Abstracts are attributes considered in their individuality, and are Singular Abstracts or Concept Abstracts; and the latter are

Concept Abstracts with Intension, or Without Intension. Concept Abstracts are also concepts, but having marks distinctive enough to warrant their being ranged apart from other concepts.

§ 26. The products now examined may all of them be embraced under the term Notion. A Notion is a single aggregate cognition (or product of cognition) forming a unit of knowledge. We are now to consider dual aggregate cognitions, in which notions are compared with each other, and pronounced to agree or differ.

CHAPTER LI.

JUDGMENTS.

§ 1. A JUDGMENT is a cognition that two or more objects before the mind agree or differ. Judgments are expressed by Propositions. Inasmuch as every cognition is a cognition of agreement and difference, it appears that judgment considered as an act is a primordial cognitive act. Cognising agreement and difference, however, is not all of cognition; the term judgment refers to that part of it considered prominently or primarily. Judgments as products of cognition are the representations of cognitions of agreement and difference. Judgments as acts are both presentative cognitions and representative.

§ 2. All the elaborations of knowledge are the results of acts of judgment. Re-percepts, concepts and abstracts all imply and are constituted of judgments; judgments form the warp and woof of knowledge. The aggregations of associated perceptions to form new singulars and to form general notions are alike permeated with judgments. The earliest and the latest, the simplest and the most complex experiences involve judgments.

§3. The most general division of judgments is into Explicit and Implicit. Explicit judgments are those in which the cognition of agreement or difference is explicit, the two objects compared being kept distinct, and the relation between them being apprehended explicitly. Implicit judgments are those involved in cognitions in which two objects compared have become fused, their distinctness lost, and the cognitions more fully integrated. This

distinction is a psychological one, and must not be confounded with a distinction between express and implied propositions. For instance, when Napoleon first beheld Moscow from a distance, he exclaimed, 'Lo! the celebrated city of the Czars.' The judgment which he formed in his mind was an explicit one; the language used, however, implies a proposition, but does not indicate necessarily an implicit judgment. When an object arrests my attention and I exclaim, 'A bird!' the judgment by which I identify the object with the class bird is explicit; but the cognition bird is made up of numerous implicit judgments. Concepts and percepts contain implicit judgments. The object of knowledge is in these cases a single unified cognition; in explicit judgments there are two separated cognitions compared. Concepts have been stated to be contracted judgments, and judgments expanded concepts. The same thing might be said of percepts, re-percepts, and abstracts, or of any analysable product of cognition. In treating of judgments as judgments we deal with those which are explicit.

§ 4. Of the two cognitions between which an agreement or difference is cognised that from which the mind moves is termed the subject; that to which it moves is termed the predicate. The copula relates entirely to the expression of the judgment in language. The subject may be precisely coincident with the predicate, in which case the cognitions may exactly coalesce; as All X is all Y. A triangle is a figure having three sides and three angles. The just are (all) the holy. Let X represent the subject and Y the predicate in the subjoined diagram in such a case as now under consideration. X is applied to Y and the two coincide exactly.

The small figures in X and the small letters in Y indicate parts into which X and Y may be divided. It is evident that a judgment that All X is all Y also implies a judgment that All Y is all X; also that Some X is some Y, and Some Y some X.

The subject may coincide with an indefinite portion of the predicate, as All X is some Y, All men are animals, in which case (fig. 15) X coincides with some indefinite portion of Y as a, b, c, d, e, or f.

It is also evident in such a case that Some Y is all X, and also that Some X is some Y, Some Y is some X.

An indefinite part of the subject may coincide with an indefinite part of the predicate, as Some X is some Y, Some metals are brittle substances. In fig. 16 an indefinite part of X, as 1, 2, or 3, etc., coincides with an indefinite part of Y, as a, b, or c, etc.

It is equally cognised that Some Y is some X.

A part of the subject may coincide with the whole predicate, as Some X is all Y, Some stars are all planets. In fig. 17 an indefinite part of X, as 1, 2, or 3, coincides with all Y.

In this judgment we judge also that All Y is some X, or Some X is no Y; Some X is not some Y.

These four modes of coincidence respect modes of agreement. Judgments of difference may be found in modes exactly corresponding. The whole subject may disagree with the whole predicate, as No X is (any) Y, No stones are animals.

This judgment implies also the judgment that No Y is (any) X;

that Some X is not Y; that No Y is some X; Some X is not some Y; Some Y is not some X.

The subject may be judged to disagree with part of the predicate, as No X is some Y, No apples are stones. In fig. 19 disagreement is indicated between the whole of X and an indefinite part of Y, as a.

This judgment implies also that Some Y is no X; Some X is not some Y; Some Y is not some X.

The subject in part may be judged to disagree with the predicate in part, as Some X is not some Y, Some apples are not (some) stones. In fig. 20, an indefinite part of X, as 1, disagrees with an indefinite part of Y, as a.

This judgment implies that Some Y is not some X.

The subject in part may be judged to disagree with the whole of the predicate, as Some X is no Y, Some apples are not (any) stones. In fig. 21, a part, as 1 of X, disagrees with Y entire.

This judgment carries with it the judgment that No Yis some X; Some X is not some Y; Some Y is not some X. The questions whether Some X is Y, All Y is some X, are left wholly undetermined.

§ 5. According to these modes of agreement and disagreement of cognitions, judgments are divided into, First, Affirmative and Negative, according as they cognise agreement or difference;

Secondly, Universal and Particular, according as the whole subject is joined to the predicate or only a part of the subject is joined to the predicate; Thirdly, Distributed, when the whole of both subject and predicate are compared; Semi-Distributed when a part of either predicate or subject is taken and is joined to a whole of the other cognition; Undistributed when neither the whole of the subject nor of the predicate is taken. Combining these divisions we have eight varieties of judgments as follows:

The letters at the left are those which by general custom have been employed to designate the respective judgments. It will be noticed that there are four varieties of universal judgments, four of particular, four of affirmative, four of negative, two of distributed, four of semi-distributed, and two of undistributed.

O, n, w, w;

Referring to the preceding section, it may be noticed that the following varieties of judgments are found in combination, the first one of each set implying the others; (I.) U, U, I, I; (II.) A, Y, I, I; (III.) I, I, ; (IV.) Y, A, w, O; (V.) E, E, (VI.) n, O, w, w; (VII.) w, w; (VIII.) O, n, w, w. But it must be observed that in the first group the second U and I do not stand for the same U and I as the first; the second U is a universal affirmative distributed judgment but one in which the subject and predicate have changed places, as compared with the first. Similarly in the second I the subject and predicate have changed places. We may represent the changed judgments by U' and I' respectively. In the second group we have a similar converse of I and a judgment whose form is precisely that of Y, with the matter transposed, Y taking the place of X and X of Y. This change may be indicated by a prime mark, as Y'. A like change occurs in the fifth group where the fourth judgment has the form. but in which the matter is transposed as in Y'. Noting these peculiarities, in like manner wherever they occur we have the groups revised as follows:

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