Immanuel Kant's Critique of Pure Reason, translated by Norman Kemp Smith





TRANSCENDENTAL analytic consists in the dissection of all our a priori knowledge into the elements that pure understanding by itself yields. In so doing, the following are the points of chief concern: (1) that the concepts be pure and not empirical; (2) that they belong, not to intuition and sensibility, but to thought and understanding; (3) that they be fundamental and be carefully distinguished from those which are derivative or composite; (4) that our table of concepts be complete, covering the whole field of the pure understanding. When a science is an aggregate brought into existence in a merely experimental manner, such completeness can never be guaranteed by any kind of mere estimate. It is possible only by means of an idea of the totality of the a priori knowledge yielded by the understanding; such an idea can furnish an exact classification of the concepts which compose that totality, exhibiting their interconnection in a system. Pure understanding distinguishes itself not merely from all that is empirical but completely also from all sensibility. It is a unity self-subsistent, self-sufficient, and not to be increased by any additions from without. The sum of its knowledge thus constitutes a system, comprehended and determined by one idea. The completeness and articulation of this system can at the same time yield a criterion of the correctness and genuineness of all its components. This part of transcendental logic requires, however, for its complete exposition, two books, the one containing the concepts, the other the principles of pure understanding.





By 'analytic of concepts' I do not understand their analysis, or the procedure usual in philosophical investigations, that of dissecting the content of such concepts as may present themselves, and so of rendering them more distinct; but the hitherto rarely attempted dissection of the faculty of the understanding itself, in order to investigate the possibility of concepts a priori by looking for them in the understanding alone, as their birthplace, and by analyzing the pure use of this faculty. This is the proper task of a transcendental philosophy; anything beyond this belongs to the logical treatment of concepts in philosophy in general. We shall therefore follow up the pure concepts to their first seeds and dispositions in the human understanding, in which they lie prepared, till at last, on the occasion of experience, they are developed, and by the same understanding are exhibited in their purity, freed from the empirical conditions attaching to them.





WHEN we call a faculty of knowledge into play, then, as the occasioning circumstances differ, various concepts stand forth and make the faculty known, and allow of their being collected with more or less completeness, in proportion as observation has been made of them over a longer time or with greater acuteness. But when the enquiry is carried on in this mechanical fashion, we can never be sure whether it has been brought to completion. Further, the concepts which we thus discover only as opportunity offers, exhibit no order and systematic unity, but are in the end merely arranged in pairs according to similarities, and in series according to the amount of their contents, from the simple on to the more composite -- an arrangement which is anything but systematic, although to a certain extent methodically instituted.

Transcendental philosophy, in seeking for its concepts, has the advantage and also the duty of proceeding according to a single principle. For these concepts spring, pure and unmixed, out of the understanding which is an absolute unity; and must therefore be connected with each other according to one concept or idea. Such a connection supplies us with a rule, by which we are enabled to assign its proper place to each pure concept of the understanding, and by which we can determine in an a priori manner their systematic completeness. Otherwise we should be dependent in these matters on our own discretionary judgment or merely on chance. [105]


Section I


The understanding has thus far been explained merely negatively, as a non-sensible faculty of knowledge. Now since without sensibility we cannot have any intuition, understanding cannot be a faculty of intuition. But besides intuition there is no other mode of knowledge except by means of concepts. The knowledge yielded by understanding, or at least by the human understanding, must therefore be by means of concepts, and so is not intuitive, but discursive. Whereas all intuitions, as sensible, rest on affections, concepts rest on functions. By 'function' I mean the unity of the act of bringing various representations under one common representation. Concepts are based on the spontaneity of thought, sensible intuitions on the receptivity of impressions. Now the only use which the understanding can make of these concepts is to judge by means of them. Since no representation, save when it is an intuition, is in immediate relation to an object, no concept is ever related to an object immediately, but to some other representation of it, be that other representation an intuition, or itself a concept. Judgment is therefore the mediate knowledge of an object, that is, the representation of a representation of it. In every judgment there is a concept which holds of many representations, and among them of a given representation that is immediately related to an object. Thus in the judgment, 'all bodies are divisible', the concept of the divisible applies to various other concepts, but is here applied in particular to the concept of body, and this concept again to certain appearances that present themselves to us. These objects, therefore, are mediately represented through the concept of divisibility. Accordingly, all judgments are functions of unity among our [106] representations; instead of an immediate representation, a higher representation, which comprises the immediate representation and various others, is used in knowing the object, and thereby much possible knowledge is collected into one. Now we can reduce all acts of the understanding to judgments, and the understanding may therefore be represented as a faculty of judgment. For, as stated above, the understanding is a faculty of thought. Thought is knowledge by means of concepts. But concepts, as predicates of possible judgments, relate to some representation of a not yet determined object. Thus the concept of body means something, for instance, metal, which can be known by means of that concept. It is therefore a concept solely in virtue of its comprehending other representations, by means of which it can relate to objects. It is therefore the predicate of a possible judgment, for instance, 'every metal is a body'. The functions of the understanding can, therefore, be discovered if we can give an exhaustive statement of the functions of unity in judgments. That this can quite easily be done will be shown in the next section.


