"I then tried to imagine all possible purposes of such a pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried like poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house, (c) Its purpose might be to point out the direction in which the boat is moving.
"In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot's position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly."[8]
The problem was to find out the use of the flag pole. No adequate explanation came as the problem presented itself; it therefore caused a state of uncertainty, of suspended judgment, and a process of thinking in order to get an answer. Each suggestion that came was analyzed, its requirements and possibilities checked up by the actual facts and the goal. The suggestions that the pole was simply to carry a flag, was an ornament, was the terminal of a wireless telegraph, were examined and rejected. The final one, that the pole was to point out the direction in which the boat was moving, upon analysis seemed most probable and was accepted. The one characteristic of the pole, that it points direction, and its position, need to be accepted as the essential facts in the situation, for the particular problem. Without control of the process, without the two steps of analysis and abstraction, no conclusion could have been reached.
Analysis and abstraction may be facilitated in three ways. First, by attentive piecemeal examination. The total situation is examined, element by element, attentively, until the element needed is reached or approximated. This method of procedure helps to emphasize minor bonds of association which the element possesses in the learner's experience but which he needs to have brought to his attention. It can only be used when the element is known to some degree. It is the method to use when elements are known in a hazy, incomplete, or indefinite way and need clearing up. Second, by varying the concomitant. An element associated with many situations, which vary in other respects, comes to be felt and recognized as independent. This is the method to use when a new element in a complex is to be taught. Third, by contrast. A new element is brought into consciousness more quickly if it is set side by side with its opposite. Of course, this is only true provided the opposite has already been learned. To present opposites, both of which are new or only partially learned, confuses the analysis instead of facilitating it.
Reasoning, as the highest type of thinking, includes all that thinking in general does, and adds some particular requirement which differentiates it from the simpler forms. Further discussion of it, then, should make clearer the essential in thinking as a process, as well as make clear its most difficult form. Reasoning is defined by Miller as "controlled thinking,--thinking organized and systematized according to laws and principles and carried on by use of superior technique."[9] Reasoning, then, is the kind of thinking that deals directly with laws and principles. Much thinking may be carried on without any overt, definite use of laws and principles, as in constructive imagination or in apperception, but, if this is so, it seems better to call the thinking by one of the other names. Of course this classification is somewhat arbitrary, but there can be no question that types of thinking do differ. As has already been noted, some psychologists have used the terms thinking and reasoning as synonyms, but such usage has resulted in confusion and has not been of practical value. It is only as the mental process desired becomes clearly conceived of, its connotations and denotation clearly defined, that it becomes a real goal towards Which a teacher or learner may strive. This, then, is the primary criterion of reasoning--that the thinker be dealing consciously with laws and principles. An acceptance of this first essential makes clear that the particular process of reasoning cannot be carried on in subjects which lack laws and principles. Spelling, elementary reading, vocabulary study, most of the early work in music and art, the acquisition of facts wherever found--these situations may offer opportunity for thinking, but little if any for reasoning. Because a teacher is using the development method does not mean necessarily that her students are reasoning. The two terms are not in any way synonymous.
The second essential in reasoning is the presence of a definite technique. This technique consists of two factors: first, certain definite mental states, and second, the use of the process of thinking by either the inductive or the deductive method.
First as to the mental states involved. The fact that the thinking deals with laws and principles necessitates the presence, in the thinking process, of constructive verbal or symbolic imagery, logical relationships, logical concepts, and explicit judgments. This does not at all exclude other types of these mental states and entirely different mental states. The kind of analysis involved simply necessitates the presence of these types, whatever others may be present. Constructive symbolic imagery has already been discussed. Logical relationships are those that are independent of accidental conditions, are not dependent on mere contiguity in time and space, but are inherent in the association involved. Such relationships are those of likeness and difference, cause and effect, subject and object, equality, concession, and the like. Logical concepts are those which are the result of thinking, whose definite meaning has been brought clearly into consciousness so that a definition could be framed. A child has some notion of the meaning of tree, or man, or chemist, and therefore possesses a concept of some kind, but the exact meaning, the particular qualities necessary, are usually lacking, and so it could not be called a logical concept. Explicit judgments are those which contain within themselves the reasons for the inference. They, too, are the result of thinking. One may say that "cheating is wrong," or that "water will not rise above its source level," or that "cleanliness is necessary to health," or that "this is a Rembrandt"--as a matter of experience, habit, but without any reflection and with no reasons for such judgment. If, on the other hand, the problems to which these judgments are answers had been a matter of thinking, the reasons or the ground for such judgment would have become conscious and the judgment then become explicit. It must be evident that in any problems dealing with laws and principles the mental states involved must be definite, clear cut, logically sound, and their implications thoroughly appreciated and understood.
