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."
III. Testing the hypothesis by deductive reasoning is the third step in
inductive reasoning. This test is made by applying the hypothetical
principle to particular facts or things; that is, to follow out mentally
the hypothetical principle to its logical conclusion. This may be done
in this way: "If _so and so_ is correct, then it follows that _thus and
so_ is true," etc. If the conclusion agrees with reason, then the test
is deemed satisfactory so far as it has gone. But if the result proves
to be a logical absurdity or inconsistent with natural facts, then the
hypothesis is discredited.
IV. Practical verification of the hypothesis is the fourth step in
inductive reasoning. This step consists of the actual comparison of
observed facts with the "logical conclusions" arising from applying
deductive reasoning to the general principle assumed as a premise. The
greater number of facts agreeing with the conclusions arising from the
premise of the hypothesis, the greater is deemed the "probability" of
the latter. The authorities generally assume an hypothesis to be
_verified_ when it accounts for _all_ the facts which properly are
related to it. Some extremists contend, however, that before an
hypothesis may be considered as absolutely verified, it must not only
account for all the associated facts but that also there must be no
other possible hypothesis to account for the same facts. The "facts"
referred to in this connection may be either (1) observed phenomena, or
(2) the conclusions of deductive reasoning arising from the assumption
of the hypothesis, or (3) the agreement between the observed facts and
the logical conclusions. The last combination is generally regarded as
the most logical. The verification of an hypothesis must be "an
all-around one," and there must be an agreement between the observed
facts and the logical conclusions in the case--the hypothesis must "fit"
the facts, and the facts must "fit" the hypothesis. The "facts" are the
glass slipper of the Cinderella legend--the several sisters of
Cinderella were discarded hypotheses, the slipper and the sisters not
"fitting." When Cinderella's foot was found to be the one foot upon
which the glass slipper fitted, then the Cinderella hypothesis was
considered to have been proved--the glass slipper was hers and the
prince claimed his bride.