6. REASONING
All the mental processes which we have so far described find their culmination and highest utility in reasoning. Not that reasoning comes last in the list of mental activities, and cannot take place until all the others have been completed, for reasoning is in some degree present almost from the dawn of consciousness. The difference between the reasoning of the child and that of the adult is largely one of degree—of reach. Reasoning goes farther than any of the other processes of cognition, for it takes the relations expressed in judgments and out of these relations evolves still other and more ultimate relations.
Nature of Reasoning.—It is hard to define reasoning so as to describe the precise process which occurs; for it is so intermingled with perception, conception, and judgment, that one can hardly separate them even for purposes of analysis, much less to separate them functionally. We may, however, define reasoning provisionally as thinking by means of a series of judgments with the purpose of arriving at some definite end or conclusion. What does this mean? Professor Angell has stated the matter so clearly that I will quote his illustration of the case:
"Suppose that we are about to make a long journey which necessitates the choice from among a number of possible routes. This is a case of the genuinely problematic kind. It requires reflection, a weighing of the pros and cons, and giving of the final decision in favor of one or other of several alternatives. In such a case the procedure of most of us is after this order. We think of one route as being picturesque and wholly novel, but also as being expensive. We think of another as less interesting, but also as less expensive. A third is, we discover, the most expedient, but also the most costly of the three. We find ourselves confronted, then, with the necessity of choosing with regard to the relative merits of cheapness, beauty, and speed. We proceed to consider these points in the light of all our interests, and the decision more or less makes itself. We find, for instance, that we must, under the circumstances, select the cheapest route."
How Judgments Function in Reasoning.—Such a line of thinking is very common to everyone, and one that we carry out in one form or another a thousand times every day we live. When we come to look closely at the steps involved in arriving at a conclusion, we detect a series of judgments—often not very logically arranged, to be sure, but yet so related that the result is safely reached in the end. We compare our concept of, say, the first route and our concept of picturesqueness, decide they agree, and affirm the judgment, "This route is picturesque." Likewise we arrive at the judgment, "This route is also expensive, it is interesting, etc." Then we take the other routes and form our judgments concerning them. These judgments are all related to each other in some way, some of them being more intimately related than others. Which judgments remain as the significant ones, the ones which are used to solve the problem finally, depends on which concepts are the most vital for us with reference to the ultimate end in view. If time is the chief element, then the form of our reasoning would be something like this: "Two of the routes require more than three days: hence I must take the third route." If economy is the important end, the solution would be as follows: "Two routes cost more than $1,000; I cannot afford to pay more than $800; I therefore must patronize the third route."
In both cases it is evident that the conclusion is reached through a comparison of two or more judgments. This is the essential difference between judgment and reasoning. Whereas judgment discovers relations between concepts, reasoning discovers relations between judgments, and from this evolves a new judgment which is the conclusion sought. The example given well illustrates the ordinary method by which we reason to conclusions.
Deduction and the Syllogism.—Logic may take the conclusion, with the two judgments on which it is based, and form the three into what is called a syllogism, of which the following is a classical type:
The first judgment is in the form of a proposition which is called the major premise, because it is general in its nature, including all men. The second is the minor premise, since it deals with a particular man. The third is the conclusion, in which a new relation is discovered between Socrates and mortality.
This form of reasoning is deductive, that is, it proceeds from the general to the particular. Much of our reasoning is an abbreviated form of the syllogism, and will readily expand into it. For instance, we say, "It will rain tonight, for there is lightning in the west." Expanded into the syllogism form it would be, "Lightning in the west is a sure sign of rain; there is lightning in the west this evening; therefore, it will rain tonight." While we do not commonly think in complete syllogisms, it is often convenient to cast our reasoning in this form to test its validity. For example, a fallacy lurks in the generalization, "Lightning in the west is a sure sign of rain." Hence the conclusion is of doubtful validity.
Induction.—Deduction is a valuable form of reasoning, but a moment's reflection will show that something must precede the syllogism in our reasoning. The major premise must be accounted for. How are we able to say that all men are mortal, and that lightning in the west is a sure sign of rain? How was this general truth arrived at? There is only one way, namely, through the observation of a large number of particular instances, or through induction.
Induction is the method of proceeding from the particular to the general. Many men are observed, and it is found that all who have been observed have died under a certain age. It is true that not all men have been observed to die, since many are now living, and many more will no doubt come and live in the world whom we cannot observe, since mortality will have overtaken us before their advent. To this it may be answered that the men now living have not yet lived up to the limit of their time, and, besides, they have within them the causes working whose inevitable effect has always been and always will be death; likewise with the men yet unborn, they will possess the same organism as we, whose very nature necessitates mortality. In the case of the premonitions of rain, the generalization is not so safe, for there have been exceptions. Lightning in the west at night is not always followed by rain, nor can we find inherent causes as in the other case which necessitates rain as an effect.
The Necessity for Broad Induction.—Thus it is seen that our generalizations, or major premises, are of all degrees of validity. In the case of some, as the mortality of man, millions of cases have been observed and no exceptions found, but on the contrary, causes discovered whose operation renders the result inevitable. In others, as, for instance, in the generalization once made, "All cloven-footed animals chew their cud," not only had the examination of individual cases not been carried so far as in the former case when the generalization was made, but there were found no inherent causes residing in cloven-footed animals which make it necessary for them to chew their cud. That is, cloven feet and cud-chewing do not of necessity go together, and the case of the pig disproves the generalization.
In practically no instance, however, is it possible for us to examine every case upon which a generalization is based; after examining a sufficient number of cases, and particularly if there are supporting causes, we are warranted in making the "inductive leap," or in proceeding at once to state our generalization as a working hypothesis. Of course it is easy to see that if we have a wrong generalization, if our major premise is invalid, all that follows in our chain of reasoning will be worthless. This fact should render us careful in making generalizations on too narrow a basis of induction. We may have observed that certain red-haired people of our acquaintance are quick-tempered, but we are not justified from this in making the general statement that all red-haired people are quick-tempered. Not only have we not examined a sufficient number of cases to warrant such a conclusion, but we have found in the red hair not even a cause of quick temper, but only an occasional concomitant.
The Interrelation of Induction and Deduction.—Induction and deduction must go hand in hand in building up our world of knowledge. Induction gives us the particular facts out of which our system of knowledge is built, furnishes us with the data out of which general truths are formed; deduction allows us to start with the generalization furnished us by induction, and from this vantage ground to organize and systematize our knowledge and, through the discovery of its relations, to unify it and make it usable. Deduction starts with a general truth and asks the question, "What new relations are made necessary among particular facts by this truth?" Induction starts with particulars, and asks the question, "To what general truth do these separate facts lead?" Each method of reasoning needs the other. Deduction must have induction to furnish the facts for its premises; induction must have deduction to organize these separate facts into a unified body of knowledge. "He only sees well who sees the whole in the parts, and the parts in the whole."
