Front Page Titles (by Subject) CHAPTER I: METHOD OF DISCOVERING ALL PURE CONCEPTS OF THE UNDERSTANDING - Critique of Pure Reason
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CHAPTER I: METHOD OF DISCOVERING ALL PURE CONCEPTS OF THE UNDERSTANDING - Friedrich Max Müller, Critique of Pure Reason 
Immanuel Kant’s Critique of Pure Reason. In Commemoration of the Centenary of its First Publication. Translated into English by F. Max Mueller (2nd revised ed.) (New York: Macmillan, 1922).
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METHOD OF DISCOVERING ALL PURE CONCEPTS OF THE UNDERSTANDING
When we watch any faculty of knowledge, different concepts, characteristic of that faculty, manifest themselves according to different circumstances, which, as the observation has been carried on for a longer or shorter time, or with more or less accuracy, may be gathered up into a more or less complete collection. Where this collection will be complete, it is impossible to say beforehand, when we follow this almost mechanical process. Concepts thus discovered fortuitously only, possess neither order nor systematic unity, but [p. 67] are paired in the end according to similarities, and, according to their contents, arranged as more or less complex in various series, which are nothing less than systematical, though to a certain extent put together methodically.
Transcendental philosophy has the advantage, but also the duty of discovering its concepts according to a fixed principle. As they spring pure and unmixed from the understanding as an absolute unity, they must be connected with each other, according to one concept or idea. This connection supplies us at the same time with a rule, according to which the place of each pure concept of the understanding and the systematical completeness of all of them can be determined a priori, instead of being dependent on arbitrary choice or chance.
Of the Logical Use of the Understanding in General
We have before defined the understanding negatively only, as a non-sensuous faculty of knowledge. As without sensibility we cannot have any intuition, [p. 68] it is clear that the understanding is not a faculty of intuition. Besides intuition, however, there is no other kind of knowledge except by means of concepts. The knowledge therefore of every understanding, or at least of the human understanding, must be by means of concepts, not intuitive, but discursive. All intuitions, being sensuous, depend on affections, concepts on functions. By this function I mean the unity of the act of arranging different representations under one common representation. Concepts are based therefore on the spontaneity of thought, sensuous intuitions on the receptivity of impressions. The only use which the understanding can make of these concepts is to form judgments by them. As no representation, except the intuitional, refers immediately to an object, no concept is ever referred to an object immediately, but to some other representation of it, whether it be an intuition, or itself a concept. A judgment is therefore a mediate knowledge of an object, or a representation of a representation of it. In every judgment we find a concept applying to many, and comprehending among the many one single representation, which is referred immediately to the object. Thus in the judgment that all bodies are divisible,1 the concept of divisible applies to various other concepts, but is here applied in particular to the concept of body, and this concept of body to certain phenomena of our experience. [p. 69] These objects therefore are represented mediately by the concept of divisibility. All judgments therefore are functions of unity among our representations, the knowledge of an object being brought about, not by an immediate representation, but by a higher one, comprehending this and several others, so that many possible cognitions are collected into one. As all acts of the understanding can be reduced to judgments, the understanding may be defined as the faculty of judging. For we saw before that the understanding is the faculty of thinking, and thinking is knowledge by means of concepts, while concepts, as predicates of possible judgments, refer to some representation of an object yet undetermined. Thus the concept of body means something, for instance, metal, which can be known by that concept. It is only a concept, because it comprehends other representations, by means of which it can be referred to objects. It is therefore the predicate of a possible judgment, such as, that every metal is a body. Thus the functions of the understanding can be discovered in their completeness, if it is possible to represent the functions of unity in judgments. That this is possible will be seen in the following section.
Of the Logical Function of the Understanding in Judgments [p. 70]
If we leave out of consideration the contents of any judgment and fix our attention on the mere form of the understanding, we find that the function of thought in a judgment can be brought under four heads, each of them with three subdivisions. They may be represented in the following table:—
As this classification may seem to differ in some, though not very essential points, from the usual technicalities of logicians, the following reservations against any [p. 71] possible misunderstanding will not be out of place.