Section 2


If we abstract from all content of a judgment, and consider only the mere form of understanding, we find that the function of thought in judgment can be brought under four heads, each of which contains three moments. They may be conveniently represented in the following table: [107]
Quantity of Judgments
Quality Relation
Affirmative Categorical
Negative Hypothetical

As this division appears to depart in some, though not in any essential respects, from the technical distinctions ordinarily recognized by logicians, the following observations may serve to guard against any possible misunderstanding.

1. Logicians are justified in saying that, in the employment of judgments in syllogisms, singular judgments can be treated like those that are universal. For, since they have no extension at all, the predicate cannot relate to part only of that which is contained in the concept of the subject, and be excluded from the rest. The predicate is valid of that concept, without any such exception, just as if it were a general concept and had an extension to the whole of which the predicate applied. If, on the other hand, we compare a singular with a universal judgment, merely as knowledge, in respect of quantity, the singular stands to the universal as unity to infinity, and is therefore in itself essentially different from the universal. If, therefore, we estimate a singular judgment (judicium singulare), not only according to its own inner validity, but as knowledge in general, according to its quantity in comparison with other knowledge, it is certainly different from general judgments (judicia communia), and in a complete table of the moments of thought in general deserves a separate place -- though not, indeed, in a logic limited to the use of judgments in reference to each other. [108]

2. In like manner infinite judgments must, in transcendental logic, be distinguished from those that are affirmative, although in general logic they are rightly classed with them, and do not constitute a separate member of the division. General logic abstracts from all content of the predicate (even though it be negative); it inquires only whether the predicate be ascribed to the subject or opposed to it. But transcendental logic also considers what may be the worth or content of a logical affirmation that is thus made by means of a merely negative predicate, and what is thereby achieved in the way of addition to our total knowledge. If I should say of the soul, 'It is not mortal', by this negative judgment I should at least have warded off error. Now by the proposition, 'The soul is non-mortal', I have, so far as the logical form is concerned, really made an affirmation. I locate the soul in the unlimited sphere of non-mortal beings. Since the mortal constitutes one part of the whole extension of possible beings, and the non-mortal the other, nothing more is said by my proposition than that the soul is one of the infinite number of things which remain over when I take away all that is mortal. The infinite sphere of all that is possible is thereby only so far limited that the mortal is excluded from it, and that the soul is located in the remaining part of its extension. But, even allowing for such exclusion, this extension still remains infinite, and several more parts of it may be taken away without the concept of the soul being thereby in the least increased, or determined in an affirmative manner. These judgments, though infinite in respect of their logical extension, are thus, in respect of the content of their knowledge, limitative only, and cannot therefore be passed over in a transcendental table of all moments of thought in judgments, since the function of the understanding thereby expressed may perhaps be of importance in the field of its pure a priori knowledge.

