§ 3. We note one other distinction between concepts viewed intensively. As comprehended, they are either involved or co-ordinate. One concept involves another when the latter forms a part of the sum of the marks constituting the comprehension of the former. Two concepts are co-ordinate when they are coexclusive, and both immediately comprehended in the same lower concept.

For example: Socrates involves both famous and Athenian. These are co-ordinate. But Athenian further involves Greek; and Greek, European; and European, human. It is evident that these latter notions are not equally proximate and immediate in "Socrates," that some are given only through others, and that they are to cach other in the relation of part and whole. Thus thought evolves the simple out of the complex; and the perfecting of knowledge consists in this progressive unfolding into clear and distinct consciousness the intension of notions originally obscure and confused.

In speaking of concepts as involving, and of marks as parts of a whole, these words are used in a peculiar sense. The parts are not partes extra partes, for each mark permeates and informs the whole concept. Thus when I think of chalk as both white and brittle, the whiteness and the brittleness are thought to coexist throughout.

§ 4. We now pass to a consideration of the relations of concepts in the quantity of extension, which, however, be it constantly kept in mind, is but a different aspect of the same thing. These relations are of three sorts, inclusion, intersection, and exclusion.

1st. Of Inclusion. One concept is included in another when the sphere or extent of the one coincides with, or is contained under, that of the other. There are two cases of inclusion:

(a.) Coextension; as when the spheres coincide or are common. (b.) Subordination; as when one is contained under the other, as a species under a genus, or as an individual under a species. 2d. Of Intersection. Two concepts intersect when their spheres have a common part, and each a part not common.

3d. Of Exclusion. One concept is excluded from another when their spheres have no part common. There are two cases of exclusion: (a.) Co-ordination; as when, though mutually exclusive, both are immediately contained under the same concept.

(b.) Non-co-ordination; as when, while mutually exclusive, they are not both immediately contained under the same concept.

LIN

2

RELATION.

UNIVERSITY

CALIFORNA

43

Let us now restate the above, and symbolize by Euler's circular notation, in which the sphere of a concept is represented by a circle ; and also by Hamilton's linear notation, in which the extent of a concept is represented by a horizontal line; the relation of two or more, by such lines standing one under the other, and by their comparatively greater or less extent; affirmation being expressed by a vertical line joining two horizontal ones; negation, by the absence of such connection.

Of these relations there are only three that call for special remark, -subordination, intersection, and co-ordination. Subordination will be treated at once; intersection under the topic Definition; and coordination under Division.

§ 5. When one concept is subordinate to or contained under another, it differs from the higher concept by comprehending more

2 The invention of this method of sensualizing the logical relations of concepts by circles is usually attributed to Euler, who made use of it in his Lettres à une Princesse d'Allemagne, 1768. It is found, however, in a posthumous work of Christian Weise, Rector of Zittau, who died in 1708. Ploucquet employed the square, and Maass the triangle, instead of the circle.-Drobisch's Logic, § 84; see also Thomson's Outline, § 104; and Hamilton's Logic, pp. 133 and 180.

3 This is a modification and an improvement of Lambert's linear notation as found in his Neues Organon, 1764. It is to be preferred to the circular notation. Both represent only relations in extension, not those in intension, and therefore, though convenient and helpful, are inadequate. See Hamilton's Logic, p. 670 sq.

marks and by extending to fewer individuals. It is called a species. Thus sword is a species of weapon; man is a species of animal. Sword is contained under weapon; it comprehends more marks, but it extends to fewer things; it is the narrower notion. The superior concept, since it contains under it more things, is the more general notion, and hence is called the genus. Thus weapon is the genus of sword; animal is the genus of man. The notion animal extends to

many things besides men; it is the broader notion.

It is manifest that genus and species are merely relative terms; for the genus may be contained under some higher concept, and then relative to this higher genus it is a species. Thus weapon is a species of the genus instrument. Of course the species may contain under it some lower concept, and then become the genus of that lower species. Thus sword is a genus containing under it the lower species sabre, rapier, etc. A concept that is alternately a genus relative to lower concepts, and a species relative to some higher concept, is called a subaltern genus.

A genus is a universal notion, or a universe, because it binds a plurality of parts into the unity of a whole. This is the logical, direct from the etymological, meaning of universe, ad unum versus. A universe, then, means, strictly, E pluribus unum. It is called, by way of eminence, the Logical Whole. A species, since it is but a part of this whole, is a particular notion. We should distinguish between the usual meaning of universe, as that unlimited highest genus which comprises all things in one, and universe considered as a limited genus which unites only some things.

