other words, a whole proposition may enter into the structure of many-worded 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.

THE PARTS OF A PROPOSITION NOT FEWER THAN

THREE.

§ 451. 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.

=

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. It 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 labor?" is equivalent to "No one would be (insane enough, without the hope of future recompense, to undertake constant labor)."

Propositions which do not explicitly contain the copula may be 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 § 506.

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?

DIVISION OF PROPOSITIONS.

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

HYPOTHETICAL Propositions are those which are expressed conditionally; as, If Cæsar 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 any thing and every thing 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 civilized.

DISTRIBUTION.

§ 453. 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 mortality 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 denote, 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 x 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 "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 savior of his country.

3. No human government allows absolute liberty.

CONVERSION.

§ 454. 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, i. e., 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.

66

All equiangular triangles are equilateral, and

All equilateral triangles are equiangular."

Here the terms are convertible.

OPPOSITION.

§ 455. 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,