SECTION CCCCLII.-DIVISION OF PROPOSITIONS.

1. CATEGORICAL Propositions are those which are expressed absolutely; as, Cæsar was a tyrant.

HYPOTHETICAL Propositions are those which are expressed conditionally; as, If Caesar was a tyrant, he deserved death.

2. Propositions are divided, according to their Quality, into AFFIRMATIVE and NEGATIVE; as Birds fly; man is not perfect. An affirmative proposition is one whose copula is affirmative, as in the first example. A negative proposition is one whose copula is negative, as in the second example.

3. Propositions are divided, according to their Quantity, into UNIVERSAL and PARTICULAR; as, England is an island; All tyrants are miserable; No spendthrift is happy. These are Universal propositions. The Subject in each of these propositions is taken Universally, as standing for anything and everything that the term is capable of being applied to in the same sense. A term so taken is said to be

"distributed."

Some islands are fertile; All tyrants are not assassinated, are Particular propositions. The Subject in each of these propositions is taken Particularly, as standing only for part of the things signified by it, and the term is said to be UNDISTRIBUTED. The words all, every, as in the last example, when prefixed to Negative propositions, are not to be considered as signs of universality. For all tyrants are not assassinated is equivalent to some tyrants are not assassinated. This last is evidently a Particular and not a Universal proposition. Singular propositions, as when a proper name is used, are reckoned as Universals; as, Brutus was a Roman, i. e., the whole of Brutus. 1. A Universal Affirmative: All cowards are cruel. U. A. 2. A Universal Negative: No coward is cruel. U. N.

3. A Particular Affirmative: Some kings are assassinated. P. A. 4. A Particular Negative: All kings are not assassinated. P. N.

EXERCISES.

Give the names of the following propositions :

1. Cicero was an eloquent patriot.

2. If Cicero was a patriot, he ought not to have been put to death.

3. Whoever is capable of deliberate crime is responsible.

4. No one is gratuitously wicked.

5. All the accused were not guilty.

6. Some blacks are civilised.

SECTION CCCCLIII.-DISTRIBUTION.

When a term, or general name, stands for each and every individual which it denotes, it is said to be DISTRIBUTED. It is equivalent to the phrase taken universally." Thus, in the proposition All men are mortal, the Subject, man, is distributed, because mor tality is affirmed of each and every man. The Predicate, mortal, is not distributed, because the only mortals who are spoken of in the proposition are those who happen to be men, while the word, for

aught it appears, may (and in fact does) comprehend under it an indefinite number of objects besides man.

In the proposition Some men are mortal, both the Subject and the Predicate are UNDISTRIBUTED, that is, they are taken particularly; in other words, only in part. In the following, No man is perfect, both the Subject and the Predicate are distributed. Not only is the attribute perfection denied of the entire class, but that class is severed and cast out from the whole of the class perfect, and not merely from some part of that class.

The Predicate of a proposition has no such sign as "all" or "some" affixed to it, which denotes, when affixed to the Subject, the distribution or non-distribution of that term. And yet it is plain that each Term of the proposition, whether subject or predicate, must always be meant to stand either for the whole or for part of what is signified by it, or, in other words, be distributed or undistributed. When I say a is y, the term y is considered as standing for part of the things to which it is applicable; in other words, is undistributed. It makes no difference whether I say "all x" or 22 some x is y. The Predicate is equally undistributed in both cases, the only thing denoted by all and some being the distribution or non-distribution of the Subject.

1. All Universal propositions (and no particular) distribute the Subject.

2. All Negative (and no Affirmative), the Predicate.

EXERCISE.

In which of the following propositions is the Subject, and in which the Predicate, distributed?

1. All men are sinful.

2. Washington was the saviour of his country.

3. No human government allows absolute liberty.

SECTION CCCCLIV.-CONVERSION.

CONVERSION of a proposition is the transposition of the terms. When the Subject is made the Predicate, and the Predicate the Subject, a proposition is said to be converted. No conversion is employed for any logical purpose, unless it be illative, that is, when the truth of the Converse is implied in the given proposition; e. g., No virtuous man is a rebel, therefore

No rebel is a virtuous man.

Some boasters are cowards, therefore
Some cowards are boasters.

Conversion can, then, be illative only when no term is distributed in the Converse which was not distributed in the given proposition. In a Just Definition the terms are exactly equivalent, or, as they are called, convertible terms; it is no matter which is made the subject and which the predicate.

"All equiangular triangles are equilateral, and
All equilateral triangles are equiangular."

Here the terms are convertible.

SECTION CCCCLV.OPPOSITION

Two propositions are said to be OPPOSED to each other when, having the same subject and predicate, they differ in quantity, in quality, or both. It is evident that with any given subject and predicate you may state four distinct propositions, any two of which are said to be opposed; hence there are four kinds of opposition, viz. :1. The two Universal (U. A. and U. N.) are called contraries. 2. The two Particular (P. A. and P. N.), sub-contraries.

3. A Universal Affirmative and a Particular Affirmative (U. A. and P. A.); or a Universal Negative and a Particular Negative (U. N. and P. N.), subalterns.

4. A Universal Affirmative and a Particular Negative (U. A. and P. N.); or a Universal Negative and a Particular Affirmative (U. N. and P. A.), contradictories.

Contrary propositions may both be false, but cannot both be true. Sub-contrary may both be true, but cannot both be false. Of two Sub-alternate propositions, the truth of the Universal proves the truth of the Particular; and the falsity of the particular proves the falsity of the universal, but not vice versa. Of two Contradictory propositions, one must be true and the other false :---

SECTION CCCCLVI.-SIMPLE PROPOSITIONS AND COMPLEX.

