alent to the introduction of a preposition, always constitute a case-inflection, or simply a case. Case-inflections show the relation that one noun bears to another; and this is precisely what is done by prepositions. Thus, the father's son the son of the father; in other words, the inflection -s is equivalent to the preposition of.

Hence, whatever inflection takes the place of a preposition is called a Case. The genitive, dative, and ablative, instrumental, and some of the rarer cases, are of this kind. The nominative, vocative, and accusative cases are not so. That this difference between what may be called the prepositional and the non-prepositional cases is a real one, is shown by the greater extent to which the genitive and dative cases retain their signs throughout the changes of language, as compared with the nominative, accusative, and vocative.

Many inflections represent (perhaps are) single words. Thus the -o in voc-o, or the -s in father-s, may once have been separate words, which afterward coalesced with the respective crude forms voc and father. This is a fact which accounts for the difference between the logic and the grammar of a proposition, not one which denies its existence. However much the -s in father may have been a true preposition at one time, it is not so now. Similarly, what was once a preposition may at an earlier period still have been a The philology which reduces all parts of speech to the noun and verb, however true in history, is false in Logic.-See LATHAM.

noun.

TRIFLING PROPOSITIONS.

§ 412. 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 predi cate 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;" "I am that I am."

THE RELATION OF CERTAIN LOGICAL FORMS TO CERTAIN STATES OF THE MIND.

§ 413. Human Language is but a transcript of the various states of the human mind in its various movements. Logical forms are but an exhibition of the movements of the mind when employed in reasoning.

§ 414. As a preliminary statement, the following extract from Whately's "Logic" may be useful in showing the connection between language and the mind.

"I. There are three operations (or states) of the mind which are immediately concerned in argument: 1st. Simple Apprehension; 2d. Judgment; 3d. Discourse or Reasoning.

"1st. Simple Apprehension (mere apprehension) is that act or condition of the mind in which it receives a notion of any object, and is analogous to the perception of the senses. It is either complex or incomplex. Incomplex apprehension is of one object or of several, without any relation being perceived between them, as of a man,' a horse,' 'cards.' Complex is of several, with such a relation, as of a man on horseback,' a pack of cards.'

"2d. Judgment is the comparing together in the mind two of the notions (or ideas) which are the objects of apprehension, whether complex or incomplex, and pronouncing that they agree or disagree with each other (or that one of them belongs or does not belong to the other); judgment is, therefore, either affirmative or negative.

"3d. Reasoning (or discourse) is the act of proceeding from one judgment to another, founded upon that one (or the result of it).

The

"II. Language affords the signs by which these operations of the mind are expressed and communicated. notion obtained in an act of apprehension is called, when ex

pressed in language, a term; an act of judgment is expressed by a Proposition; an act of reasoning by an argument (which, when regularly expressed, is a syllogism)." See § 416.

CHAPTER V.

ARGUMENT.

§ 415. THUS far we have dealt with Terms as expressing the simple apprehension of the mind, and Assertions as expressing an act of Judgment; we now proceed to the subject of Argument as expressing the act of Reasoning. Every Argu. ment consists of two parts: that which is proved, and that by means of which it is proved; the former, before it is proved, is called the question; when proved, the conclusion; that which is used to prove it, if stated last, is called the reason, and is introduced by the conjunction "because," or some other causal conjunction; as, "Cæsar deserved death because he was a tyrant." If the conclusion be stated last, which is the strict logical form, then that which is employed to prove it is called the premiss, and the conclusion is introduced by some illative, as therefore; as, "Cæsar was a tyrant, therefore he deserved death."

Arguments thus stated, without the third proposition, which is in a syllogism, are called Enthymemes. See § 420. "We are dependent, therefore we should be humble." Here the major premiss is suppressed.

SYLLOGISM.

§ 416. A SYLLOGISM is an argument so expressed that the conclusiveness of it is manifest from the mere form of ex pression alone, independently of the meaning of the words; as, every X is Y; Z is X; therefore Z is Y. If the premisses are assumed to be true, the conclusion must follow. The Premisses here are, 1. Every X is Y, which is the Major Premiss;

2. Z is X, which is the Minor Premiss. clusion.

Z is Y, is the con

Let X, Y, and Z stand for any terms whatever, the conclusion must follow from the very form of the expression, according to the following general statement:

1. Any thing whatever (as Y) affirmed of a whole class (as X),

2. Under which class something else (as Z) is comprehended,

3. May be affirmed of that (namely, Z) which is so comprehended.

§ 417. 1. Every Syllogism must have three, and only three, Terms; viz., the Middle term, and the two terms of the Conclusion or Question. Of these, 1. The subject of the conclusion is called the minor term; 2. Its predicate, the major term; and, 3. The middle term is that with which each of the others is separately compared, in order to judge of their agreement or disagreement with each other. Thus, in the syllogism in the preceding section, Z is the minor term, Y is the major term, and X is the middle term.

2. Every Syllogism must have three, and only three, Propositions; viz., 1. The Major Premiss, in which the major term is compared with the middle; 2. The Minor Premiss, in which the minor term is compared with the middle; and, 3. The Conclusion, in which the minor term is compared with the major.

1st Canon.-Two terms which agree with one and the same third, may be pronounced to agree with each other.

2d Canon.-Two terms whereof one agrees and the other disagrees with one and the same third, may be pronounced to disagree with each other.

When two Terms are brought together as subject and predicate of a proposition, they are described in technical language as agreeing or disagreeing with each other, according as the one is affirmed or denied of the other. The former of these canons applies to affirmative, the latter to negative propositions.

EXERCISE.

Point out the three Propositions in each of the following Syllogisms, and name them; also each Subject, Predicate, and Copula; also the Major term, the Minor term, and the Middle term:

1. Every dispensation of Providence is beneficial;
Afflictions are dispensations of Providence;
Therefore they are beneficial.

2. No predaceous animals are ruminant;
The lion is a predaceous animal;

Therefore the lion is not ruminant.

3. All tyrants deserve death;

Cæsar was a tyrant;

Therefore he deserved death.

4. No one who lives on terms of confidence with another is justified in killing him;

Brutus lived on terms of confidence with Cæsar; Brutus, then, was not justified in killing Cæsar. § 418. The MODE of a Syllogism is the designation of the three Propositions it contains (in the order in which they stand), according to their respective Quantity and Quality; that is, according as each proposition is universal or particular, affirmative or negative.

§ 419. The FIGURE of a Syllogism is the situation of the Middle term in the two premisses respectively with relation to the two Extremes (or Terms) of the conclusion, namely, the Major and Minor terms.

Let X be the Middle term, Y the Major term, and Z the Minor term.

In the FIRST FIGURE the Middle term is made the Subject of the Major premiss, and the predicate of the Minor; as, Every X is Y; Z is X; therefore Z is Y.