3. All relations of thought in judgments are (a) of the predicate to the subject, (b) of the ground to its consequence, (c) of the divided knowledge and of the members of the division, taken together, to each other. In the first kind of [109] judgments we consider only two concepts, in the second two judgments, in the third several judgments in their relation to each other. The hypothetical proposition, 'If there is a perfect justice, the obstinately wicked are punished', really contains the relation of two propositions, namely, 'There is a perfect justice', and 'The obstinately wicked are punished'. Whether both these propositions are in themselves true, here remains undetermined. It is only the logical sequence which is thought by this judgment. Finally, the disjunctive judgment contains a relation of two or more propositions to each other, a relation not, however, of logical sequence, but of logical opposition, in so far as the sphere of the one excludes the sphere of the other, and yet at the same time of community, in so far as the propositions taken together occupy the whole sphere of the knowledge in question. The disjunctive judgment expresses, therefore, a relation of the parts of the sphere of such knowledge, since the sphere of each part is a complement of the sphere of the others, yielding together the sum-total of the divided knowledge. Take, for instance, the judgment, 'The world exists either through blind chance, or through inner necessity, or through an external cause'. Each of these propositions occupies a part of the sphere of the possible knowledge concerning the existence of a world in general; all of them together occupy the whole sphere. To take the knowledge out of one of these spheres means placing it in one of the other spheres, and to place it in one sphere means taking it out of the others. There is, therefore, in a disjunctive judging a certain community of the known constitutes, such that they mutually exclude each other, and yet thereby determine in their totality the true knowledge. For, when taken together, they constitute the whole content of one given knowledge. This is all that need here be considered, so far as concerns what follows.

4. The modality of judgments is a quite peculiar function. Its distinguishing characteristic is that it contributes nothing to the content of the judgment (for, besides quantity, quality, and relation, there is nothing that constitutes the content of a judgment), but concerns only the value of the copula in relation to thought in general. Problematic judgments are those in which affirmation or negation is taken as merely [110] possible (optional). In assertoric judgments affirmation or negation is viewed as real (true), and in apodeictic judgments as necessary.{1} Thus the two judgments, the relation of which constitutes the hypothetical judgment (antecedens et consequens), and likewise the judgments the reciprocal relation of which forms the disjunctive judgment (members of the division), are one and all problematic only. In the above example, the proposition, 'There is a perfect justice', is not stated assertorically, but is thought only as an optional judgment, which it is possible to assume; it is only the logical sequence which is assertoric. Such judgments may therefore be obviously false, and yet, taken problematically, may be conditions of the knowledge of truth. Thus the judgment 'The world exists by blind chance', has in the disjunctive judgment only problematic meaning, namely, as a proposition that may for a moment be assumed. At the same time, like the indication of a false road among the number of all those roads that can be taken, it aids in the discovery of the true proposition. The problematic proposition is therefore that which expresses only logical (which is not objective) possibility -- a free choice of admitting such a proposition, and a purely optional admission of it into the understanding. The assertoric proposition deals with logical reality or truth. Thus, for instance, in a hypothetical syllogism the antecedent is in the major premiss problematic, in the minor assertoric, and what the syllogism shows is that the consequence follows in accordance with the laws of the understanding. The apodeictic proposition thinks the assertoric as determined by these laws of the understanding, and therefore as affirming a priori; and in this manner it expresses logical necessity. Since everything is thus incorporated in the understanding step by step -- inasmuch as we first judge something problematically, then maintain its truth assertorically, and finally affirm it as inseparably united with the understanding, that is, as necessary and apodeictic -- we are justified in regarding these three functions of modality as so many moments of thought.



Section 3


General logic, as has been repeatedly said, abstracts from all content of knowledge, and looks to some other source, whatever that may be, for the representations which it is to transform into concepts by process of analysis. Transcendental logic, on the other hand, has lying before it a manifold of a priori sensibility, presented by transcendental aesthetic, as material for the concepts of pure understanding. In the absence of this material those concepts would be without any content, therefore entirely empty. Space and time contain a manifold of pure a priori intuition, but at the same time are conditions of the receptivity of our mind -- conditions under which alone it can receive representations of objects, and which therefore must also always affect the concept of these objects. But if this manifold is to be known, the spontaneity of our thought requires that it be gone through in a certain way, taken up, and connected. This act I name synthesis.

By synthesis, in its most general sense, I understand the act of putting different representations together, and of grasping what is manifold in them in one [act of] knowledge. Such a synthesis is pure, if the manifold is not empirical but is given a priori, as is the manifold in space and time. Before we can analyze our representations, the representations must themselves be given, and therefore as regards content no concepts can first arise by way of analysis. Synthesis of a manifold (be it given empirically or a priori) is what first gives rise to knowledge. This knowledge may, indeed, at first, be crude and confused, and therefore in need of analysis. Still the synthesis is that which gathers the elements for knowledge, and unites them to [form] a certain content. It is to synthesis, therefore, [112] that we must first direct our attention, if we would determine the first origin of our knowledge.

