(12) Any student in college would stand higher in his class if he received higher marks; hence if all

marks were raised 10% every man would stand nearer the head of his class.

(13) Pine wood is good for lumber; matches are pine wood; therefore matches are good for lumber. (Hyslop.)

(14) To teach a child is to improve him; showing him how to pick pockets is teaching him; hence

that improves him.

(15) Poisons cause death; nux vomica is a poison; therefore it causes death.

(16) This reformer was working for selfish ends all the time; no more reformers for me.

(17) Since attending that socialist meeting I have had no confidence in socialistic doctrines.

(18) He cannot be innocent, for he was a member of the mob which committed the deed.

(19) Those two horses would make an excellent team, for each is the best of its class.

(20) Five is an odd number; three and two are five; and hence each is an odd number.

CHAPTER V

PROPOSITIONS

DIFFICULTIES in the use of language are not all provided against by the correct definition of terms. Many arise in the combination of words into sentences. A term, as we have seen, is the representative in language of some object of thought, real or imaginary, concrete or abstract. But the mind never rests in the contemplation of a single object; it always tends to make an assertion or judgment about this object. Most logicians are now of the opinion that, even in the simplest perception, a judgment is either present or implied. Introspection will show at once that when we hold an object before the mind, there is an inevitable tendency to think some assertion about it. The expression of this mental assertion or judgment in language is a proposition.

Kinds of Propositions. -Propositions are usually distinguished according to quality and quantity. (1) The qualities are two, affirmative and negative. The difference between affirmative and negative propositions is sufficiently familiar. It should be remembered, however, that the mere occurrence of not or some other negative particle in a proposition does not necessarily make the proposition negative. The proposition, "Those who do not study are in danger of failing," is not a negative proposition. It asserts positively something about a certain class, namely, "those who

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do not study "; these words constitute a negative term. An affirmative statement can be made about a negative subject as readily as about any other. In the proposition, "Those who do not study are unwise," the term unwise is also negative, but the proposition is affirmative. To decide whether any proposition is affirmative or negative, determine whether something is affirmed or denied of a subject. What the subject is, and what the predicate is, makes no difference; the only question is, do we affirm something or do we deny something? (2) With regard to quantity, propositions may be either universal or particular. A universal proposition is one which expresses a judgment about the whole of the class to which the subject applies. "All the stars are suns" is a universal proposition; so is "No planets are self-luminous." (The latter proposition is negative and denies something of all planets.) "Some stars are double " is called a particular proposition. It asserts something of some individuals of the class stars." By " particular proposition" is not meant a statement about some particular individual. The proposition "Jupiter is the largest of the planets" is not a particular proposition. It is a singular proposition, but, since it expresses a judgment about the whole of that for which the term "Jupiter' stands, it may be treated as a universal proposition. The so-called particular propositions are really indefinite; if the "some" in any proposition meant certain particular ones, as it does in certain cases, the proposition would really be universal; it would say something about all those of whom the assertion was made: as 99 some persons (meaning A, B, C)" are certain to be

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late." As used ordinarily, some means certain unspecified individuals, it may or may not be all. The word indefinite would certainly be more appropriate here, but the word particular, with this special meaning, is the one which has been used traditionally.

With this two-fold distinction of quality and quantity we get four different kinds of propositions: universal affirmative, universal negative, particular affirmative and particular negative. For the affirmative propositions the letters A and I are used as symbols, A standing for the universal affirmative and I for the particular affirmative. E stands for the universal negative and O for the particular negative. (These letters are from the Latin Affirmo and Nego.)

Propositions and Terms.

Negative O

The Relation of Subject to Predicate. The question of the relation of propositions and terms is one that naturally arises here. A proposition obviously contains terms. Ordinarily it is said that a proposition is made up of two terms and a copula. One of these terms is the subject and the other is the predicate. The copula is that which con

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nects subject and predicate; it is always some part of the verb to be. Some propositions do not fall naturally into this form: for example, "The earth moves." This can, however, be expressed in this form: "The earth is a body which moves."

This form, subject-copula-predicate, is called the "logical form" of the proposition. It often seems artificial, but for certain purposes it is convenient to employ it, and the attempt to restate propositions in this form is an excellent way of finding out just what the proposition means.

The subject of a proposition stands for that about which something is said.1

The predicate is that which is asserted of the subject. The copula is that which connects the two terms in a proposition; but the nature of that connection is not always the same. In the propositions, "Aristotle was the greatest pupil of Plato," "Aristotle was wise," "Aristotle was traveling in Asia Minor," and "Aristotle was a philosopher," the copula has, in each case, a different meaning. In the first, the relation is that of

1 A distinction may be made between the grammatical and the logical subjects. The grammatical subject is the subject of the proposition; it is, as we have seen, a term. The logical subject has been variously defined. The definition of the logical subject as the subject of the thought seem, on the whole, to be the best. (See for discussion, Joseph, Introduction to Logic.) The logical subject is that about which the judgment is made. For example, in the proposition, "Acid turns blue litmus paper red," the grammatical subject is, of course, the word "acid." The grammatical predicate is that which stands for what is asserted about the subject; in this case, the words "turns blue litmus paper red." Changing the proposition into the form of subject-copula-predicate, it would read "acid is that which turns blue litmus paper red," and the complete predicate would be the words following the copula. Now the form of the proposition may not indicate the real logical subject. If the statement just given were the answer to the question, “What can you say