Again, such a classification as Mill’s involves material considerations that are outside the scope of this treatise.
Without, however, professing to give any complete scheme of classification, we shall endeavour to touch upon the most fundamental differences that may exist between judgments.
54. Kant’s Classification of Judgments.—Kant classified judgments according to four different principles (Quantity, Quality, Relation, and Modality) each yielding three subdivisions, as follows:
| (1) | Quantity. | (i) | Singular | This S is P. |
| (ii) | Particular | Some S is P. | ||
| (iii) | Universal | All S is P. | ||
| (2) | Quality. | (i) | Affirmative | All S is P. |
| (ii) | Negative | No S is P. | ||
| (iii) | Infinite | All S is not-P. | ||
| (3) | Relation. | (i) | Categorical | S is P. |
| (ii) | Hypothetical | If S is P then Q is R. | ||
| (iii) | Disjunctive | Either S is P or Q is R. | ||
| (4) | Modality. | (i) | Problematic | S may be P. |
| (ii) | Assertoric | S is P. | ||
| (iii) | Apodeictic | S must be P. |
This arrangement is open to criticism from several points of view; and its symmetry, although attractive, is not really defensible. At the same time it has the great merit of making prominent what really are the fundamental distinctions between judgments.
The first distinction that we shall consider is that between simple and compound judgments (replacing Kant’s distinction according to relation). We shall then consider in turn distinctions of modality, of quantity, and of quality. 82
55. Simple Judgments and Compound Judgments.—Under the head of relation, Kant gave the well-known threefold division of judgments into categorical, where the affirmation or denial is absolute (S is P); hypothetical (or conditional), where the affirmation or denial is made under a condition (If A is B then S is P); and disjunctive, where the affirmation or denial is made with an alternative (Either S is P or Q is R).
These three kinds of judgment cannot, however, properly be co-ordinated as on an equality with one another in a threefold division. For the categorical judgment appears as an element in both the others, and hence the distinction between the categorical, on the one hand, and the hypothetical and the disjunctive, on the other, appears to be on a different level from that between the two latter. Moreover, the hypothetical and the disjunctive do not exhaust the modes in which categorical judgments may be combined so as to form further judgments. It is, therefore, better not to start from the above threefold division, but from a twofold, namely, into simple and compound.
A compound judgment may be defined as a judgment into the composition of which other judgments enter as elements.[78] There are three principal ways in which judgments may be combined, and in each case the denial of the validity of the combination yields a further form of judgment, so that there are six kinds of compound judgments to be considered.
[78] The distinction here implied has been criticised on the ground that (a) if the so-called elements are really judgments, the combination of them yields no fresh judgment; while (b) if the combination is really an independent judgment, the elements into which it can be analysed are not themselves judgments. It will be seen that (a) is intended to apply to conjunctive syntheses, and (b) to hypotheticals and disjunctives. We shall consider the argument under these heads severally.