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.

SECTION CCCCXLVII.-EXAMPLES.

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.

SECTION CCCCXLVIII.-DEFINITION.

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 ORGANISED 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 "difference an Art," and of its as 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.

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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, &c.

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 is, described, as

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Species.

Inseparable accidents.

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.

Analyse 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 :

An island,

A garden,

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 generalisation? and division, with the rules? and definition, with the rules?

CHAPTER III.

SECTION CCCCXLIX.--THE PROPOSITION.

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 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 Section CCCCLII.

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 honourable ; -was a coward.

SECTION CCCCL.-THE PARTS OF A PROPOSITION NOT MORE THAN THREE.

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 traveller, (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, &c. 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 other words, a whole proposition may enter into the structure of manyworded names, e. g.:—

1. The man (is) returning,

2. Who was sent to market.

Combine these and they form but a single designation or name. Thus, the man who was sent to market (is) returning. The words, the man who was sent to market, form but a single name or term. See LATHAM's Outlines.

SECTION CCCCLI.-THE PARTS OF A PROPOSITION NOT FEWER THAN THREE.

Apparent contradictions to the statement that the parts of a Proposition are not fewer than three, are of two sorts. The first is referable to the practice of language, more or less general; the second to the seeming properties of the copula.

1. a. The Predicate and Copula may be contained in one word; e. g., instead of saying fire is burning, we may say, as we generally do, fire burns. In this case the grammatical form of the proposition does not coincide with the logical form; nevertheless, as it is clear that the shorter and more compendious form is capable of being resolved into the longer one, the statement, that the parts of a proposition are no fewer than three, may still hold good.

b. The Subject and Copula may be contained in one word. The Latin proposition, est bonus he is good, exemplifies this.

c. The Subject, Copula, and Predicate may be contained in one word, as in the Latin voco = I am calling.

It

2. The seeming properties of the Copula.-Many logicians have considered that, when the predicate implies simple existence, it is expressed by the copula alone, as in such expressions as God is. This error arises from the word is being a copula and something more. superadds to its power of denoting the agreement or disagreement between the subject and predicate the notion of existence. The essentially relative character of the copula is, moreover, a proof of the erroneousness of the view indicated.

In the Hebrew language the copula is commonly omitted, and in the Greek this is very often the case. This is merely one proof out of many that the structure of propositions in language does not always coincide with the structure of propositions in logic.

Questions of Appeal are implied propositions, being plainly equivalent either to affirmative or negative ones. Thus, "Who would be insane enough, without the hope of future recompense, to undertake constant labour?" is equivalent to "No one would be (insane enough, without the hope of future recompense, to undertake constant labour).'

be

Propositions which do not explicitly contain the copula may easily resolved into those which do. Thus, "Gold surpasses all metals in brilliancy" may be stated, "Gold is superior to all metals in brilliancy." In this case we distinguish the copula from the predicate.

1. Where the substantive verb is introduced by the adverb there, it is itself both copula and predicate, being equivalent to exist: "There is no flesh in man's obdurate heart." See Section DVI.

2. The subject will sometimes succeed the predicate, though its common order is to precede it. In this case it is often represented at the beginning of the sentence by the pronoun it; as, It is (to be hoped) that we shall succeed. Hence it represents the subject that we shall succeed.

EXERCISE I.

Point out the Subject and the Predicate in the following examples :

1. (To tell all that we think) is inexpedient.

2. Better (to reign in hell than serve in heaven)."

3. It is unlawful to kill an innocent man.

4. Rising early is healthful.

5. There is (no such thing as witchcraft).

6. There can be no natural desire of artificial good.

7. "Sweet is the breath of morn."

EXERCISE II.

Express the following propositions in strict logical form, making the Copula, when necessary, apparent, and distinguish the Subject and Predicate :

1. Are such abilities as those of man made for no purpose?

2. Remorse follows disobedience.

3. A philosopher should understand Geometry.

4. True friendship has a tendency to secure veracity.

5. Who is pleased to have his all neglected?