The second element in the technique necessary in reasoning is the use of either the inductive or the deductive method in the process. Induction requires--a problem, search for facts with which to solve it, comparison and analysis of those facts, abstraction of the essential likenesses, and conclusion. Deduction requires--a problem, the analysis of the situation and abstraction of its essential elements, search for generals under which to classify it, comparison of it with each general found, and conclusion. It is unfortunate that in the discussions of induction and deduction the differences have been so emphasized that they have been regarded as different processes, whereas the likenesses far outweigh the differences. An examination of the requirements of each as stated above shows that the process in the two is the same. Not only do both involve reasoning and therefore require the major steps of analysis and abstraction present in all thinking, but both also involve search and comparison. Both, of course, involve the same kind of mental states. At times it is very difficult to distinguish between them. Although for practical purposes it is necessary, sometimes, to stress the differences, the inherent similarity should not be lost sight of.
The differences between these two methods of reasoning are, first, in the locus of the problem; second, in the order of the steps of the process; third, in the relative proportion of particulars and generals used; fourth, in the devices used, (1) In induction the problem is concerned with a general. In some situation a concept, law, or principle has proven inadequate as a response. The question is then raised as to what is wrong with it and the inductive process is instigated. The problem is solved when the principle or concept is perfected or enlarged--in other words, is made adequate. In deduction the problem is concerned with the individual situation. Some problem is raised by a particular fact or experience and is answered when it is placed under the law or concept to which it belongs. Deduction is, practically the classification of particulars. (2) The order of steps is different. In induction, because present knowledge falls short, the major step of analysis necessary to abstraction of the essential is impossible, and therefore the search for new facts must come first, whereas in deduction, the analysis of the particular situation results in a search for generals and a classification of the situation in question. (3) In induction many particular facts may be necessary before one concept or principle is made adequate, while in deduction many concepts or principles may be examined before one particular is classified. (4) In induction the hypothesis is used as a device to make clear the possible goal; in deduction the syllogism is used as a device to make clear the conclusion which has been reached, to throw into relief the classification and the result coming from it.
In this discussion, induction and deduction have been treated, for the sake of clearness, as if they acted independently of each other, as if a thinker might at one time use deduction and at another time induction. They have been outlined in such a way that one might think that the movement of the mind in one process was such that it precluded the possibility of the other process. This is not so--the two are inextricably mingled in the actual process of reasoning, and further, induction as used in practical life always involves deduction at two points, as an initial starting point and as an end point. The knowledge that a certain principle is inadequate comes to consciousness through the attempt to classify some particular experience under it. Failure results and the inductive process may then be initiated, but this initial attempt is deductive and if it had been successful there would have been no need of induction. After the inductive process is complete and the general principle has been classified or perfected, the final step is testing it to see if it is adequate, first by applying it to the particular problem which caused the whole process, and then to new situations. If it tests, it is accepted,--if not, further induction is necessary. This again is deduction. Not only is induction not complete without deduction, but each deduction influences the principle which is applied, making it more sure and more flexible. Even in the process of induction, there are attempts to classify these facts which are being gathered under suggested old principles, or half-formed new ones, before the process is completed. This is a deductive movement, even though it prove unsatisfactory or impossible. Dewey describes this interaction by saying, "There is thus a double movement in all reflection: a movement from the given partial and confused data to a suggested comprehension (or inclusive) entire situation; and back from this suggested whole--which as suggested is a meaning, an idea--to the particular facts, so as to connect these with one another and with additional facts to which the suggestion has directed attention."[10] However true this intermingling of induction and deduction may be, the fact still remains true that in any given case the major movement is in one direction or the other, and that therefore in order to insure effective thinking measures must be taken accordingly. As a child formulates his conception of a verb, or words the characteristic essentials of the lily-family, or frames the rule for addition of fractions or the action of a base on a metal, he is concerned primarily with the form of the reasoning process known as induction. When he classes a certain word as a conjunction, a certain city as a trade center, a certain problem as one in percentage, he is using deduction. Complexes and gradual shadings of one state into another, not clearly defined and sharply differentiated processes and states, are characteristic of all mental life.