1. A statement is any combination of words that is either true or false; e.g. (exempli gratia, "for example"),

All x's are y's.

2. To pass from one statement to another, with a consciousness that belief in the first warrants belief in the second, is to infer.

3. Two statements are equivalent when one asserts just as much as the other, neither more nor less; e.g., A equals B, and B equals A.

4. A statement is implied in a previous statement when its truth follows of necessity from the truth of the previous statement; e.g.,

All x's are y's implies some y's are x's.

Cante

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5. Any declarative sentence

e reduced to one or more simple statements, each consisting of three parts, namely, two terms or classes, and a copula, or relation, connecting them.

A equals B, x is y, are simple examples of this typical form. of all statements. Here x and y each stand for any word or group of words that may have the force of a substantive in naming a class; e.g., x is y may mean all the x's are y's; man is mortal, means, all men are mortals.

6. A sentence containing only one such statement is a logically simple sentence; e.g., Man is the only picture-making animal.

7. A sentence that contains more than one such statement is a logically composite sentence; e.g., A and B are respectively equal to C and D, is composite, containing the two statements A equals C, and B equals D.

8. Statements that are expressly conditional, such as, if A is B, then C is D, reduce to the typical form as soon as we see that they mean

(The consequence of M) is N.

9. In the typical form, bird is biped, x is y, we call x and y the terms of the statement; the first being called the subject, and the last the predicate.

10. Terms that name a single object are called individual terms; e.g., Newton.

11. Terms that name any one of a group of objects are called class terms; e.g, man, crystal. The name stands for any object that has certain properties, and these properties are possessed in common by the whole group for which the name stands.