YOUR MIND AND HOW TO USE IT/PART 26
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."
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.
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