higher abstract colour, and we should hardly think of interpolating an adjective coloured; nor should we be inclined to regard coloured as being the intension of whiteness, redness, etc.; we should rather say colour was that intension. More strikingly is this integration seen in case of the abstracts pastness, presentness, and futureness; time is their synthesis, and there is nothing between them and the higher abstract upon which the mind

rests.

§ 22. A query may be raised whether the higher abstracts are formed from other abstracts, or are formed independently of them from concrete particulars. If the latter be the case, the higher and lower abstracts having been formed separately might afterwards be found to intersect and coincide, and thus become connected in association.

In the diagram we have as particulars, sundry actions; the mind may at one time generalise a portion of them into a concept

expressed by prudent, and thus form the abstract prudence; it may also generalise a portion of them, as courageous, giving courage, and so on; or it may generalise a larger number of them under the concept virtuous, and arrive at the abstract virtue, without the aid of the inferior abstracts prudence, courage, etc. The true solution of this question probably is, that higher abstracts are formed in both ways. While sometimes such a course may be taken, it does not seem probable that the mind always goes back to concrete particulars to make its generalisations; but, on the contrary, that it avails itself of generalisations and integrations already made and passes from them to higher ones. Certainly there is very often no conscious traceable reference to particulars in the concrete, although of course concrete particulars are always implied as ultimate foundations.

§ 23. Every abstract can be rendered into its corresponding concept, based upon concrete particulars, and these particulars alone have external reality; an abstract has no meaning without a reference to those experiences that are the concrete foundations upon which these high and sometimes fragile structures are built. Hence the mind is perpetually running back to concrete particulars for verification. Whiteness very readily is run into white, and white referred to some particular objective experiences. Coldness becomes cold; goodness, good; jealousy, jealous; time, past, present, and future. The concept has a closer relation to the concrete particulars, and brings them up more directly upon occasion, and all abstracts have parallel concepts. But not every concept has a corresponding abstract to which a name is given. The use of abstract names depends upon necessity and convenience, and often there seems to be no need for employing the abstract in the process of thought, or the mind has not advanced to the stage of integration of its products which develops a particular abstract into distinct form for preservation. There seems to have been abundant use for an abstract of which man is the concrete concept; but there is no word in English to express the corresponding abstract of dog; canininity or dogginess would sound strange to our ears. To essay the expression of an abstract of anthropomorphous would only result in a clumsy aggregation of syllables.

§ 24. Abstracts are the highest and most complex products of generalisation of single cognitions. There seems to be no limit to which they may be carried, but their construction, high development, and employment, are regulated largely by the frequency with which the concretes upon which they are based are represented to the mind, and by the relative importance of the place which the latter fill in mental operations. Abstracts are exhibited in actual thought with concepts, percepts, and re-percepts, in great variety of alternation, conjunction, composition, and integration.

§ 25. To recapitulate, in conclusion, the classifications of this chapter, we find that concepts are General Notions, and are

Concepts in Extension, or Concepts in Intension.

Concepts of the First Intention or of the Second Intention. Concrete Concepts or Abstract Concepts.

Real Concepts or Fictitious Concepts.

Double Concepts (or relatively Single Concepts).

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.

§ 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. Fa instance, when Napoleon first beheld Moscow from a distance, be 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 AU 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;