1. Logicians are quite right in saying that in using judgments in syllogisms, singular judgments may be treated like universal ones. For as they have no extent at all, the predicate cannot refer to part only of that which is contained in the concept of the subject, and be excluded from the rest. The predicate is valid therefore of that concept, without any exception, as if it were a general concept, having an extent to the whole of which the predicate applies. But if we compare a singular with a general judgment, looking only at the quantity of knowledge conveyed by it, the singular judgment stands to the universal judgment as unity to infinity, and is therefore essentially different from it. It is therefore, when we consider a singular judgment (judicium singulare), not only according to its own validity, but according to the quantity of knowledge which it conveys, as compared with other kinds of knowledge, that we see how different it is from general judgments (judicia communia), and how well it deserves a separate place in a complete table of the varieties of thought in general, though not in a logic limited to the use of judgments in reference to each other.
2. In like manner infinite judgments must, in transcendental logic, be distinguished from affirmative ones, though in general logic they are properly classed together, and do not constitute a separate part in [p. 72] the classification. General logic takes no account of the contents of the predicate (though it be negative), it only asks whether the predicate be affirmed or denied. Transcendental logic, on the contrary, considers a judgment according to the value also or the contents of a logical affirmation by means of a purely negative predicate, and asks how much is gained by that affirmation, with reference to the sum total of knowledge. If I had said of the soul, that it is not mortal, I should, by means of a negative judgment, have at least warded off an error. Now it is true that, so far as the logical form is concerned, I have really affirmed by saying that the soul is non-mortal, because I thus place the soul in the unlimited sphere of non-mortal beings. As the mortal forms one part of the whole sphere of possible beings, the non-mortal the other, I have said no more by my proposition than that the soul is one of the infinite number of things which remain, when I take away all that is mortal. But by this the infinite sphere of all that is possible becomes limited only in so far that all that is mortal is excluded from it, and that afterwards the soul is placed in the remaining part of its original extent. This part, however, even after its limitation, still remains infinite, and several more parts of it may be taken away without extending thereby in the least the concept of the soul, or affirmatively determining [p. 73] it. These judgments, therefore, though infinite in respect to their logical extent, are, with respect to their contents, limitative only, and cannot therefore be passed over in a transcendental table of all varieties of thought in judgments, it being quite possible that the function of the understanding exercised in them may become of great importance in the field of its pure a priori knowledge.
3. The following are all the relations of thought in judgments:—
a. Relation of the predicate to the subject.
b. Relation of the cause to its effect.
c. Relation of subdivided knowledge, and of the collected members of the subdivision to each other.
In the first class of judgments we consider two concepts, in the second two judgments, in the third several judgments in their relation to each other. The hypothetical proposition, if perfect justice exists, the obstinately wicked is punished, contains really the relation of two propositions, namely, there is a perfect justice, and the obstinately wicked is punished. Whether both these propositions are true remains unsettled. It is only the consequence which is laid down by this judgment.
The disjunctive judgment contains the relation of two or more propositions to each other, but not as a consequence, but in the form of a logical opposition, the sphere of the one excluding the sphere of the other, and at the same time in the form of community, all the propositions together filling the whole sphere of the intended knowledge. The disjunctive judgment contains therefore [p. 74] a relation of the parts of the whole sphere of a given knowledge, in which the sphere of each part forms the complement of the sphere of the other, all being contained within the whole sphere of the subdivided knowledge. We may say, for instance, the world exists either by blind chance, or by internal necessity, or by an external cause. Each of these sentences occupies a part of the sphere of all possible knowledge with regard to the existence of the world, while all together occupy the whole sphere. To take away the knowledge from one of these spheres is the same as to place it into one of the other spheres, and to place it in one sphere is the same as to take it away from the others. There exists therefore in disjunctive judgments a certain community of the different divisions of knowledge, so that they mutually exclude each other, and yet thereby determine in their totality the true knowledge, because, if taken together, they constitute the whole contents of one given knowledge. This is all I have to observe here for the sake of what is to follow hereafter.
