have no intension. Strictly speaking they have intension, if they are general, but an intension expressed only by the name of the attribute itself. The abstracts agree in that which is the attribute; they differ by the presence of that which is not the attribute. We characterise the points of agreement (which constitute the intension) only by the name of the abstract; the points of difference (by which we are able to develop an extension) are marked by any thing that will serve to make a separation. Thus we may explicate whiteness by enumerating in the order of extension, whiteness No. 1, whiteness No. 2, whiteness No. 3, etc.; or milky whiteness, marble whiteness, dull whiteness, polished whiteness, etc. In generalising simple concrete objects we have differences primarily and agreements secondarily; we assemble and unite the agreements which thus together form the intension, leaving the differences to mark the extension; on the other hand, in generalising abstracts we have agreements primarily and differences secondarily; we mark the differences and place them in an order to give the extension, leaving the agreements to constitute the intension. But since there is really no intension which is other than the attribute itself, and only by a subtlety of thought can we detect it at all, and it is of no separate use or character when detected, we can consider and treat all such abstracts as without intension unless there be something more than has been thus far noticed. The following diagram may serve to make plainer what has been said in this connection :

The differences are seen to be those of extension, the agreement to be in that which gives name to the abstract, and this agreement constitutes all there is of the intension; for the latter we are in

§ 21. But frequently there is something more than has been noticed; some abstracts have an intension capable of separate denomination. Such are those out of which higher abstracts are developed. It is observable, for instance, that honesty, courage, temperance, justice, have certain points of agreement, which may be marked by the term virtuous; out of which is prescinded the abstract virtue. Virtuous, then, is an intension of honesty, courage, etc., and virtue has for its extension honesty, courage, temperance, and so on. The following illustration may be useful:

It will be noticed that here, in contrast with the generalisation exhibited in § 8, all the particulars constituting honesty, courage, etc., have the mark virtuous; we do not say virtuous honesty (except to indicate degree), but honesty is virtuous. The completion of the process of forming the higher abstract is given in the two lower figures, and that process is but a repetition of the one exemplified by the figures in §§ 15 and 20. Honest virtue is equivalent to honesty, courageous virtue to courage, and so forth.

Sometimes we are unable to trace an intermediate abstractconcept, but the mind seems to leap from one abstract to

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

§ 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.

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