediately perceive are vain. Idealism, however, brings forward powerful objections to these rules for proving existence mediately. This is, therefore, the proper place for its refutation.

##### REFUTATION OF IDEALISM.REFUTATION OF IDEALISM.

Idealism—I mean material idealism—is the theory which declares the existence of objects in space without us to be either (1) doubtful and indemonstrable, or (2) false and impossible. The first is the problematical idealism of Descartes, who admits the undoubted certainty of only one empirical assertion (assertio), to wit, "I am." The second is the dogmatical idealism of Berkeley, who maintains that space, together with all the objects of which it is the inseparable condition, is a thing which is in itself impossible, and that consequently the objects in space are mere products of the imagination. The dogmatical theory of idealism is unavoidable, if we regard space as a property of things in themselves; for in that case it is, with all to which it serves as condition, a nonentity. But the foundation for this kind of idealism we have already destroyed in the transcendental aesthetic. Problematical idealism, which makes no such assertion, but only alleges our incapacity to prove the existence of anything besides ourselves by means of immediate experience, is a theory rational and evidencing a thorough and philosophical mode of thinking, for it observes the rule not to form a decisive judgement befor ​e sufficient proof be shown. The desired proof must therefore demonstrate that we have experience of external things, and not mere fancies. For this purpose, we must prove, that our internal and, to Descartes, indubitable experience is itself possible only under the previous assumption of external experience.

##### THEOREM. The simple but empirically determined consciousness of my own existence proves the existence of external objects in space.THEOREM. The simple but empirically determined consciousness of my own existence proves the existence of external objects in space.

PROOF
I am conscious of my own existence as determined in time. All determination in regard to time presupposes the existence of something permanent in perception. But this permanent something cannot be something in me, for the very reason that my existence in time is itself determined by this permanent something. It follows that the perception of this permanent existence is possible only through a thing without me and not through the mere representation of a thing without me. Consequently, the determination of my existence in time is possible only through the existence of real things external to me. Now, consciousness in time is necessarily connected with the consciousness of the possibility of this determination in time. Hence it follows that consciousness in time is necessarily connected also with the existence of things without me, inasmuch as the existence of these things is the condition of determination in time. That is to say, the consciousness of my own existence is at the same time an immediate consciousness of the existence of other things without me.
Remark I. The reader will observe, that in the foregoing proof the game which idealism plays is retorted upon itself, and with more justice. It assumed that the only immediate experience is internal and that from this we can only infer the existence of external things. But, as always happens, when we reason from given effects to determined causes, idealism bas reasoned with too much haste and uncertainty, for it is quite possible that the cause of our representations may lie in ourselves, and that we ascribe it falsely to external things. But our proof shows that external experience is ​properly immediate, that only by virtue of it—not, indeed, the consciousness of our own existence, but certainly the determination of our existence in time, that is, internal experience—is possible. It is true, that the representation "I am," which is the expression of the consciousness which can accompany all my thoughts, is that which immediately includes the existence of a subject. But in this representation we cannot find any knowledge of the subject, and therefore also no empirical knowledge, that is, experience. For experience contains, in addition to the thought of something existing, intuition, and in this case it must be internal intuition, that is, time, in relation to which the subject must be determined. But the existence of external things is absolutely requisite for this purpose, so that it follows that internal experience is itself possible only mediately and through external experience.
Remark II. Now with this view all empirical use of our faculty of cognition in the determination of time is in perfect accordance. Its truth is supported by the fact that it is possible to perceive a determination of time only by means of a change in external relations (motion) to the permanent in space (for example, we become aware of the sun's motion by observing the changes of his relation to the objects of this earth). But this is not all. We find that we possess nothing permanent that can correspond and be submitted to the conception of a substance as intuition, except matter. This idea of permanence is not itself derived from external experience, but is an a priori necessary condition of all determination of time, consequently also of the internal sense in reference to our own existence, and that through the existence of external things. In the representation "I," the consciousness of myself is not an intuition, but a merely intellectual ​representation produced by the spontaneous activity of a thinking subject. It follows, that this "I" has not any predicate of intuition, which, in its character of permanence, could serve as correlate to the determination of time in the internal sense—in the same way as impenetrability is the correlate of matter as an empirical intuition.
Remark III. From the fact that the existence of external things is a necessary condition of the possibility of a determined consciousness of ourselves, it does not follow that every intuitive representation of external things involves the existence of these things, for their representations may very well be the mere products of the imagination (in dreams as well as in madness); though, indeed, these are themselves created by the reproduction of previous external perceptions, which, as has been shown, are possible only through the reality of external objects. The sole aim of our remarks has, however, been to prove that internal experience in general is possible only through external experience in general. Whether this or that supposed experience be purely imaginary must be discovered from its particular determinations and by comparing these with the criteria of all real experience.
