are two in number: 1. All fled; 2. but he did not fly. All fled but him. Here the word but is a preposition, meaning except, and the proposition is single. See § 375,

INTERJECTIONS. A word which can not enter into any proposition, or connect two propositions, but simply expresses surprise or any emotion, is called an Interjection. They have a meaning, but not a meaning connected with assertion. See § 381.

EXERCISES.

1. In two different propositions use the same word (i. e., the same in form) as a Substantive and a Verb.

2. In two different propositions use the same word as a Pronoun and a Conjunction.

3. In two different propositions use the same word as an Adjective and an Adverb.

4. In two different propositions use the same word as an Adverb and a Preposition.

5. In two different propositions use the same word as a Conjunction and a Preposition.

6. In two different propositions use the same word as a Conjunction and an Adverb.

7. In three different propositions use the same word as a Substantive or Adjective, and a Verb (stone).

8. In two different propositions express different degrees of definiteness by the articles.

9. Change two affirmative propositions into two negative ones by using different negatives.

10. Change two propositions into two questions, and mention which are their predicates.

THE

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

§ 464. 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.

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).

"Each of these operations is liable to a corresponding defect, namely, Simple Apprehension' to indistinctness; 'Judgment' to falsity; and Reasoning' to inconclusiveness.

"II. Language affords the signs by which these operations of the mind are expressed and communicated. The notion obtained in an act of apprehension is called, when expressed 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 § 466.

It is desirable to avail ourselves of any rules and caution as to the employment of language that may serve to guard against the defects just mentioned, to the utmost degree that is possible; in other words, to guard, by the best rules we can frame, against terms not conveying a distinct meaning; against false propositions, mistaken for true; and against apparent arguments, which are, in reality, inconclusive, though likely to be mistaken for real arguments.

QUESTIONS UNDER CHAPTER III.

1. What is a proposition?

2. Of how many parts does a proposition consist?

3. What is the subject? The predicate? The copula?

4. Give examples of these three parts.

5. Can the parts of a proposition be more than three?

6. How can the subject and predicate be made complex?

7. Give an example of the manner in which they can be made complex.

8. Can the parts of a proposition be fewer than three?

9. Exhibit apparent contradictions to the statement that the parts of a proposition can not be fewer than three.

10. In what language is the copula commonly omitted?

11. What is said of questions of appeal?

12. Into what can propositions which do not explicitly contain the copula be resolved?

13. What is said of the substantive verb when it is introduced by the adverb there?

14. When the subject of a proposition succeeds the predicate, by what word is it represented?

15. What are categorical propositions? Give an example.

16. What are hypothetical propositions? Give an example.

17. How are propositions divided according to their quality? Give examples.

18. How are propositions divided according to their quantity? Give an example of a universal affirmative and of a universal negative; of a particular affirmative and of a particular negative.

19. When is a term said to be distributed?

20. What propositions distribute the subject, and what propositions distrib

ute the predicate?

21. What is conversion? Give an example.

22. When are terms convertible?

23. What is opposition, and how many kinds of opposition are there? Give examples.

24. What is a simple proposition? and what is a complex proposition?

25. What are compound propositions? Give an instance.

26. What is an indefinite proposition? Give an instance.

27. What are trifling propositions? Give an instance.

28. How are the parts of speech determined? Exhibit the proof.

29. Mention the parts of speech which compose simple propositions; and those which can enter only into complex propositions; and those which do not enter into the structure of propositions,

30. How many operations of the mind are concerned with argument? To what defect is each of these exposed? What logical forms are adapted to these several operations of the mind?

CHAPTER IV.

ARGUMENT.

§ 465. 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.

An ARGUMENT is defined as an Expression in which, from something laid down (assumed as true), something else is concluded to be true, as following necessarily from the other.

A CONCLUSION is a proposition proved by Argument, and is always drawn from two other propositions, called the Premises.

The Premises are the two propositions from which the conclusion is drawn, and are so called because they are premised, or put before it.

Thus, "Every tyrant deserves death.

Cæsar was a tyrant;

Therefore he deserved death."

Here the first proposition is a Premise; the second proposition is a Premise; the third proposition is the Conclusion. The three propositions taken together is an Argument.

An Argument sometimes has only one premise expressed, while the other is suppressed, as being admitted. Thus, "Cæsar was a tyrant, therefore he deserved death." Here we have but one premise expressed, but the other is understood. This, indeed, is the more common form.

Every Argument 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 premise, 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 § 467. "We are dependent, therefore we should be humble." Here the major premise is suppressed.

In ordinary language, the word " Argument" is often employed to denote the Premises alone, or sometimes that one of the premises which is expressed when the other is understood; as when one speaks of proving so and so by this or that argument, meaning by such and such a Premise.

SYLLOGISM.

§ 466. A SYLLOGISM is an argument so expressed that the conclusiveness of it is manifest from the mere form of expression alone, independently of the meaning of the words; as, Every X is Y; Z is X; therefore Z is Y. If the premises are assumed to be true, the conclusion must follow. The Premises here are, 1. Every X is Y, which is the Major Premise; 2. Z is X, which is the Minor Premise. Z is Y, is the Conclusion.

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.

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 above syllogism, Z is the minor term, Y is the major term, and X is the middle term. The major term is so called from its being of more extensive signification than the minor.

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

Τι