Front Page Titles (by Subject) Section II: Of the Logical Function of the Understanding in Judgments [p. 70] - Critique of Pure Reason
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Section II: Of the Logical Function of the Understanding in Judgments [p. 70] - 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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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.
[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.