Finally, as regards the third postulate, it applies to material necessity in existence, and not to merely formal and logical necessity in the connection of conceptions. Now as we cannot cognize completely a priori the existence of any object of sense, though we can do so comparatively a priori, that is, relatively to some other previously given existence—a cognition, however, which can only be of such an existence as must be contained in the complex of experience, of which the previously given perception is a part—the necessity of existence can never be cognized from conceptions, but always, on the contrary, from its connection with that which is an object of perception. But the only existence cognized, under the condition of other given phenomena, as necessary, is the existence of effects from given causes in conformity with the laws of causality. It is consequently not the necessity of the existence of things (as substances), but the necessity of the state of things that we cognize, and that not immediately, but by means of the existence of other states given in perception, according to ​empirical laws of causality. Hence it follows that the criterion of necessity is to be found only in the law of possible experience—that everything which happens is determined a priori in the phenomenon by its cause. Thus we cognize only the necessity of effects in nature, the causes of which are given us. Moreover, the criterion of necessity in existence possesses no application beyond the field of possible experience, and even in this it is not valid of the existence of things as substances, because these can never be considered as empirical effects, or as something that happens and has a beginning. Necessity, therefore, regards only the relations of phenomena according to the dynamical law of causality, and the possibility grounded thereon, of reasoning from some given existence (of a cause) a priori to another existence (of an effect). "Everything that happens is hypothetically necessary," is a principle which subjects the changes that take place in the world to a law, that is, to a rule of necessary existence, without which nature herself could not possibly exist. Hence the proposition, "Nothing happens by blind chance (in mundo non datur casus)," is an a priori law of nature. The case is the same with the proposition, "Necessity in nature is not blind," that is, it is conditioned, consequently intelligible necessity (non datur fatum). Both laws subject the play of change to "a nature of things (as phenomena)," or, which is the same thing, to the unity of the understanding, and through the understanding alone can changes belong to an experience, as the synthetical unity of phenomena. Both belong to the class of dynamical principles. The former is properly a consequence of the principle of causality—one of the analogies of experience. The latter belongs to the principles of modality, which to the determination of causality adds the conception of necessity, which is itself, however, subject to a rule of the understanding. The principle of continuity forbids any leap in the series of phenomena regarded as changes (in mundo non datur saltus); and likewise, in the complex of all empirical intuitions in space, any break or hiatus between two phenomena (non datur hiatus)- for we can so express the principle, that experience can admit nothing which proves the existence of a vacuum, or which even admits it as a part of an empirical synthesis. For, as regards a vacuum or void, which we may cogitate as out and beyond the field of possible experience (the ​world), such a question cannot come before the tribunal of mere understanding, which decides only upon questions that concern the employment of given phenomena for the construction of empirical cognition. It is rather a problem for ideal reason, which passes beyond the sphere of a possible experience and aims at forming a judgement of that which surrounds and circumscribes it, and the proper place for the consideration of it is the transcendental dialectic. These four propositions, "In mundo non datur hiatus, non datur saltus, non datur casus, non datur fatum," as well as all principles of transcendental origin, we could very easily exhibit in their proper order, that is, in conformity with the order of the categories, and assign to each its proper place. But the already practised reader will do this for himself, or discover the clue to such an arrangement. But the combined result of all is simply this, to admit into the empirical synthesis nothing which might cause a break in or be foreign to the understanding and the continuous connection of all phenomena, that is, the unity of the conceptions of the understanding. For in the understanding alone is the unity of experience, in which all perceptions must have their assigned place, possible.
Whether the field of possibility be greater than that of reality, and whether the field of the latter be itself greater than that of necessity, are interesting enough questions, and quite capable of synthetic solution, questions, however, which come under the jurisdiction of reason alone. For they are tantamount to asking whether all things as phenomena do without exception belong to the complex and connected whole of a single experience, of which every given perception is a part which therefore cannot be conjoined with any other phenomena—or, whether my perceptions can belong to more than one possible experience? The understanding gives to experience, according to the subjective and formal conditions, of sensibility as well as of apperception, the rules which alone make this experience possible. Other forms of intuition besides those of space and time, other forms of understanding besides the discursive forms of thought, or of cognition by means of conceptions, we can neither imagine nor make intelligible to ourselves; and even if we could, they would still not belong to experience, which is the only mode of cognition by which objects are presented to u ​s. Whether other perceptions besides those which belong to the total of our possible experience, and consequently whether some other sphere of matter exists, the understanding has no power to decide, its proper occupation being with the synthesis of that which is given. Moreover, the poverty of the usual arguments which go to prove the existence of a vast sphere of possibility, of which all that is real (every object of experience) is but a small part, is very remarkable. "All real is possible"; from this follows naturally, according to the logical laws of conversion, the particular proposition: "Some possible is real." Now this seems to be equivalent to: "Much is possible that is not real." No doubt it does seem as if we ought to consider the sum of the possible to be greater than that of the real, from the fact that something must be added to the former to constitute the latter. But this notion of adding to the possible is absurd. For that which is not in the sum of the possible, and consequently requires to be added to it, is manifestly impossible. In addition to accordance with the formal conditions of experience, the understanding requires a connection with some perception; but that which is connected with this perception is real, even although it is not immediately perceived. But that another series of phenomena, in complete coherence with that which is given in perception, consequently more than one all-embracing experience is possible, is an inference which cannot be concluded from the data given us by experience, and still less without any data at all. That which is possible only under conditions which are themselves merely possible, is not possible in any respect. And yet we can find no more certain ground on which to base the discussion of the question whether the sphere of possibility is wider than that of experience.
I have merely mentioned these questions, that in treating of the conception of the understanding, there might be no omission of anything that, in the common opinion, belongs to them. In reality, however, the notion of absolute possibility (possibility which is valid in every respect) is not a mere conception of the understanding, which can be employed empirically, but belongs to reason alone, which passes the bounds of all empirical use of the understanding. We have, therefore, contented ourselves with a merely critical remark, leaving the subject to be explained in the sequel. ​
Before concluding this fourth section, and at the same time the system of all principles of the pure understanding, it seems proper to mention the reasons which induced me to term the principles of modality postulates. This expression I do not here use in the sense which some more recent philosophers, contrary to its meaning with mathematicians, to whom the word properly belongs, attach to it- that of a proposition, namely, immediately certain, requiring neither deduction nor proof. For if, in the case of synthetical propositions, however evident they may be, we accord to them without deduction, and merely on the strength of their own pretensions, unqualified belief, all critique of the understanding is entirely lost; and, as there is no want of bold pretensions, which the common belief (though for the philosopher this is no credential) does not reject, the understanding lies exposed to every delusion and conceit, without the power of refusing its assent to those assertions, which, though illegitimate, demand acceptance as veritable axioms. When, therefore, to the conception of a thing an a priori determination is synthetically added, such a proposition must obtain, if not a proof, at least a deduction of the legitimacy of its assertion.
The principles of modality are, however, not objectively synthetical, for the predicates of possibility, reality, and necessity do not in the least augment the conception of that of which they are affirmed, inasmuch as they contribute nothing to the representation of the object. But as they are, nevertheless, always synthetical, they are so merely subjectively. That is to say, they have a reflective power, and apply to the conception of a thing, of which, in other respects, they affirm nothing, the faculty of cognition in which the conception originates and has its seat. So that if the conception merely agree with the formal conditions of experience, its object is called possible; if it is in connection with perception, and determined thereby, the object is real; if it is determined according to conceptions by means of the connection of perceptions, the object is called necessary. The principles of modality therefore predicate of a conception nothing more than the procedure of the faculty of cognition which generated it. Now a postulate in mathematics is a practical proposition which contains nothing but the synthesis by which we present an object to ourselves, and produce the conception of it, for example—"With a given line, to describe a circle upon a plane, from ​a given point"; and such a proposition does not admit of proof, because the procedure, which it requires, is exactly that by which alone it is possible to generate the conception of such a figure. With the same right, accordingly, can we postulate the principles of modality, because they do not augment the conception of a thing but merely indicate the manner in which it is connected with the faculty of cognition.