In order for a proposition to be SIMPLE, its terms must be simple. The Substantive or pronoun, forming one of them, must be the name of an object of incomplex apprehension. The Adjective or participle, that very often forms one, must also be simple. Finally, the Verb, if it stand instead of a participle and copula, must also be simple. A complex proposition is one which has a complex term, or whose verb, if it stand for both predicate and copula, is modified by some adjunct. See Sections ccccXLII. and DXXXV.

SECTION CCCCLVII.-COMPOUND PROPOSITIONS.

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COMPOUND PROPOSITIONS are those which are made up of two or more subjects or predicates, or both. They are either Conjunctive Disjunctive, according as the connection subsisting between those different subjects or predicates is of a copulative or disjunctive character.

1. He is both a knave and a fool (Conjunctive).
2. Every action is good or bad (Disjunctive).

EXERCISE.

Distinguish the compound propositions from such as are compounded in appearance, and state which of the former are conjunctive and which disjunctive, and point out the complex.

1. Friendship either finds or makes men equal.

2. He who voluntarily lives quite alone must be either more or less than a man. 3. The doctrine which places the chief good in pleasure is unworthy of a philosopher. 4. It is not the cross, but the cause, which makes the martyr.

5. The subject and predicate are both distributed in universal negatives.

6. The sun, moon, and stars cannot all be seen at once.

7. Either this man hath sinned, or his parents.

8. Extreme riches and poverty are alike to be deprecated.

SECTION CCCCLVIII.-INDEFINITE PROPOSITIONS.

some

An INDEFINITE PROPOSITION is one in which it is left undetermined by the form of the expression whether it is to be considered Universal or Particular; as, Birds sing. We may know from facts that this ought to be considered as a particular proposition birds sing, but not from the expression itself. Birds come from eggs." We may know from facts that this ought to be considered as a universal proposition = all birds come from eggs, but not from the expression itself. We are often obliged to judge from the subject matter whether a proposition is Universal or Particular.

SECTION CCCCLIX.-TRIFLING PROPOSITIONS.

TRIFLING PROPOSITIONS are those in which the relation of the Predicate to the Subject is such that to connect the one with the other is to assert little or nothing. They have the grammatical structure of a proposition, but not the logical force of an assertion.

Under the head of such propositions we may class, (1.) All identical propositions, namely, those in which the Predicate is the same as the subject; as, "A triangle is a triangle." (2.) Those in which it is a synonym of it; as, " To pardon is to forgive." Akin to these is the enunciation of truths that are so obvious as to be truisms; as, "Man is rational."

Sometimes, however, identical propositions in form are not trifling propositions, as when an emphasis is thrown upon the copula or the predicate; as, " Home is Home;" "Home is Home;" "I am that I am."

SECTION CCCCLX.-THE RELATION OF THE PROPOSITION TO THE PARTS OF SPEECH.

The Parts of Speech are determined by the structure of propositions; and a word is a Noun, a Conjunction, or a Verb, according to either the place it takes in a proposition, or the relation it bears to one. This will be fully shown from the following statement:

1. Is the Grammatical form of a word a sufficient test? No sub stantive, in the etymological signification of the term, ends in - in Greek, while infinitive verbs do so end. Nevertheless, the infinitive forms, rò plovεiv, év Ty ploviv, are, in value, not verbs, but substan

40 (ENG. LANG. 22.]

tives. For the purposes of Syntax, at least, the logical test, as opposed to the etymological test, is indispensable. This is especially true in the English language, which is more irregular in its etymological forms than the classical languages. In a given case we do not think of saying what part of speech a word is until we have seen it used in a sentence. The etymological form, then, is an insuffi

cient test.

2. Neither is the Phonetic form (i.e., the sound) of a word a test. The same combination of sounds may have a variety of meanings, and may sometimes constitute one part of speech, sometimes another. The word up is an Adverb in the sentence I go up in a balloon; Preposition in the sentence I go up a tree.

"Love is not love

Which alters when it alteration finds."

"I do love thee so,

That I will shortly send thy soul to heaven."

"He was present at that love feast."

How do we know what part of speech love is in these several cases? Evidently from the office which it performs, and not from its form. It is a Noun, or a Verb, or an Adjective, according to its office in these three propositions. A part of speech can, in a given case, be distinguished only by examining the speech itself.

SECTION CCCCLXI.THE PARTS OF SPEECH WHICH COMPOSE SIMPLE

PROPOSITIONS.

In the classification of the parts of speech already given, we have seen what is the relation which each bears to the proposition.

The SUBSTANTIVE. A word that can enter into the structure of a simple proposition either as the subject or the predicate, is called a Substantive or noun; as, 66 Iron is hard." Here the word iron is the subject, one of the three parts of a simple proposition. "Washington was president." Here the word president is the predicate, one of the three parts of a simple proposition. A noun is the name of anything that exists, or that is conceived to exist. Hence we see how it can form the subject of a proposition. "A name," says HOBBES," is a word taken at pleasure, to serve for a mark, which may raise in our mind a thought like to some thought such as we had before, and which, being pronounced to others, may be to them a sign of what thought the speaker had before in his mind." See Section CCXLIII.

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The ADJECTIVE. A word which can enter into the structure of a simple proposition as a predicate, but not as a subject, is called an Adjective; as, "Snow is white." Here white is the predicate of a simple proposition, but it cannot be the subject. We cannot say white is snow in the sense of predicating snow of white. See Section CCLXIV.