VII. (1) Strong, (2) strength, (3) the strong, (4) strong man, (5) strength of character, (6) this strong man.

VIII. (1) Element, (2) elementary. (3) elementary attribute, (4) elementary substance, (5) the Elements of Euclid,' (6)

a chemical element.

IX. (1) Plant, (2) figure, (3) inconvenient, (4) blindness, (5) business, (6) universe, (7) heat.

X. (1) Multitude, (2) the first emperor, (3) irreligious, (4) virtue, (5) mind, (6) matter, (7) body, (8) form.

XI. (1) Atmospheric air, (2) organization, (3) life, (4) force, (5) time, (6) space, (7) cause, (8) motion, (9) substance, (10) being, (11) something, (12) nothing.

XII. (1) Sense, (2) rest, (3) speed, (4) law, (5) the circle of sciences, (6) gravity, (7) spirit, (8) higher, (9) right, (10) sen

sation, (11) knowledge, (12) feeling, (13) perception, (14) smell, (15) vision, (16) taste, (17) colour, (18) relative. XIII. (1) His Majesty, (2) His Honour, (3) Her Serene Highness, (4) elementary atoms, (5) the passage of water to the state of ice, (6) soluble in water, (7) the surfaces of bodies, (8) the number of the metals, (9) the gaseous envelope encircling the earth, (10) the theory of ideas, (11) the undulatory theory of light, (12) to reason against any of these kinds of evidence, (13) the yellowness of gold, (14) the lightest substance known, (15) the perception of the external world, (16) consciousness.

XIV. (1)

"The place which the wisdom or policy of antiquity had destined for the residence of the Abyssinian princes." (2) To attend accurately to the operation of our minds. (3) The ignition of phosphorus.

(4) A just interpretation of nature.

(5) A series of electric discharges.

XV. (1) Co-existence, (2) succession, (3) identity, (4) resemblance,

(5) causation, (6) equality, (7) relation, (8) subsistence.

CHAPTER II.

THE DENOTATION AND CONNOTATION, DIVISION AND DEFINITION, OF TERMS.

§ 1. IN the preceding chapter, we have seen that most terms denote or signify directly things, and connote or imply attributes belonging to them, that is, have, at the same time, two meanings, of which one is called their denotation, and the other their connotation. The denotation of a term consists of the individual things to each of which the term is, in the same sense, applicable. The connotation of a term consists of the attribute or collection of attributes implied by the term, and possessed by each of the individual things denoted by it. For example, the denotation of the term 'man' consists of all the individual things, called 'men,' whether now living or dead,—of all things, in fact, to which the term 'man' is applicable; while its connotation consists of the attributes, say 'animality' and 'rationality,' implied by it, and possessed in common by all men. The denotation of the term 'book' consists of all the various kinds of books written in all languages throughout the world, while its connotation consists of the attribute or attributes which all books possess in common, and which are implied by the term 'book.' The term 'triangle' in denotation signifies all the different kinds of triangles,-the individual things called triangles, while in connotation it signifies the attribute possessed in common by all triangles, namely, the attribute of being bounded by three lines.

CHAP. II.] DENOTATION AND CONNOTATION OF TERMS. 47

When a term signifies an individual, i. e., has for its denotation only a single object or thing, its connotation is the group of attributes possessed by the individual thing, and signified by the term. For example, the term 'the sun' has for its denotation one individual thing only, while its connotation consists of the attributes possessed by that individual thing, and implied by the term; the term 'the present Prime Minister of England' denotes an individual person, and connotes 'the attribute of being the Prime Minister of England'; the term 'the father of Socrates's denotes a person, and implies 'the attribute of being Socrates's father'; thus all singular terms have both a denotation and a connotation, proper names alone, according to Mill, being excepted. We have already alluded to the difference of view among logicians on this point, and need not here revert to it.

§ 2. The denotation and the connotation of a term have a close relation to each other. When the denotation of a term is increased or decreased, its connotation is decreased or increased; again, when the connotation of a term is increased or decreased, its denotation is decreased or increased. If you add a new group of things to the group denoted by a term, you subtract one or more attributes from its connotation. Include a new class within a class signified by a term, and its connotation will lose a part of its meaning, that is, the attributes possessed in common by all the individuals of the enlarged class will be fewer in number than before. The term 'man' has for its denotation the group of animals called men, and for its connotation the two attributes, 'animality' and 'rationality.' If its denotation is enlarged by including in it 'irrational animals' or all other animals than man, its connotation will no longer be the same as before, but consist of that attribute only which is possessed by all the members of the newly formed enlarged class, namely, the attribute 'animality,' and thus lose the other attribute 'rationality.' The term 'triangle' will likewise lose an attribute-'three sidedness' -from its connotation, when new groups or classes, such as 'quadrilaterals' and 'multilaterals,' are added to its denotation. The term 'animal' will lose such attributes as sensibility, loco

motion, &c., from its connotation, when its denotation is enlarged so as to include 'plants' in its sphere, the new denotation and connotation giving rise to the new term 'organized being.' This term will again lose a part of its connotation, when its denotation is enlarged by the addition of ‘inorganic things,' the increased denotation and the decreased connotation giving rise to the term 'material being' or 'body,' including inorganic as well as organic beings. Thus, we see that addition to the denotation of a term implies subtraction from its connotation, and that the new class thus produced is generally signified by a new term with a smaller connotation. Similarly, it can be shown that, when the denotation of a term is decreased, its connotation is increased. Again, if you add a new attribute to the attribute connoted by a term, you subtract a group of things from its denotation. The examples we have just given illustrate this. Add the attribute 'organization' to the connotation of the term ' material body,' the attribute 'sensibility' to the connotation of the term 'organized being,' the attribute 'rationality' to the connotation of the term 'animal,' the attribute 'three-sidedness' to the connotation of the term 'rectilineal figure'; and, in each case, the denotation of the corresponding term is decreased, that is, a smaller number of things possess the added attributes; and the increased connotation and the decreased denotation give rise to a new term. Similarly, it can be shown that, when the connotation of a term is decreased, its denotation is increased.

§ 3. The relation between the denotation and the connotation of a term may be explained by figures as follows:

Let A, B, C, D, be four terms, their denotations being represented by the circles A, B, C, D, and their connotations by the

small letters in them. First, if the things represented by A, and those by B, be brought under one class, the connotation of the class-name or general term will be the two attributes, a and b, common to A and B. Again, if C and D be brought together under a new class, the connotation of the name of this class will be the two attributes, a and e, common to C and D. Similarly, if the denotation of the two new classes be brought together to form a still larger class, the connotation of the name of this larger class will be still smaller, the attribute a being the only one common to all the circles.

Secondly, if the connotation of the highest class M, be increased by b, then its denotation will be only A + B, or

M−(C+D); and if by e, then its denotation will be C+D, or M-(A+B); that is, addition to the connotation of a term causes subtraction from its denotation. Again, if the connotation of A+B be increased by c, then its denotation will be only A, or A+B-B; if by d, then only B, and so forth.

It should be observed that the denotation of a term will neither increase nor decrease, if its connotation increases by any attributes that are found to be possessed by all the members of the class, or that follow from any part of the connotation. Thus, there will be no alteration in the size of the circle A, if the attributes m and n be added to a, b, c, provided that m and n are found to be possessed by all A, or follow from a, b, c. Similarly, the connotation will remain unaltered, if the circle is enlarged by the addition of any individuals that are found to possess the known marks or attributes of the class. Thus a, b, c