Synthesis in general, as we shall hereafter see, is the mere result of the power of imagination, a blind but indispensable function of the soul, without which we should have no knowledge whatsoever, but of which we are scarcely ever conscious. To bring this synthesis to concepts is a function which belongs to the understanding, and it is through this function of the understanding that we first obtain knowledge properly so called.

Pure synthesis, represented in its most general aspect, gives the pure concept of the understanding. By this pure synthesis I understand that which rests upon a basis of a priori synthetic unity. Thus our counting, as is easily seen in the case of larger numbers, is a synthesis according to concepts, because it is executed according to a common ground of unity, as, for instance, the decade. In terms of this concept, the unity of the synthesis of the manifold is rendered necessary.

By means of analysis different representations are brought under one concept -- a procedure treated of in general logic. What transcendental logic, on the other hand, teaches, is how we bring to concepts, not representations, but the pure synthesis of representations. What must first be given -- with a view to the a priori knowledge of all objects -- is the manifold of pure intuition; the second factor involved is the synthesis of this manifold by means of the imagination. But even this does not yet yield knowledge. The concepts which give unity to this pure synthesis, and which consist solely in the representation of this necessary synthetic unity, furnish the third requisite for the knowledge of an object; and they rest on the understanding.

The same function which gives unity to the various representations in a judgment also gives unity to the mere synthesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure concept of the understanding. The same understanding, through the same operations by which in concepts, by means of analytical unity, it produced the logical form of a judgment, also introduces a transcendental content into its representations, by means of the synthetic unity of the manifold in intuition [113] in general. On this account we are entitled to call these representations pure concepts of the understanding, and to regard them as applying a priori to objects -- a conclusion which general logic is not in a position to establish.

In this manner there arise precisely the same number of pure concepts of the understanding which apply a priori to objects of intuition in general, as, in the preceding table, there have been found to be logical functions in all possible judgments. For these functions specify the understanding completely, and yield an exhaustive inventory of its powers. These concepts we shall, with Aristotle, call categories, for our primary purpose is the same as his, although widely diverging from it in manner of execution.

Of Quantity
Of Quality Of Relation
Reality Of Inherence and Subsistence
Negation(substantia et accidens)
LimitationOf Causality and Dependence
(cause and effect)
Of Community (reciprocity
between agent and patient)
Of Modality
Possibility -- Impossibility
Existence -- Non-existence
Necessity -- Contingency

This then is the list of all original pure concepts of synthesis that the understanding contains within itself a priori. [114] Indeed, it is because it contains these concepts that it is called pure understanding; for by them alone can it understand anything in the manifold of intuition, that is, think an object of intuition. This division is developed systematically from a common principle, namely, the faculty of judgment (which is the same as the faculty of thought). It has not arisen rhapsodically, as the result of a haphazard search after pure concepts, the complete enumeration of which as based on induction only, could never be guaranteed. Nor could we, if this were our procedure, discover why just these concepts, and no others, have their seat in the pure understanding. It was an enterprise worthy of an acute thinker like Aristotle to make search for these fundamental concepts. But as he did so on no principle, he merely picked them up as they came his way, and at first procured ten of them, which he called categories (predicaments). Afterwards he believed that he had discovered five others, which he added under the name of post-predicaments. But his table still remained defective. Besides, there are to be found in it some modes of pure sensibility (quando, ubi, situs, also prius, simul), and an empirical concept (motus), none of which have any place in a table of the concepts that trace their origin to the understanding. Aristotle's list also enumerates among the original concepts some derivative concepts (actio, passio); and of the original concepts some are entirely lacking.

In this connection, it is to be remarked that the categories, as the true primary concepts of the pure understanding, have also their pure derivative concepts. These could not be passed over in a complete system of transcendental philosophy, but in a merely critical essay the simple mention of the fact may suffice.

