Higher Forms of Reasoning.
The two higher forms of reasoning are known, respectively, as (1) inductive reasoning, or inference from particular facts to general laws; and (2) deductive reasoning, or inference from general truths to particular truths. While the class distinction is made for the purpose of clear consideration, it must not be forgotten that the two forms of reasoning are generally found in combination. Thus, in inductive reasoning many steps are taken by the aid of deductive reasoning; and, likewise, before we can reason deductively from general truths to particular ones we must have discovered the general truths by inductive reasoning from particular facts. Thus there is a unity in all reasoning processes as there is in all mental operations. Inductive reasoning is a synthetical process; deductive reasoning, an analytical one. In the first we combine and build up, in the latter we dissect and separate.
CHAPTER XXVI.
Inductive Reasoning.
INDUCTIVE reasoning is based upon the axiom: "What is true of the many is true of the whole." This axiom is based upon man's belief in the uniformity of nature. Inductive reasoning is a mental ladder by which we climb from particular facts to general laws, but the ladder rests upon the belief that the universe is governed by law.
The steps in inductive reasoning are as follows:—
I. Observation, investigation, and examination of particular facts or things. If we wish to know the general characteristics of the bird family, we must first examine a sufficient number of birds of many kinds so as to discover the comparatively few general characteristics possessed by all of the bird family, as distinct from the particular characteristics possessed by only some of that family. The greater the number of individuals examined, the narrower becomes our list of the general qualities common to all. In the same way we must examine many kinds of flowers before we come to the few general qualities common to all flowers, which we combine in the general concept of "flower." The same, of course, is true regarding the discovery of general laws from particular facts. We examine the facts and then work toward a general law which will explain them. For instance, the Law of Gravitation was discovered by the observation and investigation of the fact that all objects are attracted to the earth; further investigation revealed the fact that all material objects are attracted to each other; then the general law was discovered, or, rather, the hypothesis was advanced, was found to explain the facts, and was verified by further experiments and observation.
II. The second step in inductive reasoning is the making of an hypothesis. An hypothesis is a proposition or principle assumed as a possible explanation for a set or class of facts. It is regarded as a "working theory," which must be examined and tested in connection with the facts before it is finally accepted. For instance, after the observation that a number of magnets attracted steel, it was found reasonable to advance the hypothesis that "all magnets attract steel." In the same way was advanced the hypothesis that "all birds are warm-blooded, winged, feathered, oviparous vertebrates." Subsequent observation and experiment established the hypothesis regarding the magnet, and regarding the general qualities of the bird family. If a single magnet had been found which did not attract steel, then the hypothesis would have fallen. If a single bird had been discovered which was not warm-blooded, then that quality would have been stricken from the list of the necessary characteristics of all birds.
A theory is merely an hypothesis which has been verified or established by continued and repeated observation, investigation, and experiment.
Hypotheses and theories arise very frequently from the subconscious assimilation of a number of particular facts and the consequent flashing of a "great guess," or "sacred suspicion of the truth," into the conscious field of attention. The scientific imagination plays an important part in this process. There is, of course, a world of difference between a "blind guess" based upon insufficient data and a "scientific guess" resulting from the accumulation of a vast store of careful and accurate information. As Brooks says: "The forming of an hypothesis requires a suggestive mind, a lively fancy, a philosophic imagination that catches a glimpse of the idea through the form or sees the law standing behind the fact." But accepted theories, in the majority of cases, arise only by testing out and rejecting many promising hypotheses and finally settling upon the one which best answers all the requirements and best explains the facts. As an authority says: "To try wrong guesses is with most persons the only way to hit upon right ones."