will neither increase nor decrease, if the circle A increases by the birth, manufacture, or discovery of new individuals possessing the attributes a, b, c of the class.

The denotation and the connotation of a term are not absolutely fixed. Both may increase or decrease with the advance of knowledge. Given the connotation of a term, its denotation is more or less indefinite. Given the denotation, the connotation is more or less indefinite. Suppose, for example, that the term 'metal' has for its connotation the three attributes a, b, c, what is then its denotation? Every individual thing that possesses those three attributes. Not only the metals at present known but all substances that may hereafter be found to possess those three attributes, will be included in its denotation; thus the circle representing the denotation of the term 'metal' may go on increasing with the progress of discovery in chemistry. Or some substances that are now recognized as metals may turn out to be compound; and thus the circle may decrease in extent with the progress of chemical analysis. Suppose, on the other hand, that the denotation of the term 'metal' is fixed and definite, that is, consists of a certain number of known elements, and is represented by a certain circle, what is then its connotation? The attributes connotated by the term 'metal,' and possessed in common by all the substances denoted by it. Now, these attributes may increase in number with the progress of chemical knowledge, and the term 'metal' may afterwards come to connote many attributes which it does not at present. Thus, both the denotation and the connotation of a term may vary with the increase of knowledge.

§ 4. Exercises :—

1. Describe the change in the denotation and connotation of each of the terms in the following series as you pass from the 1st to the 2nd, from the 2nd to the 3rd, and so forth, and, again, in the reverse order, as you pass from the last to the last but one, and so on.

i. Element, metal, gold.

ii. Animal, man, Englishman.

iii. Right-angled triangle, triangle, rectilineal figure, figure.

iv. Literature, English literature, philosophical literature in

English.

v. Force, gravity, the mutual attraction of the sun and the earth.

vi. Solid, stone, precious stone, ruby.

vii. Rock, igneous rock, volcanic rock, pumice.

2. Give as many examples as you can of series of three, four, or more terms each, in which each term of greater extension stands before a term of less extension.

3. "The denotation and the connotation of a term vary inversely." Explain and criticise this statement.

4. Can you give any example of terms whose denotation may increase without any change in the connotation, and also of terms whose connotation may increase without any change in the denotation?

5. What determines the denotation and the connotation of a term? Has every term a denotation and a connotation?

§ 5. If a number of terms be related to one another as represented in this figure,—

containing and the contained term are called respectively genus and species in relation to each other. The distinction between them is however relative, for the same term may be a genus in relation to one, and a species in relation to another; here, for instance, B is a genus in relation to A, and a species in relation

to C. The attribute 'b' is called the differentia of the species B in relation to the genus C, and the attribute 'c' the differentia of the species A in relation to the genus B. The differentia of a species is that attribute which being added to the connotation of the genus gives the connotation of the species; here the attribute 'b' being added to 'a' the connotation of the genus C, gives ab, the connotation of the species B, and is thus the differentia of the species B. By the differentia a species is distinguished from the other species contained in the same genus; C as a genus, for example, contains two species B and not-B, that is, those C's that are B, and those C's that are not-B; and by the differentia 'b' the species B is distinguished from the other species not-B contained in the same genus C. The two species B and not-B included in the genus C are called co-ordinate species. In the figure on page 54, the three subclasses A, B and C contained in the class G are, similarly, co-ordinate species of the genus G; and the terms A, B, and C are called co-ordinate in relation to each other and subordinate in relation to G, while G is called super-ordinate in relation to them. C and not-C are called contradictory terms or concepts, not-C including everything except C: that is, C and not-C cover the whole sphere of thought and existence; every thing and every thought is included in either C or not-C. A and not-A, B and not-B, taking not-A and not-B in their widest sense, are also contradictory terms, and cover the whole sphere of thought and existence. Two contradictory terms are so related to each other, that both can be neither affirmed nor denied of one and the same thing, that if one be true, the other must be false, and if one be false, the other must be true, of one and the same thing. For example, both the terms 'organized being' and 'not-organized being' cannot be affirmed of one and the same thing, nor can both be denied of it; if 'organized being' be affirmed, 'not-organized being' must be denied, and if the latter be affirmed, the former must be denied, of a thing; for every possible thing must fall into one or other of the two comprehensive classes which divide between them the whole

sphere of thought and existence; a thing not included in one or other of the two all-embracing classes, has existence neither in nature nor in thought. But if two terms be so related to each other, that both cannot be affirmed, but that both may be denied, of one and the same thing, that if one be true, the other must be false, but, not conversely, if one be false, the other must be true, of it, then they are called contrary terms. For example, of the two terms 'black' and 'white,' if 'black' be affirmed, 'white' must be denied, of one and the same thing, but, not conversely, if 'black' be denied, 'white' must be affirmed, of it, for both may be denied of it, that is, the thing in question may be neither black nor white, but of some other colour or of no colour at all. Thus 'cold' and 'hot,' 'up' and 'down,' 'virtue' and 'vice,' 'light' and 'darkness,' &c., are contrary terms, while 'cold' and 'not-cold,' 'hot' and 'not-hot,' 'light' and 'not-light,' &c., are contradictory terms. Two contrary terms do not completely cover the whole sphere of thought and existence, while two contradictory terms do. The difference between them may be thus shown by diagrams:-Suppose that the whole sphere of thought and existence is represent

ed by the largest circle D, then the two contrary terms 'black' and 'white' are represented by the two small circles, A and B, lying outside each other, but both falling under the circle of colour C, and jointly covering only a part of the largest circle, while the two contra

dictory terms 'black' and

D

A

B

and 'not-black' are represented, respectively, by the small circle A, and the remainder of the largest circle, jointly covering the whole of thought and existence.

Exercises on the Mutual Relations of Terms.

1. Give the genus, species, and differentia of the following terms:

(1) Plant, (2) Figure, (3) Triangle, (4) Body, (5) Metal, (6) Element, (7) Book, (8) Flower, (9) Rock, (10) Mind.

2. Give a subordinate, a super-ordinate, and a co-ordinate of the following terms:

(1) Animal, (2) Solid, (3) Virtue, (4) Rock, (5) Substance. 3. Give the contradictory and a contrary of the following terms:— (1) White, (2) Simple, (3) High, (4) Liquid, (5) Good, (6) Moral, (7) Vice, (8) Mortal, (9) Animal, (10) Mind, (11) Matter, (12) Form, (13) Beautiful.

4. Has every term a genus and species?

§ 6. Division and Definition of Terms :-The orderly statement of the denotation of a term, or the grouping of the denotation into smaller classes according to the presence or absence, or varying degree of an attribute, is the division of the term. And the setting forth of the connotation of a term is its definition, or the definition of the things or class denoted by the term. The definition is more or less complete according as the connotation of a term, or the group of attributes in which the things agree, is more or less exhaustive. The definition of a

term, being a statement of its connotation, varies with any change in the latter. The division of a term likewise varies with its denotation. With the increase in denotation the sub-classes increase in number or in extent. If A, B, C are smaller classes under G, and if G is enlarged into G', A, B, C will no longer cover the whole extent. They must increase

in extent as represented by the dotted lines, or the larger class