I beg permission to entitle these pure but derivative concepts of the understanding the predicables of the pure understanding -- to distinguish them from the predicaments [i.e. the categories]. If we have the original and primitive concepts, it is easy to add the derivative and subsidiary, and so to give a complete picture of the family tree of the [concepts of] pure understanding. Since at present we are concerned not with the completeness of the system, but only with the principles to be followed in its construction, I reserve this supplementary work [115] for another occasion. It can easily be carried out, with the aid of the ontological manuals -- for instance, by placing under the category of causality the predicables of force, action, passion; under the category of community the predicables of presence, resistance; under the predicaments of modality the predicables of coming to be, ceasing to be, change, etc. The categories, when combined with the modes of pure sensibility, or with one another, yield a large number of derivative a priori concepts. To note, and, where possible, to give a complete inventory of these concepts, would be a useful and not unpleasant task, but it is a task from which we can here be absolved.

In this treatise, I purposely omit the definitions of the categories, although I may be in possession of them. I shall proceed to analyze these concepts only so far as is necessary in connection with the doctrine of method which I am propounding. In a system of pure reason, definitions of the categories would rightly be demanded, but in this treatise they would merely divert attention from the main object of the enquiry, arousing doubts and objections which, without detriment to what is essential to our purposes, can very well be reserved for another occasion. Meanwhile, from the little that I have said, it will be obvious that a complete glossary, with all the requisite explanations, is not only a possible, but an easy task. The divisions are provided; all that is required is to fill them; and a systematic 'topic', such as that here given, affords sufficient guidance as to the proper location of each concept, while at the same time indicating which divisions are still empty.


This table of categories suggests some nice points, which may perhaps have important consequences in regard to the scientific form of all modes of knowledge obtainable by reason. For that this table is extremely useful in the theoretical part of philosophy, and indeed is indispensable as supplying the complete plan of a whole science, so far as that science rests on a priori concepts, and as dividing it systematically according to [116] determinate principles, is already evident from the fact that the table contains all the elementary concepts of the understanding in their completeness, nay, even the form of a system of them in the human understanding, and accordingly indicates all the momenta of a projected speculative science, and even their order, as I have elsewhere{2} shown.

The first of the considerations suggested by the table is that while it contains four classes of the concepts of understanding, it may, in the first instance, be divided into two groups; those in the first group being concerned with objects of intuition, pure as well as empirical, those in the second group with the existence of these objects, in their relation either to each other or to the understanding.

The categories in the first group I would entitle the mathematical, those in the second group the dynamical. The former have no correlates; these are to be met with only in the second group. This distinction must have some ground in the nature of the understanding.

Secondly, in view of the fact that all a priori division of concepts must be by dichotomy, it is significant that in each class the number of the categories is always the same, namely, three. Further, it may be observed that the third category in each class always arises from the combination of the second category with the first.

Thus allness or totality is just plurality considered as unity; limitation is simply reality combined with negation; community is the causality of substances reciprocally determining one another; lastly, necessity is just the existence which is given through possibility itself. It must not be supposed, however, that the third category is therefore merely a derivative, and not a primary, concept of the pure understanding. For the combination of the first and second concepts, in order that the third may be produced, requires a special act of the understanding, which is not identical with that which is exercised in the case of the first and the second. Thus the concept of a number (which belongs to the category of totality) is not always possible simply upon the presence of concepts of plurality and unity [117] (for instance, in the representation of the infinite); nor can I, by simply combining the concept of a cause and that of a substance, at once have understanding of influence, that is, how a substance can be the cause of something in another substance. Obviously in these cases, a separate act of the understanding is demanded; and similarly in the others.

Thirdly, in the case of one category, namely, that of community, which is found in the third group, its accordance with the form of a disjunctive judgment -- the form which corresponds to it in the table of logical functions -- is not as evident as in the case of the others.

To gain assurance that they do actually accord, we must observe that in all disjunctive judgments the sphere (that is, the multiplicity which is contained in any one judgment) is represented as a whole divided into parts (the subordinate concepts), and that since no one of them can be contained under any other, they are thought as co-ordinated with, not subordinated to, each other, and so as determining each other, not in one direction only, as in a series, but reciprocally, as in an aggregate -- if one member of the division is posited, all the rest are excluded, and conversely.

