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.