4. The modality of judgments is a very peculiar function, for it contributes nothing to the contents of a judgment (because, besides quantity, quality, and relation, there is nothing else that could constitute the contents of a judgment), but refers only to the nature of the copula in relation to thought in general. Problematical judgments are those in which affirmation or negation are taken as possible (optional) only, while in assertory judgments affirmation or negation is taken as real (true), in apodictic as necessary.1 Thus the two judgments, [p. 75] 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 subdivision), are always problematical only. In the example given above, the proposition, there exists a perfect justice, is not made as an assertory, but only as an optional judgment, which may be accepted or not, the consequence only being assertory. It is clear therefore that some of these judgments may be wrong, and may yet, if taken problematically, contain the conditions of the knowledge of truth. Thus, in our disjunctive judgment, one of its component judgments, namely, the world exists by blind chance, has a problematical meaning only, on the supposition that some one might for one moment take such a view, but serves, at the same time, like the indication of a false road among all the roads that might be taken, to find out the true one. The problematical proposition is therefore that which expresses logical (not objective) possibility only, that is, a free choice of admitting such a proposition, and a purely optional admission of it into the understanding. The assertory proposition implies logical reality or truth. Thus, for instance, in a hypothetical syllogism the antecedens in the major is problematical, in the [p. 76] minor assertory, showing that the proposition conforms to the understanding according to its laws. The apodictic proposition represents the assertory as determined by these very laws of the understanding, and therefore as asserting a priori, and thus expresses logical necessity. As in this way everything is arranged step by step in the understanding, inasmuch as we begin with judging problematically, then proceed to an assertory acceptation, and finally maintain our proposition as inseparably united with the understanding, that is as necessary and apodictic, we may be allowed to call these three functions of modality so many varieties or momenta of thought.
Of the Pure Concepts of the Understanding, or of the Categories
General logic, as we have often said, takes no account of the contents of our knowledge, but expects that representations will come from elsewhere in order to be turned into concepts by an analytical process. Transcendental logic, on the contrary, has before it the manifold contents of sensibility a priori, supplied by transcendental [p. 77] æsthetic as the material for the concepts of the pure understanding, without which those concepts would be without any contents, therefore entirely empty. It is true that space and time contain what is manifold in the pure intuition a priori, but they belong also to the conditions of the receptivity of our mind under which alone it can receive representations of objects, and which therefore must affect the concepts of them also. The spontaneity of our thought requires that what is manifold in the pure intuition should first be in a certain way examined, received, and connected, in order to produce a knowledge of it. This act I call synthesis.
In its most general sense, I understand by synthesis the act of arranging different representations together, and of comprehending what is manifold in them under one form of knowledge. Such a synthesis is pure, if the manifold is not given empirically, but a priori (as in time and space). Before we can proceed to an analysis of our representations, these must first be given, and, as far as their contents are concerned, no concepts can arise analytically. Knowledge is first produced by the synthesis of what is manifold (whether given empirically or a priori). That knowledge may at first be crude and confused and in need of analysis, but it is synthesis which really collects the elements of knowledge, and unites them to a certain extent. It is therefore the first thing which we [p. 78] have to consider, if we want to form an opinion on the first origin of our knowledge.
We shall see hereafter that synthesis in general is the mere result of what I call the faculty of imagination, a blind but indispensable function of the soul, without which we should have no knowledge whatsoever, but of the existence of which we are scarcely conscious. But to reduce this synthesis to concepts is a function that belongs to the understanding, and by which the understanding supplies us for the first time with knowledge properly so called.
Pure synthesis in its most general meaning gives us the pure concept of the understanding. By this pure synthesis I mean that which rests on the foundation of what I call synthetical unity a priori. Thus our counting (as we best perceive when dealing with higher numbers) is a synthesis according to concepts, because resting on a common ground of unity, as for instance, the decade. The unity of the synthesis of the manifold becomes necessary under this concept.
By means of analysis different representations are brought under one concept, a task treated of in general logic; but how to bring, not the representations, but the pure synthesis of representations, under concepts, that is what transcendental logic means to teach. The first that must be given us a priori for the sake of knowledge of all objects, is the manifold in pure intuition. The second is, the synthesis of the manifold by means of [p. 79] imagination. But this does not yet produce true knowledge. The concepts which impart unity to this pure synthesis and consist entirely in the representation of this necessary synthetical unity, add the third contribution towards the knowledge of an object, and rest on the understanding.
