or, in other words, are formed on several distinct principles of Division.

III. A Division should not be arbitrary; that is, its members should be distinguished from each other by "Differences" either expressed or readily understood, instead of being set apart from each other at random, or without sufficient ground.

IV. A Division should be clearly arranged as to its Members. Three rules are to be observed in correct division: 1. The constituent species, called the dividing members, must exclude one another. 2. The constituent species must be equal, together, to the genus divided. 3. The division must be made according to one principle.

EXAMPLES.

§ 447. Goodness of Memory may be divided into Susceptibility, retentiveness, readiness.-DUGALD STEWART.

Happiness consists in, 1. The exercise of the social affections. 2. The exercise of our faculties in some engaging end. 3. The prudent constitution of the habits. 4. Health.-PALEY.

Distinguish by the proper conjunctions, viz., either and or, the cross divisions in the following enumerations:

1. Men are Merchants, farmers, lawyers, negroes, whites, Pagans, Christians.

2. Substantives are Masculine, feminine, proper, common. 3. Verbs are Transitive, Intransitive, principal, auxiliary, Substantive, Adjective.

DEFINITION.

§ 448. Logical DEFINITION always consists of the Genus and Differentia. The former serves to mark the points in which it

agrees with others of the same kind, the latter those in which it differs from them. A plant would Logically be defined an orGANIZED BEING, destitute of sensation; the former of these expressions denoting the Genus, the latter the Difference, which are the parts of which Logic considers every species as consisting, and which are evidently separable by the mind alone. Thus, if Logic were defined to be the Art of Reasoning, we should explain this definition to consist in the statement of its "Genus" as "an Art," and of its "difference" as the art of Reasoning."

This is accounted the most perfect and proper kind of Definition. The "Genus" and "Difference" are called technically the "metaphysical parts," as not being parts into which an individual object can be actually divided.

What is called a PHYSICAL DEFINITION is made by an enumeration of such parts of some object as are actually separable; as a Tree, for instance, is defined by an enumeration of the root, trunk, branches, bark, leaves, flower, etc.

A Definition which is made by enumerating several Properties, or, in the case of an individual, Inseparable accidents, is called a DESCRIPTION, or, according to some writers, an Accidental Definition. An Individual can be defined only by a description, that is, by stating the Species and the Inseparable accidents. Thus "Alexander the Great" would be Defined, that

Species.

Inseparable accidents.

is, described, as "a king" "of Macedon who subdued Persia." Definitions have been distinguished into nominal and real. A Nominal definition explains merely the meaning of the word defined. A Real definition explains the nature of the thing signified by the word. They sometimes coincide; as, for instance, in the case of the circle, and so of scientific terms generally, where the meaning of the name and the nature of the thing are one and the same. They, however, often differ, as they do when the object defined has an actual real existence in nature independently of our thoughts, and which, therefore, may possess attributes not implied by the meaning which we attach to the name, and which are to be discovered by observations and experiments. Thus a real definition of a Diamond or a Planet would extend much beyond a Nominal definition of the same.

The Rules for framing a Definition are,

I. That a Definition should be adequate, comprehending neither more nor less than the Term to be defined. For instance, if, in a definition of "Money," you should specify its being "made of metal," that would be too narrow, as excluding the shells used as money in some parts of Africa. If, on the other hand, you should define it as an "article of value given in exchange for something else," that would be too wide, as it would include things exchanged by barter.

II. A Definition should be clearer than the Term defined; clearer, that is, to the persons you are speaking to.

EXERCISE I.

Analyze into their respective "Genera" and "differences" the following definitions of terms:

1. A meadow is a field devoted to pasturage.
2. A pension is an allowance for past services.
3. Rhetoric is the art of speaking persuasively.
4. Bigotry is exclusive attachment to party.

EXERCISE II.

Define, by "Genus" and "difference," the following terms:

QUESTIONS UNDER CHAPTER II.

1. What is the origin and meaning of the word term?

2. Mention the several kinds of terms, and define them.

3. Are terms limited to single words, or are they often made up of several words?

4. Mention the five predicables, and give an instance of each.

5. Of what does the species consist as related to the genus?

6. What is abstraction? and generalization? and division, with the rules? and definition, with the rules?

CHAPTER III.

THE PROPOSITION.

$449. A PROPOSITION is a sentence in which something is affirmed or denied of something else. A proposition defined logically is a "Sentence assertive," i. e., affirming or denying, "Sentence" being the Genus, and "assertive" the difference. This definition expresses the whole essence, and it relates entirely to the words of a proposition.

In a proposition there are two somethings, the something spoken about and the something said concerning it. Thus, in the proposition Gold is yellow, the quality, property, or attribute expressed by the word yellow is affirmed of the substance gold, so that yellow is one part of the proposition, and gold another.

Again, in the proposition ice is not hot, the property, quality, or attribute expressed by the word hot is denied of ice. Ice, therefore, is one part of the proposition, and hot another.

But to say Gold yellow is to employ words to no purpose. The combination conveys no meaning. There are only two separate somethings. The expression is imperfect. It needs a bond. to connect them together.

Hence every proposition consists of three parts:

I. The SUBJECT. The thing concerning which we make a statement, whether in the way of affirmation or denial, is called the Subject. In the examples above, gold, ice, are subjects, and we can assert of them that they are yellow or hot, or else that they are not so, i. e., that they are not yellow, not hot. In the first case, the proposition is Affirmative; in the second, Negative.

II. The PREDICATE. The thing which we connect with the subject is the Predicate: Yellow, hot, are predicates. They are asserted or predicated of the subjects gold, ice.

III. The COPULA. That part of a proposition which connects the subject and predicate is called the Copula. It is the word which serves as a sign to denote the existence of either an affirmation or a denial. Man-mortal: Each of these words now stands isolated from the other. Place between them the magical

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word is, and the twain become one proposition. In this case the copula is affirmative. In the proposition man is not mortal, the copula is negative. See § 452.

EXERCISE.

Form propositions by supplying the parts that are wanting in the following pairs: 1. The Copula to the subject and predicate: Summer-pleasant; Autumn-sober; Winter-sighing; Spring-a season. 2. The Predicate to the subject and copula: The air is; The sky is—; The snow was—; The storm was-. 3. The Subject to the copula and predicate: —is brave; -was a hero; -is honorable; was a coward.

THE PARTS OF A PROPOSITION NOT MORE THAN

THREE.

§ 450. In the proposition the sun (is) shining, we have a Simple proposition. We readily see that there are but three parts. But it must be evident to every one who reflects upon either what he hears or reads, that propositions are in reality much less simple than they have been described as being. If propositions are so short, how is it that sentences are so long? If subjects and predicates are so simple, how became periods so complex ?

The fact is, that both subjects and predicates may be made complex by the addition of subordinate parts. A term may consist of several words:

The sun (is) shining.

The early sun (is) brightly shining.

The early sun, with glad beams, (is) brightly shining through the air.

The early sun, with glad beams, having awakened the traveler, (is) brightly shining through the air upon his path.

Terms like those of the last three examples are called Mixed terms. The objects which they express are called objects of complex Apprehension, in opposition to objects of simple apprehension, like the sun, etc. The names of objects of complex apprehension (i. e., mixed terms) are sometimes called Many-worded Names.

Again, one proposition may be subordinate to another; in