##### GENERAL REMARK ON THE SYSTEM OF PRINCIPLES.GENERAL REMARK ON THE SYSTEM OF PRINCIPLES.

It is very remarkable that we cannot perceive the possibility of a thing from the category alone, but must always have an intuition, by which to make evident the objective reality of the pure conception of the understanding. Take, for example, the categories of relation. How (1) a thing can exist only as a subject, and not as a mere determination of other things, that is, can be substance; or how (2), because something exists, some other thing must exist, consequently how a thing can be a cause; or how (3), when several things exist, from the fact that one of these things exists, some consequence to the others follows, and reciprocally, and in this way a community of substances can be possible—are questions whose solution cannot be obtained from mere conceptions. The very same is the case with the other categories; for example, how a thing can be of the same sort with many others, that is, can be a quantity, and so on. So long as we have not intuition we cannot know whether we do really think an object by the categories, and where an object can anywhere be found to cohere with them, and thus the truth is established, that the categories are not in themselves cognitions, but mere forms of thought for the construction of cognitions from given intuitions. For the same reason is it true that from categories alone no synthetical proposition can be made. For example: "In every existence there is substance," that is, something that can exist only as a subject and not as mere predicate; or, "Everything is a quantity"—to construct propositions such as these, we require something ​to enable us to go out beyond the given conception and connect another with it. For the same reason the attempt to prove a synthetical proposition by means of mere conceptions, for example: "Everything that exists contingently has a cause," has never succeeded. We could never get further than proving that, without this relation to conceptions, we could not conceive the existence of the contingent, that is, could not a priori through the understanding cognize the existence of such a thing; but it does not hence follow that this is also the condition of the possibility of the thing itself that is said to be contingent. If, accordingly; we look back to our proof of the principle of causality, we shall find that we were able to prove it as valid only of objects of possible experience, and, indeed, only as itself the principle of the possibility of experience, Consequently of the cognition of an object given in empirical intuition, and not from mere conceptions. That, however, the proposition: "Everything that is contingent must have a cause," is evident to every one merely from conceptions, is not to be denied. But in this case the conception of the contingent is cogitated as involving not the category of modality (as that the non-existence of which can be conceive but that of relation (as that which can exist only as the consequence of something else), and so it is really an identical proposition: "That which can exist only as a consequence, has a cause." In fact, when we have to give examples of contingent existence, we always refer to changes, and not merely to the possibility of conceiving the opposite. But change is an event, which, as such, is possible only through a cause, and considered per se its non-existence is therefore possible, and we become cognizant of its contingency from the fact ​that it can exist only as the effect of a cause. Hence, if a thing is assumed to be contingent, it is an analytical proposition to say, it has a cause.
But it is still more remarkable that, to understand the possibility of things according to the categories and thus to demonstrate the objective reality of the latter, we require not merely intuitions, but external intuitions. If, for example, we take the pure conceptions of relation, we find that (1) for the purpose of presenting to the conception of substance something permanent in intuition corresponding thereto and thus of demonstrating the objective reality of this conception, we require an intuition (of matter) in space, because space alone is permanent and determines things as such, while time, and with it all that is in the internal sense, is in a state of continual flow; (2) in order to represent change as the intuition corresponding to the conception of causality, we require the representation of motion as change in space; in fact, it is through it alone that changes, the possibility of which no pure understanding can perceive, are capable of being intuited. Change is the connection of determinations contradictorily opposed to each other in the existence of one and the same thing. Now, how it is possible that out of a given state one quite opposite to it in the same thing should follow, reason without an example can not only not conceive, but cannot even make intelligible without intuition; and this intuition is the motion of a point in space; the existence of which in different spaces (as a consequence of opposite determinations) alone makes the intuition of change possible. For, in order to make even internal change cognitable, we require to represent time, as the form of the internal sense, figuratively by a line, and the internal change by the drawing of that line (motion), and consequently are obliged to employ external intuition to be able to represent the successive existence of ourselves in different states. The proper ground of this fact is that all change to be perceived as change presupposes something permanent in intuition, while in the internal sense no permanent intuition is to be found. Lastly, the objective possibility of the category of community cannot be conceived by mere reason, and consequently its objective reality cannot be demonstrated without an intuition, and that external in space. For how can we conceive the possibility of community, ​that is, when several substances exist, that some effect on the existence of the one follows from the existence of the other, and reciprocally, and therefore that, because something exists in the latter, something else must exist in the former, which could not be understood from its own existence alone? For this is the very essence of community—which is inconceivable as a property of things which are perfectly isolated. Hence, Leibnitz, in attributing to the substances of the world—as cogitated by the understanding alone—a community, required the mediating aid of a divinity; for, from their existence, such a property seemed to him with justice inconceivable. But we can very easily conceive the possibility of community (of substances as phenomena) if we represent them to ourselves as in space, consequently in external intuition. For external intuition contains in itself a priori formal external relations, as the conditions of the possibility of the real relations of action and reaction, and therefore of the possibility of community. With the same ease can it be demonstrated, that the possibility of things as quantities, and consequently the objective reality of the category of quantity, can be grounded only in external intuition, and that by its means alone is the notion of quantity appropriated by the internal sense. But I must avoid prolixity, and leave the task of illustrating this by examples to the reader's own reflection.
The above remarks are of the greatest importance, not only for the confirmation of our previous confutation of idealism, but still more when the subject of self-cognition by mere internal consciousness and the determination of our own nature without the aid of external empirical intuitions is under discussion, for the indication of the grounds of the possibility of such a cognition.
