tion is in the experimental and tentative stage of its development we call it an hypothesis. If it seems to be fruitful of results, yet we do not wish to imply that it is altogether satisfactory or fully tested, we often refer to it as a working hypothesis. If we have reached the point where we no longer regard it as tentative, but satisfactory, we call it a concept, a principle, a law, or a theory, according to the degree of its generality or the width of its application. Thus, we speak of the concept of house, a principle of percentage, the law of falling bodies, the theory of evolution. 3. COMPLETE INDUCTION INCLUDES DEDUCTION.

There is a sense in which deduction can be isolated from induction. There are certain problems whose solution demands only the application of already established and accepted concepts within a definite organization of knowledge. For these deduction may be adequate. But induction cannot be isolated. It is always inclusive of deduction. We have seen that hypotheses are not established, that general notions are not perfected, except as they are deductively applied in some way and found capable of interpreting and controlling particulars. Furthermore, our discussion has made it evident that in many cases the first hypothesis is vague and tentative in the extreme. The process of its development is through application and reconstruction repeatedly. In these cases deductive processes are inextricably woven into the very fabric of the inductive process. 4. APPLICATIONS TO TEACHING.

(1) Training in thinking must recognize the dynamic aspect of inductive and deductive processes.

Logical power cannot be developed merely by going through the forms of induction and deduction. In our illustration from geometric demonstration (deduction) and in the illustration of the manner in which the logical concept trade center was attained (induction), we have seen that the actual movements of thought involved a great deal

of tension and struggle of mind. The ransacking of one's mental resources and intense processes of judgment are characteristic of real induction and real deduction. The method of instruction employed by the teacher, if it is to yield fruit in training the power to think, must not be so carefully controlled and directed as to leave no room for the child's mind to struggle with the problem on his own

account.

In both forms of thinking, the starting point is something problematic. Neither of them can have any real motivation unless the problem is felt by the child. Unless the nature of the problem is rightly conceived, neither of them can have anything of teleological character, that is, they cannot be truly voluntary. If this is so, they are not processes which move directly toward any goal, and they cannot be in any right sense of the word processes of conscious adjustment of means to ends, they must be more or less aimess, arbitrary, and artificial, if not purely imitative.

In genuine, full and complete inductive and deductive processes, the conception of the real nature of the problem is more vital than any idea of the formal order of steps in the process. The mind that really grasps the problem will inevitably hit upon the order and nature of the steps in the thinking process relevant to that type of problem. Having hit upon the order and nature of the steps in simple situations, the formal aspect of the process can be brought definitely to consciousness by instruction; and training can be given in the perfection of the technique of procedure as a tool to more rapid and more effective solution of problems. But, in early training at least, there can be no doubt that more attention should be given to getting at the locus of the problem and less attention given to the question of whether we shall proceed from the general to particulars or from particulars to the general.

(2) We must recognize the child's system of already

organized knowledge as a determining factor in his thinking processes.

Both induction and deduction, as we have seen, work within systems of knowledge. The child's system of knowledge is vaguer and less logical than that of the adult or of the trained thinker. We must not, then, apply the teacher's standard of deduction or of induction to the thinking of the child. A process of thinking that would be very unsatisfactory from the teacher's standard of essentials may yet be very really and genuinely a thinking process from the standpoint of the system of knowledge within which the child is working.

Every time the child is asked a reason for a statement which he makes, and succeeds in basing it upon something else consonant with his experience, he has been going through a true process of deduction. His reason may be very unsatisfactory in the light of our knowledge; but if it is a reason which is harmonious with his system of knowledge and experience, then the thinking process is good. For example, the child may ask, "Why does the stone sink in the water?" If he is asked to say what he thinks about it himself, and replies, "Because it is heavy," that may be a very good answer for him. If there is a man in his neighborhood who is known to steal and to lie, and the child explains the fact on the basis that "the man is bad, that's why he steals," he is thinking deductively just as truly as if his explanation were better. If his thinking in these cases is based on reasons within his own system of experience and knowledge, it will not be a bit better as thinking if we compel him to carry it on a few points further in our terms so as to harmonize with scientific or ethical facts and principles which we know, unless these facts and principles are within the grasp of the child and have been taught to him. Here, as elsewhere in the teaching process, we may be altogether too anxious for the finished product and thus violate the fundamental principle of the thinking process

of the child, namely, that it is not vital and dynamic to him except as it operates within his own system of knowledge.

In cases where the child's answer is palpably wrong, even where it seems justifiable in the light of his experience and knowledge, we may do either one of two things. First, we may make it the occasion for further observation and reflection on his part and thus lead him to a reconstruction of his experience so that it will be adequate to the right interpretation of the case in question. In other words, the weakness in his system of knowledge is the natural occasion for a vital inductive process. Secondly, we may, if we feel that the child cannot be led to see the truth in more scientific terms, merely tell him dogmatically that his answer is wrong and give him the right one without explanation. This can do no harm, if we give him to understand that there is a reason and that he will some day be able to understand it. For example, if the child has come across the idea in some story that the earth is round, it is not necessary to give him a complete explanation of the grounds upon which we believe this to be true, if he questions it. We might better answer him dogmatically unless we are convinced that he will be able to interpret our explanation in terms of his own experience or knowledge.

Certainly any explanation that has to go outside of the child's own system of knowledge to get its binding force is valueless to him and may even be harmful. How much more genuine reasoning there would be among people if so many had not been deluded into supposing that they were actually thinking when they are only juggling with formulæ which are not an integral part of their system of knowledge! Otherwise intelligent people, by virtue of the fact that they possess and can manipulate a few catchwords of political, social, religious, or moral philosophy, are often actually held in bondage to fixed ideas and prejudices of every sort on the supposition that they have thought the problems through and settled them.

The teacher who follows up the statements of children with demands for their justification, within the limits suggested above, the teacher of the everlasting "Why?" is not only giving them constant practice in deductive thinking, but is also putting them in situations in which they feel the inadequacy of their present system of knowledge either in respect to the extent of its materials or in the matter of their organization for use. Thus he is putting the child into the most favorable attitude of mind for the welcoming of further knowledge given either through direct telling or gained through inductive processes. It is fallacious to suppose that because we work under limitations in the training of children to think, because we cannot push the inductive and deductive processes through in such a way as to satisfy our ideal of completeness and adequacy, the ideal of the finished product, therefore we cannot give them training at all in thinking, both deductive and inductive. If we do not give children training in thinking at the stage of their development in which the cruder forms only are possible, how can we expect them to grow up to the point of appreciation of the more perfect forms or to power in their use?

Suggestions previously made in our study of the development of the child's imagination would be relevant at this point. We must remember that the child's system of knowledge is one that is held together in large part by ties of connection that get their force from his interest in concrete wholes rather than by ties of connection that spring from the appreciation of far-reaching abstract principles. His training in inductive and deductive processes previous to adolescence, that is, in the period of the graded school, should be largely, then, within systems of knowledge in which cause and effect, conditions and consequences, are quite closely related within more or less concrete wholes. The period of the graded school, or the elementary school as it is now more commonly called, is one for the training in that kind of thinking which builds up the habit of looking