state of affairs involves a corresponding variation in some other aspect. To infer we must know what some one aspect of the situation really is and the rule according to which it involves another aspect. Our knowledge of the first aspect is the premise of our reasoning, and from our knowledge of this aspect and of the rule we can reach the conclusion, or a knowledge of the other aspect. But if various aspects of a situation did not involve each other whether we reasoned about them or not, we should not be able to reason at all.

It is thus not the business of logic--or of any part of itas most writers have said that it is, to describe necessary forms or laws of thought' connecting one idea with another, but rather to direct attention to the most fundamental laws or relations of things which all reasoning takes for granted and which alone make it possible for any one state of affairs to involve any other.

If this is a correct account of the nature of inference in general, the only way to test the validity of any specific case of inference is to ask: Is there any possible way in which the relations asserted in the premises could exist in the absence of those asserted in the conclusion? Is it possible for one and the same object or general state of affairs to have the one set of relations without the other also? If it is possible, then the denial of the conclusion may be consistent with the affirmation of the premises; if it is not possible, this denial is not consistent, and the conclusion follows.

Logical Consistency is thus a matter of possibility and impossibility in the objects under discussion. This will become clearer as we proceed.

Though the ultimate justification of every act of inference must be found in the nature of the things about which the inference is drawn, it would not be possible for us to draw an inference unless we were able to think of these things in some coherent and The fundamental elements involved in all such coherent and rational thinking are known as the 'Three

The three 'Laws of Thought'.

rational way.

Laws of Thought'; and we must now explain what these so-called laws of thought really mean.

The first of these is called the Law of Identity; it is usually stated in some such form as this: What is, is', 'A is A', 'Everything is what it is'; and this law with the two others are treated as axioms or first principles to which doubtful arguments should be referred, and by which alone they can always be tested.

This first law of thought-the law of identity-does not mean that objects cannot change or cease to exist, that A cannot become B or be wiped out of existence altogether, that what is true at one moment is always true. It merely expresses the fact that we know what we are thinking about and what we are thinking about it; that we can recognize an old object of thought as the same even when what we think about it is not the same, and that in a similar way we can recognize whether a new statement about it is or is not the same as an old one. We can consider an object or a situation in as many aspects as we please and still recognize that we are concerned with the same object or situation. A person can say, for example, that a certain house is red, that it is four stories high, that it is old, and that it was once inhabited by George Washington; and the speaker and his hearers can both recognize that he is talking about the same house all the time. But if he should add something about its pale-green color, its snowy peaks, its delicious flavor, its angry billows, its flushed and anxious countenance and its relation to the square root of the difference, we should then say that his mind was wandering, his thought was not consecutive, his various 'its' did not refer to the same object. We, the hearers, could say that the objects referred to must all be different, but if the speaker's mind were really wandering, if he were utterly incapable of holding fast to an old object of thought and identifying it, he would not know that his various sentences referred to different objects, for without the power to identify an old object of thought he

would have no more idea of difference than of identity.

Το

him no pronoun could have an antecedent and the words 'same' and different' would be absolutely meaningless.

6

This illustration has particular reference to the object thought about, but the power of remembering and recognizing statements made about it is just as essential to sanity. The law of identity thus expresses the fact that thought points to objects and that we can know or recognize what objects we are thinking about and what we are thinking about them.

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The second law of thought' is called the Law of Contradiction, and is expressed in such formulæ as these: 'Nothing can both be and not be', 'A is not not-A', 'A cannot be both Band not-B'. While the law of identity rests upon our power of identifying an object of thought, the law of contradiction rests upon our power of distinguishing between an affirmation and a denial, between the meaning of 'is' and the meaning of 'is not', of 'yes' and of 'no'. The law, in its primary sense, at least, simply means,-what everybody knows,— that we cannot both affirm and deny the same thing about the same object. Understanding by S whatever can be named in the subject of a sentence, and by P whatever can be named in the predicate, the law means: If it is true that S is P, then it is false that S is not P and if it is true that S is not P, then it is false that S is P. The law as thus stated does not depend upon any particular knowledge about things; it follows inevitably from the nature of thought. Why thought should take the form of a judgment, and why affirmative and negative judgments should exclude each other we do not know, but as soon as we know anything about ourselves we know that such is the case.

There is a secondary meaning often attached to the law of contradiction, namely: that we must not ascribe incompatible qualities or relations to the same object. According to the primary sense of the law we contradict ourselves if we say that a certain thing is white and that it isn't white; accord

ing to the secondary sense we contradict ourselves if we say it is white and that it is black. In the first case we had in mind the same quality—white, and the law said we could not both affirm and deny it; in the second case we had in mind two different qualities, and the law said we could not affirm them both. In the first case the sense of contradiction is due to the fact that it is mentally impossible to affirm and to deny the same thing at the same time, just as it is physically impossible to say yes and no at the same time, to nod the head and to shake it, to approach or draw a thing toward you and to recede or push it away; in the second case it rests upon our knowledge that the same object cannot have two different colors at once. In the first case the contradiction rests upon the nature of a judgment and could be recognized by any one who could distinguish between the meanings of is' and 'is not', however limited his experience; in the second case it rests upon the nature of things as people gifted with sight believe them to be.

If we did not believe in the existence of a world so constituted that the presence of any quality in a thing excludes certain other qualities, we should not recognize any contradiction in saying that a thing is both white and black, three feet long and one inch long, round and square, before and after.

The qualities which do not, or cannot, exist together in the same thing happen to be those which appeal to the same sense, and which we are therefore able to compare together, and for which we usually have some general name, such as 'color', 'size', 'shape', 'time', 'place'. Incomparable qualities, such as red and square, may or may not coexist in the same object, and we have no difficulty in imagining any combination of them. Either because of the nature of our faculties or because of the limitations of our experience, we cannot imagine an object which has at the same time two different qualities of the same general kind. Because we cannot imagine a thing to have at once two

qualities of the same general kind, we assume that such qualities cannot really coexist, and when we assume this, it follows that to affirm one quality of an object is equivalent to denying another, so that when any one says that a thing is large and small, white and black, we take it for granted he means that it is large and isn't large, that it is white and isn't white, and that he is therefore contradicting himself. Thus through the limitations of our imagination the law of contradiction, which in its primary sense is concerned only with the imposibility of both affirming and denying the same qualities or relations, comes to take on a secondary meaning concerned with the inconsistency of affirming certain different qualities or relations.* It is this secondary sense of the law that is expressed in the last two formulæ I gave for its expression. The third general principle or law of thought is called the Law of Excluded Middle. The usual formula is 'Everything must either be or not be', 'A must be either B or not B'. This law is the complement of the Law of Contradiction and means that every statement must be either true or false. If it is false that S is P, then it is true that S is not P, and if it is false that S is not P, then it is true that. S is P. This law, like the law of contradiction in its primary and proper sense, is not derived from an examination of things, but follows inevitably from the nature of thought in judging; for not only do affirmative and negative judgments necessarily exclude each other, as the law of contradiction says, but every positive or active judgment must either affirm something or deny it; there is no middle ground.

Like the law of contradiction, the law of excluded middle has also acquired a secondary meaning, concerned not with the difference between affirmation and negation, but with the mutual implications of various qualities and relations in the objects judged about.

* If we distinguish between the copula and the predicate we can say that in its primary sense the law is a mere matter of the copula; but in its secondary sense is made a matter of the predicate.