The result of the whole of this part of the analytic of principles is, therefore: "All principles of the pure understanding are nothing more than a priori principles of the possibility of experience, and to experience alone do all a priori synthetical propositions apply and relate"; indeed, their possibility itself rests entirely on this relation. ​

#### CHAPTER III. Of the Ground of the Division of all Objects into Phenomena and Noumena.CHAPTER III. Of the Ground of the Division of all Objects into Phenomena and Noumena.

We have now not only traversed the region of the pure understanding and carefully surveyed every part of it, but we have also measured it, and assigned to everything therein its proper place. But this land is an island, and enclosed by nature herself within unchangeable limits. It is the land of truth (an attractive word), surrounded by a wide and stormy ocean, the region of illusion, where many a fog-bank, many an iceberg, seems to the mariner, on his voyage of discovery, a new country, and, while constantly deluding him with vain hopes, engages him in dangerous adventures, from which he never can desist, and which yet he never can bring to a termination. But before venturing upon this sea, in order to explore it in its whole extent, and to arrive at a certainty whether anything is to be discovered there, it will not be without advantage if we cast our eyes upon the chart of the land that we are about to leave, and to ask ourselves, firstly, whether we cannot rest perfectly contented with what it contains, or whether we must not of necessity be contented with it, if we can find nowhere else a solid foundation to build upon; and, secondly, by what title we possess this land itself, and how we hold it secure against all hostile claims? Although, in the course of our analytic, we have already given sufficient answers to these questions, yet a summary recapitulation of these solutions may be useful in strengthening our conviction, by uniting in one point the momenta of the arguments.
We have seen that everything which the understanding draws from itself, without borrowing from experience, it nevertheless possesses only for the behoof and use of experience. The principles of the pure understanding, whether constitutive a priori (as the mathematical principles), or merely regulative (as the dynamical), contain nothing but the pure schema, as it were, of possible experience. For experience possesses ​its unity from the synthetical unity which the understanding, originally and from itself, imparts to the synthesis of the imagination in relation to apperception, and in a priori relation to and agreement with which phenomena, as data for a possible cognition, must stand. But although these rules of the understanding are not only a priori true, but the very source of all truth, that is, of the accordance of our cognition with objects, and on this ground, that they contain the basis of the possibility of experience, as the ensemble of all cognition, it seems to us not enough to propound what is true—we desire also to be told what we want to know. If, then, we learn nothing more by this critical examination than what we should have practised in the merely empirical use of the understanding, without any such subtle inquiry, the presumption is that the advantage we reap from it is not worth the labour bestowed upon it. It may certainly be answered that no rash curiosity is more prejudicial to the enlargement of our knowledge than that which must know beforehand the utility of this or that piece of information which we seek, before we have entered on the needful investigations, and before one could form the least conception of its utility, even though it were placed before our eyes. But there is one advantage in such transcendental inquiries which can be made comprehensible to the dullest and most reluctant learner—this, namely, that the understanding which is occupied merely with empirical exercise, and does not reflect on the sources of its own cognition, may exercise its functions very well and very successfully, but is quite unable to do one thing, and that of very great importance, to determine, namely, the bounds that limit its employment, and to know what lies within or without its own sphere. This purpose can be obtained only by such profound investigations as we have instituted. But if it cannot distinguish whether certain questions lie within its horizon or not, it can never be sure either as to its claims or possessions, but must lay its account with many humiliating corrections, when it transgresses, as it unavoidably will, the limits of its own territory, and loses itself in fanciful opinions and blinding illusions. ​
That the understanding, therefore, cannot make of its a priori principles, or even of its conceptions, other than an empirical use, is a proposition which leads to the most important results. A transcendental use is made of a conception in a fundamental proposition or principle, when it is referred to things in general and considered as things in themselves; an empirical use, when it is referred merely to phenomena, that is, to objects of a possible experience. That the latter use of a conception is the only admissible one is evident from the reasons following. For every conception are requisite, firstly, the logical form of a conception (of thought) general; and, secondly, the possibility of presenting to this an object to which it may apply. Failing this latter, it has no sense, and utterly void of content, although it may contain the logical function for constructing a conception from certain data. Now, object cannot be given to a conception otherwise than by intuition, and, even if a pure intuition antecedent to the object is a priori possible, this pure intuition can itself obtain objective validity only from empirical intuition, of which it is itself but the form. All conceptions, therefore, and with them all principles, however high the degree of their a priori possibility, relate to empirical intuitions, that is, to data towards a possible experience. Without this they possess no objective validity, but are mere play of imagination or of understanding with images or notions. Let us take, for example, the conceptions of mathematics, and first in its pure intuitions. "Space has three dimensions"—"Between two points there can be only one straight line," etc. Although all these principles, and the representation of the object with which this science occupies itself, are generated in the mind entirely a priori, they would nevertheless have no significance if we were not always able to exhibit their significance in and by means of phenomena (empirical objects). Hence it is requisite that an abstract conception be made sensuous, that is, that an object corresponding to it in intuition be forthcoming, otherwise the conception remains, as we say, without sense, that is, without meaning. Mathematics fulfils this requirement by the construction of the figure, which is a phenomenon evident to the senses. The same science finds support and significance in number; this in its turn finds it in the fingers, or in counters, or in lines and points. The conception ​itself is always produced a priori, together with the synthetical principles or formulas from such conceptions; but the proper employment of them, and their application to objects, can exist nowhere but in experience, the possibility of which, as regards its form, they contain a priori.
That this is also the case with all of the categories and the principles based upon them is evident from the fact that we cannot render intelligible the possibility of an object corresponding to them without having recourse to the conditions of sensibility, consequently, to the form of phenomena, to which, as their only proper objects, their use must therefore be confined, inasmuch as, if this condition is removed, all significance, that is, all relation to an object, disappears, and no example can be found to make it comprehensible what sort of things we ought to think under such conceptions.