The same function which imparts unity to various representations in one judgment imparts unity likewise to the mere synthesis of various representations in one intuition, which in a general way may be called the pure concept of the understanding. The same understanding, and by the same operations by which in concepts it achieves through analytical unity the logical form of a judgment, introduces also, through the synthetical unity of the manifold in intuition, a transcendental element into its representations. They are therefore called pure concepts of the understanding, and they refer a priori to objects, which would be quite impossible in general logic.
In this manner there arise exactly so many pure concepts of the understanding which refer a priori to objects of intuition in general, as there were in our table logical functions in all possible judgments, because those functions completely exhaust the understanding, and comprehend every one of its faculties. Borrowing a term of Aristotle, we shall call these concepts categories, [p. 80] our intention being originally the same as his, though widely diverging from it in its practical application.
This then is a list of all original pure concepts of synthesis, which belong to the understanding a priori, and for which alone it is called pure understanding; for it is by them alone that it can understand something in the manifold of intuition, that is, think an object in it. The classification is systematical, and founded on a common principle, namely, the faculty of judging (which is the same as the faculty of thinking). It is not the [p. 81] result of a search after pure concepts undertaken at haphazard, the completeness of which, as based on induction only, could never be guaranteed. Nor could we otherwise understand why these concepts only, and no others, abide in the pure understanding. It was an enterprise worthy of an acute thinker like Aristotle to try to discover these fundamental concepts; but as he had no guiding principle he merely picked them up as they occurred to him, and at first gathered up ten of them, which he called categories or predicaments. Afterwards he thought he had discovered five more of them, which he added under the name of post-predicaments. But his table remained imperfect for all that, not to mention that we find in it some modes of pure sensibility (quando, ubi, situs, also prius, simul), also an empirical concept (motus), none of which can belong to this genealogical register of the understanding. Besides, there are some derivative concepts, counted among the fundamental concepts (actio, passio), while some of the latter are entirely wanting.
With regard to these, it should be remarked that the categories, as the true fundamental 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 [p. 82] essay the mention of the fact may suffice.
I should like to be allowed to call these pure but derivative concepts of the understanding the predicabilia, in opposition to the predicamenta of the pure understanding. If we are once in possession of the fundamental and primitive concepts, it is easy to add the derivative and secondary, and thus to give a complete image of the genealogical tree of the pure understanding. As at present I am concerned not with the completeness, but only with the principles of a system, I leave this supplementary work for a future occasion. In order to carry it out, one need only consult any of the ontological manuals, and place, for instance, under the category of causality the predicabilia of force, of action, and of passion; under the category of community the predicabilia of presence and resistance; under the predicaments of modality the predicabilia of origin, extinction, change, etc. If we associate the categories among themselves or with the modes of pure sensibility, they yield us a large number of derivative concepts a priori, which it would be useful and interesting to mark and, if possible, to bring to a certain completeness, though this is not essential for our present purpose.
I intentionally omit here the definitions of these categories, though I may be in possession of them.1 In the sequel I shall dissect these concepts so far as is [p. 83] sufficient for the purpose of the method which I am preparing. In a complete system of pure reason they might be justly demanded, but at present they would only make us lose sight of the principal object of our investigation, by rousing doubts and objections which, without injury to our essential object, may well be relegated to another time. The little I have said ought to be sufficient to show clearly that a complete dictionary of these concepts with all requisite explanations is not only possible, but easy. The compartments exist; they have only to be filled, and with a systematic topic like the present the proper place to which each concept belongs cannot easily be missed, nor compartments be passed over which are still empty.1
[1 ]Veränderlich in the First Edition is rightly corrected into theilbar in later editions, though in the Second it is still veränderlich.
[1 ]As if in the first, thought were a function of the understanding, in the second, of the faculty of judgment, in the third, of reason; a remark which will receive its elucidation in the sequel.
[1 ]See, however, Karl’s remarks on p. 210 (p. 241 of First Edition).
[1 ]Here follows in the Second Edition, Supplement XII.