38.  Induction and Deduction.  Our next step is to consider how we get the generalizations on which we base so much of our reasoning.  As we have seen, the science which deals with the making of them, with their basis, and with the rules which govern inferences made from them is logic.

Logicians generally distinguish between two branches of their science, inductive and deductive reasoning.  In inductive reasoning we pass from individual facts to general principles; in deductive reasoning we pass from general principles to conclusions about individual facts.  The distinction, however, draws less interest in recent times than formerly, and logicians of the present generation tend to doubt whether it has any vital significance.[33] They point out that in practice we intermingle the two kinds almost inextricably, that the distinction between facts and principles is temporary and shifting, and that we cannot fit some of the common forms of inference into these categories without difficult and complicated restatement.

Nevertheless, as deductive logic and inductive logic are ancient and time-honored terms which have become a part of the vocabulary of educated men, it is worth while to take some note of the distinction between them, I shall not attempt here to do more than to explain a few of the more important principles.  I shall begin with inductive logic, since that is the branch which deals with the making of generalizations from individual fact, and therefore that which has most concern in the arguments of the average man in his passage through life.

39.  Inductive Reasoning.  In inductive reasoning we put individual facts and cases together into a class on the basis of some definable similarity, and then infer from them a general principle.  The types of inductive reasoning have been reduced by logicians to certain canons, but these reduce themselves to two main methods, which depend on whether in a given piece of reasoning we start from the likeness between the instances or the differences between them.  On these two methods, the method of agreement and the method of difference, hang all the processes of modern science, and most of our everyday arguments.

The method of agreement has been defined as follows: 

If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon.[34]

A few examples, which might easily be multiplied, will show how constantly we use this method in everyday life.  Suppose that a teacher is annoyed at somewhat irregular intervals by whispering and laughing in the back of the schoolroom, for which he can find no cause, but that presently he notices that whenever a certain pair of boys sit together there the trouble begins; he infers that these two boys are the cause of the trouble.