Now in a whole which is made up of things, a similar combination is being thought; for one thing is not subordinated, as effect, to another, as cause of its existence, but, simultaneously and reciprocally, is co-ordinated with it, as cause of the determination of the other (as, for instance, in a body the parts of which reciprocally attract and repel each other). This is a quite different kind of connection from that which is found in the mere relation of cause to effect (of ground to consequence), for in the latter relation the consequence does not in its turn reciprocally determine the ground, and therefore does not constitute with it a whole -- thus the world, for instance, does not with its Creator serve to constitute a whole. The procedure which the understanding follows in representing to itself the sphere of a divided concept it likewise follows when it thinks a thing as divisible; and just as, in the former case, the members of a division exclude each other, and yet are combined [118] in one sphere, so the understanding represents to itself the parts of the latter as existing (as substances) in such a way that, while each exists independently of the others, they are yet combined together in one whole.


In the transcendental philosophy of the ancients there is included yet another chapter containing pure concepts of the understanding which, though not enumerated among the categories, must, on their view, be ranked as a priori concepts of objects. This, however, would amount to an increase in the number of the categories, and is therefore not feasible. They are propounded in the proposition, so famous among the Schoolmen, quodlibet ens est unum, verum, bonum. Now, although the application of this principle has proved very meager in consequences, and has indeed yielded only propositions that are tautological, and therefore in recent times has retained its place in metaphysics almost by courtesy only, yet, on the other hand, it represents a view which, however empty it may seem to be, has maintained itself over this very long period. It therefore deserves to be investigated in respect of its origin, and we are justified in conjecturing that it has its ground in some rule of the understanding which, as often happens, has only been wrongly interpreted. These supposedly transcendental predicates of things are, in fact, nothing but logical requirements and criteria of all knowledge of things in general, and prescribe for such knowledge the categories of quantity, namely, unity, plurality, and totality. But these categories, which, properly regarded, must be taken as material, belonging to the possibility of the things themselves [empirical objects], have, in this further application, been used only in their formal meaning, as being of the nature of logical requisites of all knowledge, and yet at the same time have been incautiously converted from being criteria of thought to be properties of things in themselves. In all knowledge of an object there is unity of concept, which may be entitled qualitative unity, so far as we think by it only the unity in the combination of the manifold of our knowledge: as, for example, the unity of the theme in a play, a speech, or a story. Secondly, there is [119] truth, in respect of its consequences. The greater the number of true consequences that follow from a given concept, the more criteria are there of its objective reality. This might be entitled the qualitative plurality of characters, which belong to a concept as to a common ground (but are not thought in it, as quantity). Thirdly, and lastly, there is perfection, which consists in this, that the plurality together leads back to the unity of the concept, and accords completely with this and with no other concept. This may be entitled the qualitative completeness (totality). Hence it is evident that these logical criteria of the possibility of knowledge in general are the three categories of quantity, in which the unity in the production of the quantum has to be taken as homogeneous throughout; and that these categories are here being transformed so as also to yield connection of heterogeneous knowledge in one consciousness, by means of the quality of the knowledge as the principle of the connection. Thus the criterion of the possibility of a concept (not of an object) is the definition of it, in which the unity of the concept, the truth of all that may be immediately deduced from it, and finally, the completeness of what has been thus deduced from it, yield all that is required for the construction of the whole concept. Similarly, the criterion of an hypothesis consists in the intelligibility of the assumed ground of explanation, that is, in its unity (without any auxiliary hypothesis); in the truth of the consequences that can be deduced from it (their accordance with themselves and with experience); and finally, in the completeness of the ground of explanation of these consequences, which carry us back to neither more nor less than was assumed in the hypothesis, and so in an a posteriori analytic manner give us back and accord with what has previously been thought in a synthetic a priori manner. We have not, therefore, in the concepts of unity, truth, and perfection, made any addition to the transcendental table of the categories, as if it were in any respect imperfect. All that we have done is to bring the employment of these concepts under general logical rules, for the agreement of knowledge with itself -- the question of their relation to objects not being in any way under discussion.

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{1} Just as if thought were in the problematic a function of the understanding; in the assertoric, of the faculty of judgment; in the apodeictic, of reason. This is a remark which will be explained in the sequel. [Back}

{2} Metaphysical First Principles of Natural Science. [Back}

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