The conception of quantity cannot be explained except by saying that it is the determination of a thing whereby it can be cogitated how many times one is placed in it. But this "how many times" is based upon successive repetition, consequently upon time and the synthesis of the homogeneous therein. Reality, in contradistinction to negation, can be explained only by cogitating a time which is either filled therewith or is void. If I leave out the notion of permanence (which is existence in all time), there remains in the conception of substance nothing but the logical notion of subject, a notion of which I endeavour to realize by representing to myself something that can exist only as a subject. But not only am I perfectly ignorant of any conditions under which this logical prerogative can belong to a thing, I can make nothing out of the notion, and draw no inference from it, because no object to which to apply the conception is determined, and we consequently do not know whether it has any meaning at all. In like manner, if I leave out the notion of time, in which something follows upon some other thing in conformity with a rule, I can find nothing in the pure category, except that there is a something of such a sort that from it a conclusion may be drawn as to the existence of some ​other thing. But in this case it would not only be impossible to distinguish between a cause and an effect, but, as this power to draw conclusions requires conditions of which I am quite ignorant, the conception is not determined as to the mode in which it ought to apply to an object. The so-called principle: "Everything that is contingent has a cause," comes with a gravity and self-assumed authority that seems to require no support from without. But, I ask, what is meant by contingent? The answer is that the non-existence of which is possible. But I should like very well to know by what means this possibility of non-existence is to be cognized, if we do not represent to ourselves a succession in the series of phenomena, and in this succession an existence which follows a non-existence, or conversely, consequently, change. For to say, that the non-existence of a thing is not self-contradictory is a lame appeal to a logical condition, which is no doubt a necessary condition of the existence of the conception, but is far from being sufficient for the real objective possibility of non-existence. I can annihilate in thought every existing substance without self-contradiction, but I cannot infer from this their objective contingency in existence, that is to say, the possibility of their non-existence in itself. As regards the category of community, it may easily be inferred that, as the pure categories of substance and causality are incapable of a definition and explanation sufficient to determine their object without the aid of intuition, the category of reciprocal causality in the relation of substances to each other (commercium) is just as little susceptible thereof. Possibility, existence, and necessity nobody has ever yet been able to explain without being guilty of manifest tautology, when the definition has been drawn entirely from the pure understanding. For the substitution of the logical possibility of the conception—the condition of which is that it be not self-contradictory, for the transcendental possibility of things—the condition of which is that there be an object corresponding to the conception, is a trick which can only deceive the inexperienced. ​
It follows incontestably, that the pure conceptions of the understanding are incapable of transcendental, and must always be of empirical use alone, and that the principles of the pure understanding relate only to the general conditions of a possible experience, to objects of the senses, and never to things in general, apart from the mode in which we intuite them.
Transcendental analytic has accordingly this important result, to wit, that the understanding is competent' effect nothing a priori, except the anticipation of the form of a possible experience in general, and that, as that which is not phenomenon cannot be an object of experience, it can never overstep the limits of sensibility, within which alone objects are presented to us. Its principles are merely principles of the exposition of phenomena, and the proud name of an ontology, which professes to present synthetical cognitions a priori of things in general in a systematic doctrine, must give place to the modest title of analytic of the pure understanding.
Thought is the act of referring a given intuition to an object. If the mode of this intuition is unknown to us, the object is merely transcendental, and the conception of the understanding is employed only transcendentally, that is, to produce unity in the thought of a manifold in general. Now a pure category, in which all conditions of sensuous intuition—as the only intuition we possess—are abstracted, does not determine an object, but merely expresses the thought of an object in general, according to different modes. Now, to employ a conception, the function of judgement is required, by which an object is subsumed under the conception, consequently the at least formal condition, under which something can be given in intuition. Failing this condition of judgement (schema), subsumption is impossible; for there is in such a case nothing given, which may be subsumed under the conception. The merely transcendental use of the categories is therefore, in fact, no use at all and has no determined, or even, as regards its form, determinable object. Hence it follows that the pure category is incompetent to establish a synthetical a priori principle, and that the principles of the pure understanding are only of empirical and never of transcendental use, and that beyond the sphere of possible experience no synthetical a priori principles are possible.
It may be advisable, therefore, to express ourselves thus. The pure categories, apart from the formal conditions of sensibility, ​have a merely transcendental meaning, but are nevertheless not of transcendental use, because this is in itself impossible, inasmuch as all the conditions of any employment or use of them (in judgements) are absent, to wit, the formal conditions of the subsumption of an object under these conceptions. As, therefore, in the character of pure categories, they must be employed empirically, and cannot be employed transcendentally, they are of no use at all, when separated from sensibility, that is, they cannot be applied to an object. They are merely the pure form of the employment of the understanding in respect of objects in general and of thought, without its being at the same time possible to think or to determine any object by their means.
But there lurks at the foundation of this subject an illusion which it is very difficult to avoid. The categories are not based, as regards their origin, upon sensibility, like the forms of intuition, space, and time; they seem, therefore, to be capable of an application beyond the sphere of sensuous objects. But this is not the case. They are nothing but mere forms of thought, which contain only the logical faculty of uniting a priori in consciousness the manifold given in intuition. Apart, then, from the only intuition possible for us, they have still less meaning than the pure sensuous forms, space and time, for through them an object is at least given, while a mode of connection of the manifold, when the intuition which alone gives the manifold is wanting, has no meaning at all. At the same time, when we designate certain objects as phenomena or sensuous existences, thus distinguishing our mode of intuiting them from their own nature as things in themselves, it is evident that by this very distinction we as it were place the latter, considered in this their own nature, although we do not so intuite them, in opposition to the former, or, on the other hand, we do so place other possible things, which are not objects of our senses, but are cogitated by the understanding alone, and call them intelligible existences (noumena). Now the question arises whether the pure conceptions of our understanding do possess significance in respect of these latter, and may possibly be a mode of cognizing them.
But we are met at the very commencement with an ambiguity, which may easily occasion great misapprehension. ​The understanding, when it terms an object in a certain relation phenomenon, at the same time forms out of this relation a representation or notion of an object in itself, and hence believes that it can form also conceptions of such objects. Now as the understanding possesses no other fundamental conceptions besides the categories, it takes for granted that an object considered as a thing in itself must be capable of being thought by means of these pure conceptions, and is thereby led to hold the perfectly undetermined conception of an intelligible existence, a something out of the sphere of our sensibility, for a determinate conception of an existence which we can cognize in some way or other by means of the understanding.
If, by the term noumenon, we understand a thing so far as it is not an object of our sensuous intuition, thus making abstraction of our mode of intuiting it, this is a noumenon in the negative sense of the word. But if we understand by it an object of a non-sensuous intuition, we in this case assume a peculiar mode of intuition, an intellectual intuition, to wit, which does not, however, belong to us, of the very possibility of which we have no notion—and this is a noumenon in the positive sense.
