37. Reasoning by Causal Relation. Reasoning by generalization rises greatly in certainty, however, whenever you can show the workings of cause and effect. If a college receives every year from a certain school a number of boys who are slack and lazy students, the dean of that college may come to generalize and expect most of the boys from that school to be poor timber. If, however, he finds that the master of the school will take and keep any boy who lives in the town, he is able to argue from this as a cause to the conclusion that the standards of the school are low, and then from these low standards as a cause to the poor quality of the graduates of the school.
Here is another example, from Professor James:
I am sitting in a railroad car, waiting for the train to start. It is winter, and the stove fills the car with pungent smoke. The brakeman enters, and my neighbor asks him to "stop that stove smoking." He replies that it will stop entirely as soon as the car begins to move. "Why so?" asks the passenger. "It always does," replies the brakeman. It is evident from this "always" that the connection between car moving and smoke stopping was a purely empirical one in the brakeman's mind, bred of habit. But if the passenger had been an acute reasoner ... [and had] singled out of all the numerous points involved in a stove's not smoking the one special point of smoke pouring freely out of the stove-pipe's mouth, he would probably ... have been immediately reminded of the law that a fluid passes more rapidly out of a pipe's mouth if another fluid be at the same time streaming over that mouth.[32][!--Note--]
Here the passenger's certainty that the smoking would stop would have been much increased if he had, as Professor James suggests, reasoned to the cause, instead of trusting to the brakeman's generalization from experience.
In scientific matters search for cause and effect is the chief mode of progress. General Sternberg's article "Yellow Fever and Mosquitoes" (p. 251) is an admirable account of this advance from probability to certainty, which comes from demonstrating the necessary sequence which we call cause and effect. When Major Reed and his associates had shown that in cases where mosquitoes were kept away there was no yellow fever, but that in cases where infected mosquitoes were allowed to bite patients yellow fever followed, they turned the probability that mosquitoes were the transmitting agent of the fever into a certainty. Likewise with the glacial theory: it had already in the time of the elder Professor Agassiz been established that certain regions of northern Europe and America could be classed together by the occurrence of certain phenomena—rounded hills, ledges of rock smoothed off and marked with scratches running more or less north and south, deposits of clean gravel and sand, boulders of various foreign kinds of rock scattered over the surface of the country; when he showed that glaciers in their movements produce all these phenomena, he laid bare the cause of the phenomena, and so demonstrated with practical certainty the theory of the former existence of a huge glacial sheet in the northern hemisphere. Wherever you can show that your case not only belongs to a recognized class of cases, with recognized characteristics, but also that in those characteristics there is a necessary sequence of cause and effect, you have proved your point.
In the example above, of an argument for the establishment of a municipal gymnasium, if after showing that all the boys and young men who get into the courts have no normal and healthy way of working off their natural animal spirits, you can show that in places where through settlements or municipal action gymnasiums have been provided, the number of arrests of boys and young men has greatly fallen off, you have established the grounds for an inference of cause and effect which gives your argument a wholly new strength. In the case of the argument for a return to a classical course in a college, this sequence of cause and effect would be very difficult to establish, for here you would be deep down in the most complex and subtle region of human nature. Wherever it is possible, however, lead the inference from a classification or generalization on to an inference of cause and effect.
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][!--Note--] 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.