A universe or genus is usually present to the mind of a speaker, within which his thoughts revolve, and under which, often without naming it, he is bringing in his statements. If we apprehend his assumed universe, we may follow and understand his thoughts; if not, confusion is inevitable from the ambiguities of language. Thus the word "civil" has many meanings; it is opposed to "natural," to military," to "ecclesiastical," to "discourteous," and so on. Now if "civil service" be spoken of, and it is apprehended that the talk is under the tacitly implied universe of "the departments of government," then we understand that it is intended to exclude "military" and "ecclesiastical," and confusion is avoided. In rude parlance we

3 "Universale totum quoddam est; quippe multa complectitur ut partes. Dicitur totum logicum, quia logicæ munus est de universis disputare.”—Burgersdyck.

say, we must know what, in general, one is talking about, in order to understand his particular statements.

Both genera and species are called classes, and the arrangement of things according to genera and species is called classification. The psychological process by which we classify has been somewhat anticipated in the account given of generalization and specialization, which terms are synonymous with generification and specification. When we think the similar to be the same, we form a genus including all the similar things. Thus in contemplating man and brute we experience the shock of similarity; we abstract from each what is similar; we think it the same, or common to both; we give it a name, and thus establish the class, the genus, animal, containing under it man and brute as species. On the other hand, when we think the dissimilar to be diverse, we form a species, excluding a portion of the things considered. Thus in contemplating animals we experience the shock of dissimilarity; we abstract from man the quality rational, which marks the diversity; we affirm it of man and deny it of the rest. Thus we establish two species of animals, the rational and the irrational, or men and brutes.

Finally, the species as parts make up the genus as a whole. These are partes extra partes, for they do not coexist, as do marks, but are actually separable groups of things; c. g., diamonds and rubies are species of jewels. Consequently, it is possible to symbolize geometrically, by circles or lines, the relations of concepts viewed in extension, which is not practicable when they are viewed in intension.

§ 6. It should be observed that subordination in the quantity of extension corresponds to involution in the quantity of intension. Also while the term generalization is applicable to either quantity, the term specification relates to extension, and corresponds to the intensive term determination. For determination is a thinking in, a synthesis, a concretion of marks, and this, since it throws out things, specifies a concept. Determination, then, restricts the denotation by amplifying the connotation, and terminates only in individualization.

Ac

§ 7. Many concepts are related to each other as correlatives. cording to the Law of Relativity, knowledge always includes two things. We know heat by transition from cold; light by passing out of the dark; up by contrast to down. There is no such thing as an absolute knowledge of any one property; we could not know mo

tion if we were debarred from knowing rest; our first parents had no knowledge of good until it was "bought dear by knowing ill." We may be thinking more of one member of the couple than of the other, of the heat rather than of the cold, of the straight line rather than of the crooked; but if either exists, the other always coexists with it in consciousness. The one is the explicit, the other the implicit, subject of the thought.

This would seem to occasion double names throughout all the universe of things, and language, if complete, would contain no single names, but consist of couples. Accordingly we find a great many couples, specifically called "Correlative Terms," in each of which, if either member be expressed, the other is implied; as "Parent and child," "Ruler and subject," "Cause and effect," "Heavy and light," "Rich and poor," "Genus and species," "Positive and negative."

The last example, "Positive and negative," "To affirm and to deny," is probably the basis, or origin, and the generalization of all the rest. One of the two has usually more or less of a negative character; and in cases where names have not been adopted for both correlatives, one exists in thought as a negative. Hence for every positive concrete name a corresponding negative may be framed as correlative to it by attaching a negative particle, such as the prefixes un-, in-, and the suffix -less; as "Conscious and unconscious," "Temperate and intemperate," "Godly and godless," "A and non-A."

§ 8. Another mode in which concepts are related is expressed by the old and almost disused logical terms First Intention and Second Intention. A first notion or intention is a concept of things formed by the first or direct application of the mind to the object. It denotes things. The concepts which we have been using as illustrations are all first intentions. The object Socrates is regarded by the mind as Greek, man, animal, body, etc. A mental state may be thought as a smell, a sensation, a feeling, a consciousness. All these are first intentions. A second notion or intention is a concept generalized from first intentions. It denotes first intentions or concepts of things. It is the conception under which the mind regards its first intentions as related to each other. Thus the relation of animal to man, and of

'See Bain's Logic, p. 2 and p. 55.

In-tendere. "Ego dico intentionem nil aliud esse quam attentionem ac diligentiam animæ in alicujus rei consideratione."-Zabarella, De Reb. Nat. p. 871.