The doctrine of sensibility is also the doctrine of noumena in the negative sense, that is, of things which the understanding is obliged to cogitate apart from any relation to our mode of intuition, consequently not as mere phenomena, but as things in themselves. But the understanding at the same time comprehends that it cannot employ its categories for the consideration of things in themselves, because these possess significance only in relation to the unity of intuitions in space and time, and that they are competent to determine this unity by means of general a priori connecting conceptions only on account of the pure ideality of space and time. Where this unity of time is not to be met with, as is the case with noumena, the whole use, indeed the whole meaning of the categories is entirely lost, for even the possibility of things to correspond to the categories is in this case incomprehensible. On this point, I need only refer the reader to what I have said at the commencement of the General Remark appended to the foregoing chapter. Now, the possibility of a thing can never be proved from the fact that the conception of it is ​not self-contradictory, but only by means of an intuition corresponding to the conception. If, therefore, we wish to apply the categories to objects which cannot be regarded as phenomena, we must have an intuition different from the sensuous, and in this case the objects would be a noumena in the positive sense of the word. Now, as such an intuition, that is, an intellectual intuition, is no part of our faculty of cognition, it is absolutely impossible for the categories to possess any application beyond the limits of experience. It may be true that there are intelligible existences to which our faculty of sensuous intuition has no relation, and cannot be applied, but our conceptions of the understanding, as mere forms of thought for our sensuous intuition, do not extend to these. What, therefore, we call noumenon must be understood by us as such in a negative sense.
If I take away from an empirial intuition all thought (by means of the categories), there remains no cognition of any object; for by means of mere intuition nothing is cogitated, and, from the existence of such or such an affection of sensibility in me, it does not follow that this affection or representation has any relation to an object without me. But if I take away all intuition, there still remains the form of thought, that is, the mode of determining an object for the manifold of a possible intuition. Thus the categories do in some measure really extend further than sensuous intuition, inasmuch as they think objects in general, without regard to the mode (of sensibility) in which these objects are given. But they do not for this reason apply to and determine a wider sphere of objects, because we cannot assume that such can be given, without presupposing the possibility of another than the sensuous mode of intuition, a supposition we are not justified in making.
I call a conception problematical which contains in itself no contradiction, and which is connected with other cognitions as a limitation of given conceptions, but whose objective reality cannot be cognized in any manner. The conception of a noumenon, that is, of a thing which must be cogitated not as an object of sense, but as a thing in itself (solely through the pure understanding), is not self-contradictory, for we are not entitled to maintain that sensibility is the only possible mode of intuition. Nay, further, this ​conception is necessary to restrain sensuous intuition within the bounds of phenomena, and thus to limit the objective validity of sensuous cognition; for things in themselves, which lie beyond its province, are called noumena for the very purpose of indicating that this cognition does not extend its application to all that the understanding thinks. But, after all, the possibility of such noumena is quite incomprehensible, and beyond the sphere of phenomena, all is for us a mere void; that is to say, we possess an understanding whose province does problematically extend beyond this sphere, but we do not possess an intuition, indeed, not even the conception of a possible intuition, by means of which objects beyond the region of sensibility could be given us, and in reference to which the understanding might be employed assertorically. The conception of a noumenon is therefore merely a limitative conception and therefore only of negative use. But it is not an arbitrary or fictitious notion, but is connected with the limitation of sensibility, without, however, being capable of presenting us with any positive datum beyond this sphere.
The division of objects into phenomena and noumena, and of the world into a mundus sensibilis and intelligibilis is therefore quite inadmissible in a positive sense, although conceptions do certainly admit of such a division; for the class of noumena have no determinate object corresponding to them, and cannot therefore possess objective validity. If we abandon the senses, how can it be made conceivable that the categories (which are the only conceptions that could serve as conceptions for noumena) have any sense or meaning at all, inasmuch as something more than the mere unity of thought, namely, a possible intuition, is requisite for their application to an object? The conception of a noumenon, considered as merely problematical, is, however, not only admissible, but, as a limitative conception of sensibility, absolutely necessary. But, in this case, a noumenon is not a particular intelligible object for our understanding; on the contrary, the kind of understanding to which it could belong is itself a problem, for we cannot form the most distant conception of the possibility of an understanding which should cognize an object, not discursively by means of categories, but intuitively in a non-sensuous intuition. Our understanding attains in this way a sort of negative extension. That is to say, it is not limited by, but rather limits, sensibility, by giving the name of no ​umena to things, not considered as phenomena, but as things in themselves. But it at the same time prescribes limits to itself, for it confesses itself unable to cognize these by means of the categories, and hence is compelled to cogitate them merely as an unknown something.
I find, however, in the writings of modern authors, an entirely different use of the expressions, mundus sensibilis and intelligibilis, which quite departs from the meaning of the ancients—an acceptation in which, indeed, there is to be found no difficulty, but which at the same time depends on mere verbal quibbling. According to this meaning, some have chosen to call the complex of phenomena, in so far as it is intuited, mundus sensibilis, but in so far as the connection thereof is cogitated according to general laws of thought, mundus intelligibilis. Astronomy, in so far as we mean by the word the mere observation of the starry heaven, may represent the former; a system of astronomy, such as the Copernican or Newtonian, the latter. But such twisting of words is a mere sophistical subterfuge, to avoid a difficult question, by modifying its meaning to suit our own convenience. To be sure, understanding and reason are employed in the cognition of phenomena; but the question is, whether these can be applied when the object is not a phenomenon and in this sense we regard it if it is cogitated as given to the understanding alone, and not to the senses. The question therefore is whether, over and above the empirical use of the understanding, a transcendental use is possible, which applies to the noumenon as an object. This question we have answered in the negative.
