LESSON XXXVII. REASONING. (Continued.) We have seen that the only difference between inductive and deductive reasoning is that the one is based on an implicit and the other on an explicit universal. We will now consider that kind of deductive reasoning that is usually called induction, and to avoid circumlocution I will give it the name that it usually bears. - But Relation of Induction to Generalization. — Induction very closely resembles generalization. Generalization, you remember, is the last of the three processes involved in the formation of a concept. A child directs his attention to two or more objects at the same time— comparison — and after noting their like and unlike qualities, fixes his attention upon the former-abstraction and thinks of them as the characteristics of a class - generalization. there is no going from the known to the unknown, and, consequently, no reasoning in the act of generalization. When a child, noting that two or more objects resembling each other in a number of particulars, and all used to sit in, thinks of the qualities in which they resemble each other as the characteristics of a class-extends, in other words, the name given to them to all objects possessing similar qualities-he does not make an inference about He does not say that since the objects he does not see. these chairs have this and that and the other quality, therefore all chairs have them that would be an induc tion. But he says, Since these objects are alike in certain respects, I will make a class of them, and if there are any other objects that possess the same qualities, I will put them in the same class call them by the same name. Of course a child does not definitely think any such thoughts. We know that there is a great difference between what the mind really does and what it is conscious of doing. And when a child sees two objects and calls them dogs thus putting them in the same class — and when seeing another dog, he says, "dog"-putting it in the same class-it is plain that his mind has taken the course I have endeavored to describe. This is generalization. But there is a wide difference between generalization (making a class of objects) and induction (concluding because one or more members of a class have such and such characteristics, therefore they all have it; or because something is true of one or more members of a class, therefore it will be true of all). In the one case, we are merely arranging objects into classes; in the other, we reason from one or more members of the class to the entire class. From this it is evident that induction presupposes generalization. If in induction I reason from one or more members of a class to the whole class, I must have the idea of the class already formed in my mind. Let We have already seen that inductive reasoning assumes that certain individuals are types of an entire class. us consider this further. INDUCTIVE REASONING. 34I Two Assumptions Underlying All Inductive Reasoning. - When I reason that all crows are black because all the crows I have seen were black, I assume that the crows I have seen are types or examples of the entire class. This assumption that we can regard a greater or less number of individuals as types of a class clearly underlies a large part of our inductions, and we never can be quite sure in any case that we have a right to make it. Of course, it is more likely to be true when the instances which we assume to represent the entire class are very numerous. But, no matter how many cases we have examined, it will always be possible that some member of the class that we have not seen may be unlike those we have seen. An hypothesis is an assumption that we make to account for facts. Our minds are of such a nature that we feel a certain uneasiness when we know a fact that we can not explain, and therefore it is natural for us to try to make some hypothesis or supposition to account for any fact we know. And since, of course, we do not make improbable suppositions to account for facts, or rather since we do not make suppositions that seem to us improbable, we are inclined to regard them as true, so long as they explain the facts. And this is another assumption upon which the greater part, if not all, of our inductions are based. This assumption can not be so definitely stated as the preceding one. It would not be correct to state it in this form: An hypothesis which explains facts is true. For one great reason why people differ from each other so widely in their opinions is that of two hypotheses that equally well explain the facts, one seems true to one, and the other to another. A dozen men on a jury listen to the same evidence, and part of them base one conclusion upon it, and the rest of them another. This is only another way of saying that one hypothesis that explains the facts seems probable to a part of them, and another to the rest of them. I do not believe that a more definite account of this assumption can be given than the following: We are naturally disposed to believe any hypothesis that does not seem improbable in itself, which explains facts for which we have, apart from it, no explanation. Law of Parsimony. — It is evident that of two hypotheses, one which assumes a cause certainly known to exist, to account for the facts, and one which assumes an unknown cause, the former is the more reasonable. That is the reason why we are bound to account for the actions of animals by means of the hypothesis of mechanical association, if we can. Animals certainly do associate things mechanically. If, then, we can explain their actions by means of laws known to be in operation, we have no right to assume any other. That is the meaning of the law of Parsimony: Causes must not be multiplied beyond necessity. Since we can Need of Care in Making Inductions. not rid our inductions of an element of uncertainty, no matter how cautiously and carefully we frame them, it is evident that, unless we make them as cautiously and as carefully as we can, they are likely to have very little value. "I do not like Jews," says one. Get him to tell you why, and you will find that the reason is that he has known two or three Jews who were not pleasant persons. "It does not do boys any good to go to college," says another. "John Jones went to college, and he does not NEED OF CARE IN MAKING INDUCTIONS. - 343 as though an know any more than Will Smith does" examination of the case of John Jones entitled one to an opinion of the whole class of students that attend college. "I do not like people with little noses," says a third; "they are always mean and stingy." The foundation for which is that he has seen one or two people with little noses who were stingy. Doubtless the great majority of the popular superstitions, "Thirteen is an unlucky number," "Bad luck to begin anything on Friday," etc., origi nated the same way. The best thing we can do to guard our pupils against such inductions is so constantly to call their attention to the necessity of founding their beliefs upon a wide basis of facts that they may get a realization of the danger of doing anything else. How to Impress this upon Pupils. Of course, the first condition of doing this successfully is that you have a vivid appreciation of the dangers of such inductions yourself. If you have such an appreciation, by encouraging them to express their opinions upon the various matters that come up, you can do something to develop such an appreciation in them. And when you are trying to develop it, first of all in your own mind, and then in the minds of your pupils, remember that the greatest foe of progress is Ignorance, and that the strongest friends of Ignorance are the dogmatism and prejudice to which careless and slovenly reasoning naturally give birth. We have seen that when we appeal to a general proposition to prove our conclusion, the reasoning is called deductive; when we appeal to particular facts, inductive. When we try to prove one fact by appealing to another which is only valid to prove the one fact we have inferred, |