The theory and practice of argumentation and debate

by Victor Alvin Ketcham

Inductive reasoning is the process by which we arrive at a general conclusion through the observation of concrete particulars. I have read Treasure Island and I found it interesting. Moreover, I have read Kidnapped, David Balfour, Prince Otto, and St. Ives, all of which were interesting to me. All of these books were written by Robert Louis Stevenson, and after I had read them I arrived at the general conclusion that all books written by Robert Louis Stevenson were interesting. I made use of this conclusion by searching in the library for other books by this same author, for I felt sure that if I could find another of his books it would be interesting. However, we are not now concerned with the uses to be made of this process of reasoning, but rather with its exact form. The process by which I arrived at the conclusion that all of Stevenson’s works are interesting is a fair example of inductive reasoning. I had five specific instances all pointing to the same conclusion. I had observed five of Stevenson’s books and I reached a conclusion regarding all of them. The conclusion included those which I had not read as well as those which I had read. This process conforms to our definition that inductive reasoning is the process by which we arrive at a general conclusion through the observation of concrete particulars.

In this way we arrive at many conclusions upon which we rely in our daily life. We go to a certain place at ten minutes past the hour for the purpose of boarding a street car which will take us to the city. We do this because for many months we have been accustomed to go to this same place at this particular time and there we have always found a street car which took us to the city. Each one of the instances in which we have done this is a concrete particular tending to support the general conclusion that if we go to a certain place at a certain time we shall find a car which will take us to the city.

A further investigation of this process of inductive reasoning reveals the fact that it may be divided into two sharply defined classes, (1) perfect inductions, and (2) imperfect inductions. A perfect induction is one in which all the particular instances upon which a conclusion is based can be examined directly. For example, if I am aware that each one of the twenty men who are taking this course in Argumentation expect to be civil engineers I may safely state the general conclusion that “All the men who are taking this course in Argumentation expect to be civil engineers.” This is a perfect induction, because I have included in the conclusion only those men who are taking this course; there are only twenty men and investigation has shown that each of them expects to be a civil engineer. Therefore, it is plain that there can be no opportunity for error. Every particular instance relied upon can be accounted for and no instance outside of these is brought within the conclusion. The induction is therefore perfect.

An imperfect induction is one in which the conclusion extends beyond the concrete specific instances upon which it is based. The examples already given regarding Stevenson’s novels and the street car are imperfect inductions. I have not read all of Stevenson’s novels and I may yet find one that is not interesting to me. Regarding the induction about the street car, it is sufficient to note that if the car were late or failed to appear at all, the conclusion would be of no value in that specific instance. Likewise I may state the general inductive conclusion that all roses are fragrant. I base this conclusion upon a great number of specific instances. The rose that I plucked yesterday was fragrant; those which I observed in the conservatory last month were fragrant; the roses which bloom in my door-yard each summer are fragrant; all the roses that I have known since I was old enough to notice such matters have been fragrant. Upon this great number of specific instances I base my inductive conclusion. It will be observed, however, that my conclusion is not confined to the roses which I have seen but that it extends beyond and includes all roses of every kind everywhere. It is therefore an imperfect induction. As it stands it would be impossible to make this induction a perfect one, because it would be an impossible task to examine every rose in the world. The only way in which the induction can be made perfect is to restrict the conclusion to cover only the specific instances upon which it is based. The conclusion would then be, “All the roses to which I have ever given attention were fragrant.”

But it may not suit our purpose thus to restrict the conclusion. We may wish to make use of it in its broad general significance. Every day we are compelled to act upon imperfect inductions, as in the case of the street car. In such cases we must resort to certain rules or tests whereby we can determine the probability of the truth of the imperfect induction. We shall consider these rules or tests after we have discussed the application of inductive reasoning to inductive argument.

III. The application of inductive reasoning to inductive argument.

We have seen the nature of the process of induction and have observed the distinction between the perfect and the imperfect. Let us now consider the application of the inductive process to arguments. The occurrence of this process in all argumentative discourse is frequent. A simple illustration of its application is furnished in connection with the proposition “Resolved, that the Federal Government should levy an income tax.” The affirmative in the course of its investigation finds that this tax has proved practicable in Switzerland, Germany, France, and England. Further investigation discloses the fact that these are the only countries in which this particular form of taxation has been adopted. From these particular instances, namely,—Switzerland, Germany, France, and England, the general inductive conclusion may be drawn that “The income tax has proved practicable in all the countries in which it has been adopted.” This is a perfect inductive conclusion.

In presenting this induction in an argument, the conclusion should be stated first. Then each of the countries in which the income tax has been adopted should be discussed and evidence introduced to show that it has proved practicable in every case. Finally, evidence should be brought forth to show that the countries named are the only ones in which the tax has been adopted. The conclusion should be stated in the form of a summary, which leaves the argument complete. It is a perfect inductive argument. While the reasoning process cannot be assailed, the facts upon which the induction is based may be disproved. Those advancing the argument must therefore be sure that the facts alleged are supported by sufficient evidence, while those seeking to overthrow the argument should be diligent in their search for evidence showing the weakness or impracticability of the tax in one or all of the countries cited.

From the above illustration it is plain that the validity of the reasoning of a perfect induction is easily determined. The mind at once determines whether or not the specific instances presented warrant the conclusion reached. The question of the validity of a perfect inductive argument is largely a question of fact. With the imperfect induction, however, the situation is somewhat different, for we have seen that the conclusion extends beyond the actual facts upon which it is based. From an examination of several observed specific instances a conclusion is drawn which covers instances unobserved. By it we pass from the known to the unknown. This process is sometimes called the inductive hazard. The application of this form of reasoning to argument is illustrated by the imperfect induction which is made by Lincoln in his Cooper Institute Address. Here he draws a conclusion as to what all the framers of the original Constitution thought about the slavery problem, by producing evidence to show what a part of them thought about it. After introducing specific evidence to show what each of twenty-three of these men thought, he says:

“Here then we have twenty-three of our thirty-nine fathers ‘who framed the government under which we live’, who have, upon their official responsibility and their corporeal oaths, acted upon the very question which the text affirms ‘they understood just as well, and even better, than we do now’; and twenty-one of them—a clear majority of the whole thirty-nine—so acting upon it as to make them guilty of gross political impropriety and willful perjury, if, in their understanding, any proper division between local and Federal authority, or anything in the Constitution they had made themselves, and sworn to support, forbade the Federal Government to control as to slavery in the Federal Territories. Thus the twenty-one acted; and as actions speak louder than words, so actions under such responsibility speak still louder....