THE ART OF LOGICAL THINKING/PART 12
CHAPTER XII.
REASONING BY INDUCTION
The
term "Induction," in its logical usage, is defined as follows:
"(a) The process of investigating and collecting facts; and (b) the
deducing of an inference from these facts; also (c) sometimes loosely used in
the sense of an inference from observed facts." Mill says: "Induction,
then, is that operation of the mind, by which we infer that what we know to be
true in a particular case or cases, will be true in all cases which resemble
the former in certain assignable respects. In other words, Induction is
the process by which we conclude that what is true of certain individuals of a
class, is true of the whole class, or that what is true at certain times will
be true in similar circumstances at all times."
The Basis
of Induction is the axiom that: "What is true of the many is
true of the whole." Esser, a well known authority, states this axiom
in rather more complicated form, as follows: "That which belongs or does
not belong to many things of the same kind, belongs or does not belong to
all things of the same kind."
This
basic axiom of Induction rests upon the conviction that Nature's laws and
manifestations are regular, orderly and uniform. If we assume that
Nature does not manifest these qualities, then the axiom must fall, and all
inductive reason must be fallacious. As Brooks well says: "Induction has
been compared to a ladder upon which we ascend from facts to laws. This ladder
cannot stand unless it has something to rest upon; and this something is our
faith in the constancy of Nature's laws." Some authorities have held that
this perception of the uniformity of Nature's laws is in the nature of an intuitive truth,
or an inherent law of our intelligence. Others hold that it is in itself
an inductive truth, arrived at by experience and observation
at a very early age. We are held to have noticed the uniformity in natural
phenomena, and almost instinctively infer that this uniformity is continuous
and universal.
The
authorities assume the existence of two kinds of Induction, namely: (1) Perfect
Induction; and (2) Imperfect Induction. Other, but similar, terms are employed
by different authorities to designate these two classes.
Perfect
Induction necessitates a knowledge of all the
particulars forming a class; that is, all the individual
objects, persons, things or facts comprising a class must be known and
enumerated in this form of Induction. For instance, if we knew
positively all of Brown's children, and that their names were John,
Peter, Mark, Luke, Charles, William, Mary and Susan, respectively; and that
each and every one of them were freckled and had red hair; then, in that case,
instead of simply generalizing and stating that: "John,
Peter, Mark, Luke, Charles, William, Mary and Susan, who are all of
Brown's children, are freckled and have red hair," we would save words,
and state the inductive conclusion: "All Brown's children are freckled and
have red hair." It will be noticed that in this case we include in
the process only what is stated in the premise itself, and we do not extend
our inductive process beyond the actual data upon which it is based. This form
of Induction is sometimes called "Logical Induction," because the
inference is a logical necessity, without the possibility of error or
exception. By some authorities it is held not to be Induction at all, in the
strict sense, but little more than a simplified form of enumeration. In actual
practice it is seldom available, for it is almost impossible for us to know all
the particulars in inferring a general law or truth. In view of this
difficulty, we fall back upon the more practical form of induction known as:
Imperfect
Induction, or as it is sometimes called "Practical Induction," by
which is meant the inductive process of reasoning in which we assume that the
particulars or facts actually known to us correctly represent those which are not
actually known, and hence the whole class to which they belong. In this process
it will be seen that the conclusion extends beyond the data
upon which it is based. In this form of Induction we must actually employ the
principle of the axiom: "What is true of the many is true of the
whole"—that is, must assume it to be a fact, not because
we know it by actual experience, but because we infer it from
the axiom which also agrees with past experience. The conclusion arrived
at may not always be true in its fullest sense, as in the case of the
conclusion of Perfect Induction, but is the result of an inference based upon a
principle which gives us a reasonable right to assume its truth in absence of
better knowledge.
In
considering the actual steps in the process of Inductive Reasoning we can do no
better than to follow the classification of Jevons, mentioned in the preceding
chapter, the same being simple and readily comprehended, and therefore
preferable in this case to the more technical classification favored by some
other authorities. Let us now consider these four steps.
First
Step. Preliminary observation. It follows that without the
experience of oneself or of others in the direction of observing and
remembering particular facts, objects, persons and things, we cannot hope to
acquire the preliminary facts for the generalization and inductive inference
necessary in Inductive Reasoning. It is necessary for us to form a variety of
clear Concepts or ideas of facts, objects, persons and things, before we may hope
to generalize from these particulars. In the chapters of this book devoted
to the consideration of Concepts, we may see the fundamental importance of the
formation and acquirement of correct Concepts. Concepts are the fundamental
material for correct reasoning. In order to produce a perfect finished product,
we must have perfect materials, and a sufficient quantity of them. The greater
the knowledge one possesses of the facts and objects of the outside world, the
better able is he to reason therefrom. Concepts are the raw material which must
feed the machinery of reasoning, and from which the final product of perfected
thought is produced. As Halleck says: "There must first be a presentation
of materials. Suppose that we wish to form the concept fruit. We
must first perceive the different kinds of fruit—cherry, pear, quince, plum,
currant, apple, fig, orange, etc. Before we can take the next step, we must be
able to form distinct and accurate images of the various kinds of fruit. If the
concept is to be absolutely accurate, not one kind of fruit must be overlooked.
Practically this is impossible; but many kinds should be examined. Where
perception is inaccurate and stinted, the products of thought cannot be
trustworthy. No building is firm if reared on insecure foundations."
In
the process of Preliminary Observation, we find that there are two ways of
obtaining a knowledge of the facts and things around us. These two ways are as
follows:
I.
By Simple Observation, or the perception of the happenings which
are manifested without our interference. In this way we perceive the motion of
the tides; the movement of the planets; the phenomena of the weather; the
passing of animals, etc.
II.
By the Observation of Experiment, or the perception of happenings
in which we interfere with things and then observe the result. An experiment is:
"A trial, proof, or test of anything; an act, operation, or process
designed to discover some unknown truth, principle or effect, or to test some
received or reputed truth or principle." Hobbes says: "To have had
many experiments is what we call experience."
Jevons says: "Experimentation is observation with something more; namely,
regulation of the things whose behavior is to be observed. The
advantages of experiment over mere observation are of two kinds. In the
first place, we shall generally know much more certainly and accurately with
what we are dealing, when we make experiments than when we simply observe
natural events.... It is a further advantage of artificial experiments, that
they enable us to discover entirely new substances and to learn their
properties.... It would be a mistake to suppose that the making of an
experiment is inductive reasoning, and gives us without further trouble the
laws of nature. Experiments only give us the facts upon which we may
afterward reason.... Experiments then merely give facts, and it is
only by careful reasoning that we can learn when the same facts will be
observed again. The general rule is that the same causes will produce
the same effects. Whatever happens in one case will happen in all like
cases, provided that they are really like, and not merely apparently so....
When we have by repeated experiments tried the effect which all the surrounding
things might have on the result, we can then reason with much confidence as to
similar results in similar circumstances.... In order that we may, from
our observations and experiments, learn the law of nature and become able to
foresee the future, we must perform the process of generalization. To generalize
is to draw a general law from particular cases, and to infer that what we see
to be true of a few things is true of the whole genus or class to which these
things belong. It requires much judgment and skill to generalize correctly,
because everything depends upon the number and character of the instances about
which we reason."
Having
seen that the first step in Inductive Reasoning is Preliminary Observation, let
us now consider the next steps in which we may see what we do with the facts
and ideas which we have acquired by this Observation and Experiment.
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