CHAPTER XI.
INDUCTIVE REASONING
Inductive Reasoning, as we have said, is the process of discovering general truth from particular truths, or inferring general laws from particular facts. Thus, from the experience of the individual and the race regarding the particular truth that each and every man under observation has been observed to die sooner or later, it is inferred that all men die, and hence, the induction of the general truth that "All men must die." Or, as from experience we know that the various kinds of metals expand when subjected to heat, we infer that all metals are subject to this law, and that consequently we may arrive by inductive reasoning at the conclusion that: "All metals expand when subjected to heat." It will be noticed that the conclusion arrived at in this way by Inductive Reasoning forms the fundamental premise in the process of Deductive Reasoning. As we have seen elsewhere, the two processes, Inductive and Deductive Reasoning, respectively are interdependent—resting upon one another.
Jevons says of Inductive Reasoning: "In Deductive Reasoning we inquire how we may gather the truth contained in some propositions called Premises, and put into another proposition called the Conclusion. We have not yet undertaken to find out how we can learn what propositions really are true, but only what propositions are true when other ones are true. All the acts of reasoning yet considered would be called deductive because we deduce, or lead down the truth from premises to conclusion. It is an exceedingly important thing to understand deductive inference correctly, but it might seem to be still more important to understand inductive inference, by which we gather the truth of general propositions from facts observed as happening in the world around us." Halleck says: "Man has to find out through his own experience, or that of others, the major premises from which he argues or draws his conclusions. By induction we examine what seems to us a sufficient number of individual cases. We then conclude that the rest of these cases, which we have not examined, will obey the same general law.... Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can deduction be employed."
Strange as may now appear, it is a fact that until a comparatively recent period in the history of man, it was held by philosophers that the only way to arrive at all knowledge was by means of Deductive Reasoning, by the use of the Syllogism. The influence of Aristotle was great and men preferred to pursue artificial and complicated methods of Deductive Reasoning, rather than to reach the truth by obtaining the facts from Nature herself, at first hand, and then inferring general principle from the facts so gathered. The rise of modern scientific methods of reasoning, along the lines of Inductive Inference, dates from about 1225-1300. Roger Bacon was one of the first to teach that we must arrive at scientific truth by a process of observation and experimentation on the natural objects to be found on all sides. He made many discoveries by following this process. He was ably seconded by Galileo who lived some three hundred years later, and who also taught that many great general truths might be gained by careful observation and intelligent inference. Lord Francis Bacon, who lived about the same time as Galileo, presented in his Novum Organum many excellent observations and facts regarding the process of Inductive Reasoning and scientific thought. As Jevons says: "Inductive logic inquires by what manner of reasoning we can gather the laws of nature from the facts and events observed. Such reasoning is called induction, or inductive inquiry, and, as it has actually been practiced by all the great discoverers in science, it consists in four steps."
The Four Steps in Inductive Reasoning, as stated by Jevons, are as follows:
First Step.—Preliminary observation.
Second Step.—The making of hypotheses.
Third Step.—Deductive reasoning.
Fourth Step.—Verification.