When therefore we say, the senses represent objects as they appear, the understanding as they are, the latter statement must not be understood in a transcendental, but only in an empirical signification, that is, as they must be represented in the complete connection of phenomena, and not according to what they may be, apart from their relation to possible experience, consequently not as objects of the pure understanding. For this must ever remain unknown to us. Nay, it is also quite unknown to us whether any such transcendental or extraordinary ​cognition is possible under any circumstances, at least, whether it is possible by means of our categories. Understanding and sensibility, with us, can determine objects only in conjunction. If we separate them, we have intuitions without conceptions, or conceptions without intuitions; in both cases, representations, which we cannot apply to any determinate object.
If, after all our inquiries and explanations, any one still hesitates to abandon the mere transcendental use of the categories, let him attempt to construct with them a synthetical proposition. It would, of course, be unnecessary for this purpose to construct an analytical proposition, for that does not extend the sphere of the understanding, but, being concerned only about what is cogitated in the conception itself, it leaves it quite undecided whether the conception has any relation to objects, or merely indicates the unity of thought—complete abstraction being made of the modi in which an object may be given: in such a proposition, it is sufficient for the understanding to know what lies in the conception—to what it applies is to it indifferent. The attempt must therefore be made with a synthetical and so-called transcendental principle, for example: "Everything that exists, exists as substance," or, "Everything that is contingent exists as an effect of some other thing, viz., of its cause." Now I ask, whence can the understanding draw these synthetical propositions, when the conceptions contained therein do not relate to possible experience but to things in themselves (noumena)? Where is to be found the third term, which is always requisite PURE site in a synthetical proposition, which may connect in the same proposition conceptions which have no logical (analytical) connection with each other? The proposition never will be demonstrated, nay, more, the possibility of any such pure assertion never can be shown, without making reference to the empirical use of the understanding, and thus, ipso facto, completely renouncing pure and non-sensuous judgement. Thus the conception of pure and merely intelligible objects is completely void of all principles of its application, because we cannot imagine any mode in which they might be given, and the problematical thought which leaves a place open for them serves only, like a void space, to limit the use of empirical principles, without containing at the same time any other object of cognition beyond their sphere. ​

#### 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.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.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 e ​ven 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.
* ↑ Just as if thought were in the first instance a function of the understanding; in the second, of judgement; in the third, of reason. A remark which will be explained in the sequel.
* ↑ The predicables of Kant are quite different from those of Aristotle and ancient and modern logicians. The five predicables are of a logical, and not, like those of Kant, of a metaphysico-ontological import. They were enounced as a complete enumeration of all the possible modes of prediction. Kant's predicables, on the contrary, do not possess this merely formal and logical character, but have a real or metaphysical content. — Tr.
* ↑ In the "Metaphysical Principles of Natural Science."
* ↑ Kant's meaning is: A necessary existence is an existence whose existence is given in the very possibility of its existence.—Tr.
* ↑ Whether the representations are in themselves identical, and consequently whether one can be thought analytically by means of and through the other, is a question which we need not at present consider. Our Consciousness of the one, when we speak of the manifold, is always distinguishable from our consciousness of the other; and it is only respecting the synthesis of this (possible) consciousness that we here treat.
* ↑ All general conceptions—as such—depend, for their existence, on the analytical unity of consciousness. For example, when I think of red in general, I thereby think to myself a property which (as a characteristic mark) can be discovered somewhere, or can be united with other representations; consequently, it is only by means of a forethought possible synthetical unity that I can think to myself the analytical. A representation which is cogitated as common to different representations, is regarded as belonging to such as, besides this common representation, contain something different; consequently it must be previously thought in synthetical unity with other although only possible representations, before I can think in it the analytical unity of consciousness which makes it a conceptas communis. And thus the synthetical unity of apperception is the highest point with which we must connect every operation of the understanding, even the whole of logic, and after it our transcendental philosophy; indeed, this faculty is the understanding itself.
* ↑ Space and time, and all portions thereof, are intuitions; consequently are, with a manifold for their content, single representations. (See the Transcendental Aesthetic.) Consequently, they are not pure conceptions, by means of which the same consciousness is found in a great number of representations; but, on the contrary, they are many representations contained in one, the consciousness of which is, so to speak, compounded. The unity of consciousness is nevertheless synthetical and, therefore, primitive. From this peculiar character of consciousness follow many important consequences. (See § 21.)
* ↑ The tedious doctrine of the four syllogistic figures concerns only categorical syllogisms; and although it is nothing more than an artifice by surreptitiously introducing immediate conclusions (consequentiae immediatae) among the premises of a pure syllogism, to give ism' give rise to an appearance of more modes of drawing a conclusion than that in the first figure, the artifice would not have had much success, had not its authors succeeded in bringing categorical judgements into exclusive respect, as those to which all others must be referred—a doctrine, however, which, according to SS 5, is utterly false.
* ↑ The proof of this rests on the represented unity of intuition, by means of which an object is given, and which always includes in itself a synthesis of the manifold to be intuited, and also the relation of this latter to unity of apperception.
* ↑ Motion of an object in space does not belong to a pure science, consequently not to geometry; because, that a thing is movable cannot be known a priori, but only from experience. But motion, considered as the description of a space, is a pure act of the successive synthesis of the manifold in external intuition by means of productive imagination, and belongs not only to geometry, but even to transcendental philosophy.
* ↑ I do not see why so much difficulty should be found in admitting that our internal sense is affected by ourselves. Every act of attention exemplifies it. In such an act the understanding determines the internal sense by the synthetical conjunction which it cogitates, conformably to the internal intuition which corresponds to the manifold in the synthesis of the understanding. How much the mind is usually affected thereby every one will be able to perceive in himself.
* ↑ The "I think" expresses the act of determining my own existence. My existence is thus already given by the act of consciousness; but the mode in which I must determine my existence, that is, the mode in which I must place the manifold belonging to my existence, is not thereby given. For this purpose intuition of self is required, and this intuition possesses a form given a priori, namely, time, which is sensuous, and belongs to our receptivity of the determinable. Now, as I do not possess another intuition of self which gives the determining in me (of the spontaneity of which I am conscious), prior to the act of determination, in the same manner as time gives the determinable, it is clear that I am unable to determine my own existence as that of a spontaneous being, but I am only able to represent to myself the spontaneity of my thought, that is, of my determination, and my existence remains ever determinable in a purely sensuous manner, that is to say, like the existence of a phenomenon. But it is because of this spontaneity that I call myself an intelligence.
