The theory and practice of argumentation and debate

by Victor Alvin Ketcham

“The remaining sixteen of the ‘thirty-nine’, so far as I have discovered, have left no trace of their understanding upon the direct question of Federal control in the Federal Territories. But there is much reason to believe that their understanding upon that question would not have appeared different from that of their twenty-three compeers, had it been manifested at all....

“The sum of the whole is that of our thirty-nine fathers who framed the original Constitution, twenty-one—a clear majority of the whole—certainly understood that no proper division of local from Federal authority, nor any part of the Constitution, forbade the Federal Government to control as to slavery in the Federal Territories; while all the rest had probably the same understanding. Such, unquestionably, was the understanding of our fathers who framed the original Constitution; and the text affirms that they understood the question ‘better than we.’”

The true test of an imperfect induction is not its sufficiency for the person who uses it, but its sufficiency for those to whom it is addressed. The argument is designed to produce a definite effect and in order to do this it must fulfil certain conditions. Even when these conditions are fulfilled the effect of the argument is problematical. Nevertheless, in order to approach its maximum efficiency an inductive argument must meet the requirements explained in the following section.

IV. Requirements for an effective inductive argument.

1. Perfect inductions.

In a perfect induction in which we have seen that the conclusion includes only the specific instances that have actually been examined, the only requirement is that the facts upon which it is based be true. The student must observe the rules regarding the sufficiency of evidence. He must be sure that he has introduced evidence which shows conclusively that each specific instance cited in support of the conclusion is true as a matter of fact. If he allows conjecture to enter into any one of them he cannot claim for his argument the solidity which characterizes the perfect induction. If in arguing for the necessity of additional sources of revenue for the United States government, he has stated the perfect inductive conclusion that “The expenditures of the United States government for the last three years have greatly exceeded its receipts,” he must substantiate his induction by exact reference to the reports of the Treasurer of the United States for the last three years. An investigation of these references must reveal the fact that each of these years has shown a large deficit. The greatest temptation against which the student will have to guard is that of careless generalization. He may know that a conclusion includes four specific instances. He may be certain that three of them support the conclusion, but he is not quite sure about the fourth. Nevertheless he conjectures regarding its validity and heedlessly proceeds to his conclusion. This is a bad habit to cultivate, because it results in loose, inaccurate thinking. A perfect induction should never be stated in an argument until each specific instance upon which it is based, and which it includes, has been determined to be an unquestioned fact.

2. Imperfect inductions.

The requirements for an imperfect induction are somewhat involved and demand the exercise of sound judgment in their application. An imperfect induction can never be relied upon with the same confidence that may be reposed in a perfect induction. This truth is apparent from the nature of the imperfect induction. In order to measure up to a high standard of effectiveness an imperfect induction must comply with the following requirements.

A. The number of specific instances supporting the conclusion must be sufficiently large to offset the probability of coincidence.

The problem of determining the number of specific instances which will justify us in relying upon an imperfect induction is most difficult. As we shall presently see, this number varies greatly with different classes of persons, events, and things about which we wish to reach conclusions. But before we consider this difficulty we must be sure that we have enough instances at hand to eliminate the element of chance. At least from the argumentative standpoint this is the most practical method of procedure. Suppose the student in his preparation for an argument finds that during the last year there has been a decrease in the value of manufactured articles produced in the state of Texas, that a similar decrease is shown in the state of New York, and that statistics relating to the state of Delaware show the same result. These facts could not be used to support the conclusion that the value of manufactured products of all the states of the Union has decreased during the last year, because it may be only a coincidence that their value has decreased in the states named. In all the other states of the Union there may have been an increase. The conclusion stated should belong to a perfect induction and could only stand upon proof of the fact that the value of the products manufactured in each and every one of the states showed a decrease. Moreover, it would not be safe to state the conclusion that the value of manufactured products in general shows a falling off in value during the past year and to cite the three instances named in support of that contention. In fact, the probability of coincidence is too great to enable us to arrive at any inductive conclusion other than that the manufactured products of Texas, New York, and Delaware for the past year show a decrease in value.