* ↑ Space represented as an object (as geometry really requires it to be) contains more than the mere form of the intuition; namely, a combination of the manifold given according to the form of sensibility into a representation that can be intuited; so that the form of the intuition gives us merely the manifold, but the formal intuition gives unity of representation. In the aesthetic, I regarded this unity as belonging entirely to sensibility, for the purpose of indicating that it antecedes all conceptions, although it presupposes a synthesis which does not belong to sense, through which alone, however, all our conceptions of space and time are possible. For as by means of this unity alone (the understanding determining the sensibility) space and time are given as intuitions, it follows that the unity of this intuition a priori belongs to space and time, and not to the conception of the understanding (SS 20).
* ↑ In this manner it is proved, that the synthesis of apprehension, which is empirical, must necessarily be conformable to the synthesis of apperception, which is intellectual, and contained a priori in the category. It is one and the same spontaneity which at one time, under the name of imagination, at another under that of understanding, produces conjunction in the manifold of intuition.
* ↑ Lest my readers should stumble at this assertion, and the conclusions that may be too rashly drawn from it, I must remind them that the categories in the act of thought are by no means limited by the conditions of our sensuous intuition, but have an unbounded sphere of action. It is only the cognition of the object of thought, the determining of the object, which requires intuition. In the absence of intuition, our thought of an object may still have true and useful consequences in regard to the exercise of reason by the subject. But as this exercise of reason is not always directed on the determination of the object, in other words, on cognition thereof, but also on the determination of the subject and its volition, I do not intend to treat of it in this place.
* ↑ Deficiency in judgement is properly that which is called stupidity; and for such a failing we know no remedy. A dull or narrow-minded person, to whom nothing is wanting but a proper degree of understanding, may be improved by tuition, even so far as to deserve the epithet of learned. But as such persons frequently labour under a deficiency in the faculty of judgement, it is not uncommon to find men extremely learned who in the application of their science betray a lamentable degree this irremediable want.
* ↑ I generate time because I generate succession, name, in the successive addition of one to one.—Tr.
* ↑ Mental synthesis—Tr.
* ↑ Mathematically, in the Kantian sense—Tr.
* ↑ All combination (conjunctio) is either composition (compositio) or connection (nexus). The former is the synthesis of a manifold, the parts of which do not necessarily belong to each other. For example, the two triangles into which a square is divided by a diagonal, do not necessarily belong to each other, and of this kind is the synthesis of the homogeneous in everything that can be mathematically considered. This synthesis can be divided into those of aggregation and coalition, the former of which is applied to extensive, the latter to intensive quantities. The second sort of combination (nexus) is the synthesis of a manifold, in so far as its parts do belong necessarily to each other; for example, the accident to a substance, or the effect to the cause. Consequently it is a synthesis of that which though heterogeneous, is represented as connected a priori. This combination—not an arbitrary one—I entitle dynamical because it concerns the connection of the existence of the manifold. This, again, may be divided into the physical synthesis, of the phenomena divided among each other, and the metaphysical synthesis, or the connection of phenomena a priori in the faculty of cognition.
* ↑ [Persius, Satirae, iii.83-84. "Nothing can be produced from nothing; nothing can be returned into nothing."]
* ↑ It must be remarked that I do not speak of the change of certain relations, but of the change of the state. Thus, when a body moves in a uniform manner, it does not change its state (of motion); but only when all motion increases or decreases.
* ↑ German.
* ↑ The unity of the universe, in which all phenomena to be connected, is evidently a mere consequence of the admitted principle of the community of all substances which are coexistent. For were substances isolated, they could not as parts constitute a whole, and were their connection (reciprocal action of the manifold) not necessary from the very fact of coexistence, we could not conclude from the fact of the latter as a merely ideal relation to the former as a real one. We have, however, shown in its place that community is the proper ground of the possibility of an empirical cognition of coexistence, and that we may therefore properly reason from the latter to the former as its condition.
* ↑ The immediate consciousness of the existence of external things is, in the preceding theorem, not presupposed, but proved, by the possibility of this consciousness understood by us or not. The question as to the possibility of it would stand thus: "Have we an internal sense, but no external sense, and is our belief in external perception a mere delusion?" But it is evident that, in order merely to fancy to ourselves anything as external, that is, to present it to the sense in intuition we must already possess an external sense, and must thereby distinguish immediately the mere receptivity of an external intuition from the spontaneity which characterizes every act of imagination. For merely to imagine also an external sense, would annihilate the faculty of intuition itself which is to be determined by the imagination.
* ↑ When I think the reality of a thing, I do really think more than the possibility, but not in the thing; for that can never contain more in reality than was contained in its complete possibility. But while the notion of possibility is merely the notion of a position of thing in relation to the understanding (its empirical use), reality is the conjunction of the thing with perception.
* ↑ We can easily conceive the non-existence of matter; but the ancients did not thence infer its contingency. But even the alternation of the existence and non-existence of a given state in a thing, in which all change consists, by no means proves the contingency of that state—the ground of proof being the reality of its opposite. For example, a body is in a state of rest after motion, but we cannot infer the contingency of the motion from the fact that the former is the opposite of the latter. For this opposite is merely a logical and not a real opposite to the other. If we wish to demonstrate the contingency of the motion, what we ought to prove is that, instead of the motion which took place in the preceding point of time, it was possible for the body to have been then in rest, not, that it is afterwards in rest; for in this case, both opposites are perfectly consistent with each other.
* ↑ In one word, to none of these conceptions belongs a corresponding object, and consequently their real possibility cannot be demonstrated, if we take away sensuous intuition—the only intuition which we possess—and there then remains nothing but the logical possibility, that is, the fact that the conception or thought is possible—which, however, is not the question; what we want to know being, whether it relates to an object and thus possesses any meaning.
* ↑ If any one wishes here to have recourse to the usual subterfuge, and to say, that at least realitates noumena cannot be in opposition to each other, it will be requisite for him to adduce an example of this pure and non-sensuous reality, that it may be understood whether the notion represents something or nothing. But an example cannot be found except in experience, which never presents to us anything more than phenomena; and thus the proposition means nothing more than that the conception which contains only affirmatives does not contain anything negative—a proposition nobody ever doubted.