INDUCTIVE REASONING
Inductive Reasoning, as we have said, is the process of discovering
general truth from particular truths, or inferring general laws from
particular facts. Thus, from the experience of the individual and the
race regarding the particular truth that each and every man under
observation has been observed to die sooner or later, it is inferred
that _all_ men die, and hence, the induction of the general truth that
"All men must die." Or, as from experience we know that the various
kinds of metals expand when subjected to heat, we infer that _all_
metals are subject to this law, and that consequently we may arrive by
inductive reasoning at the conclusion that: "All metals expand when
subjected to heat." It will be noticed that the conclusion arrived at in
this way by Inductive Reasoning forms the fundamental premise in the
process of Deductive Reasoning. As we have seen elsewhere, the two
processes, Inductive and Deductive Reasoning, respectively are
interdependent--resting upon one another.
Jevons says of Inductive Reasoning: "In Deductive Reasoning we inquire
how we may gather the truth contained in some propositions called
Premises, and put into another proposition called the Conclusion. We
have not yet undertaken to find out how we can learn what propositions
really are true, but only _what propositions are true when other ones
are true_. All the acts of reasoning yet considered would be called
_deductive because we deduce, or lead down the truth from premises to
conclusion_. It is an exceedingly important thing to understand
deductive inference correctly, but it might seem to be still more
important to understand _inductive inference_, by which we gather the
truth of general propositions from facts observed as happening in the
world around us." Halleck says: "Man has to find out through his own
experience, or that of others, the major premises from which he argues
or draws his conclusions. By induction we examine what seems to us a
sufficient number of individual cases. We then conclude that the rest of
these cases, which we have not examined, will obey the same general
law.... Only after general laws have been laid down, after objects have
been classified, after major premises have been formed, can deduction be
employed."
Strange as may now appear, it is a fact that until a comparatively
recent period in the history of man, it was held by philosophers that
the only way to arrive at all knowledge was by means of Deductive
Reasoning, by the use of the Syllogism. The influence of Aristotle was
great and men preferred to pursue artificial and complicated methods of
Deductive Reasoning, rather than to reach the truth by obtaining the
facts from Nature herself, at first hand, and then inferring general
principle from the facts so gathered. The rise of modern scientific
methods of reasoning, along the lines of Inductive Inference, dates from
about 1225-1300. Roger Bacon was one of the first to teach that we must
arrive at scientific truth by a process of observation and
experimentation on the natural objects to be found on all sides. He made
many discoveries by following this process. He was ably seconded by
Galileo who lived some three hundred years later, and who also taught
that many great general truths might be gained by careful observation
and intelligent inference. Lord Francis Bacon, who lived about the same
time as Galileo, presented in his _Novum Organum_ many excellent
observations and facts regarding the process of Inductive Reasoning and
scientific thought. As Jevons says: "Inductive logic inquires by what
manner of reasoning we can gather the laws of nature from the facts and
events observed. Such reasoning is called induction, or inductive
inquiry, and, as it has actually been practiced by all the great
discoverers in science, it consists in four steps."
The _Four Steps in Inductive Reasoning_, as stated by Jevons, are as
follows:
_First Step._--Preliminary observation.
_Second Step._--The making of hypotheses.
_Third Step._--Deductive reasoning.
_Fourth Step._--Verification.
It will be seen that the process of Inductive Reasoning is essentially
_a synthetic process_, because it operates in the direction of combining
and uniting particular facts or truths into general truths or laws which
comprehend, embrace and include them all. As Brooks says: "The
particular facts are united by the mind into the general law; the
general law embraces the particular facts and binds them together into a
unity of principle and thought. Induction is thus a process of thought
from the parts to the whole--a synthetic process." It will also be seen
that the process of Inductive Reasoning is essentially _an ascending
process_, because it ascends from particular facts to general laws;
particular truths to universal truths; from the lower to the higher, the
narrower to the broader, the smaller to the greater.
Brooks says of Inductive Reasoning: "The relation of induction to
deduction will be clearly seen. Induction and Deduction are the
converse, the opposites of each other. Deduction derives a particular
truth from a general truth; Induction derives a general truth from
particular truths. This antithesis appears in every particular.
Deduction goes from generals to particulars; Induction goes from
particulars to generals. Deduction is an analytic process; Induction is
a synthetic process. Deduction is a descending process--it goes from
the higher truth to the lower truth; Induction is an ascending
process--it goes from the lower truth to the higher. They differ also in
that Deduction may be applied to necessary truths, while Induction is
mainly restricted to contingent truths." Hyslop says: "There have been
several ways of defining this process. It has been usual to contrast it
with Deduction. Now, deduction is often said to be reasoning from
general to particular truths, from the containing to the contained
truth, or from cause to effect. Induction, therefore, by contrast is
defined as reasoning from the particular to the general, from the
contained to the containing, or from effect to cause. Sometimes
induction is said to be reasoning from the known to the unknown. This
would make deduction, by contrast, reasoning from the unknown to the
known, which is absurd. The former ways of representing it are much the
better. But there is still a better way of comparing them. Deduction _is
reasoning in which the conclusion is contained in the premises_. This is
a ground for its certitude and we commit a fallacy whenever we go beyond
the premises as shown by the laws of the distribution of terms. In
contrast with this, then, we may call inductive reasoning _the process
by which we go beyond the premises in the conclusion_.... The process
here is to start from given facts and to infer some other probable facts
more general or connected with them. In this we see the process of going
beyond the premises. There are, of course, certain conditions which
regulate the legitimacy of the procedure, just as there are conditions
determining deduction. They are _that the conclusion shall represent the
same general kind as the premises_, with a possibility of accidental
differences. But it goes beyond the premises in so far as _known_ facts
are concerned."
The following example may give you a clearer idea of the processes of
Inductive Reasoning:
_First Step._ Preliminary Observation. _Example_: We notice that all the
particular _magnets_ which have come under our observation _attract
iron_. Our mental record of the phenomena may be stated as: "A, B, C, D,
E, F, G, etc., and also X, Y, and Z, all of which are _magnets_, in all
observed instances, and at all observed times, _attract iron_."
_Second Step._ The Making of Hypotheses. _Example_: Upon the basis of
the observations and experiments, as above stated, and applying the
axiom of Inductive Reasoning, that: "What is true of the many, is true
of the whole," we feel justified in forming a hypothesis or inference of
a general law or truth, applying the facts of the particulars to the
general, whole or universal, thus: "_All_ magnets attract iron."
_Third Step._ Deductive Reasoning. _Example_: Picking up a magnet
regarding which we have had no experience and upon which we have made no
experiments, we reason by the syllogism, as follows: (1) _All_ magnets
attract iron; (2) _This thing_ is a magnet; therefore (3) _This thing_
will attract iron. In this we apply the axiom of Deductive Reasoning:
"Whatever is true of the whole is true of the parts."
_Fourth Step._ Verification. _Example_: We then proceed to test the
hypothesis upon the particular magnet, so as to ascertain whether or not
it agrees with the particular facts. If the magnet does not attract
iron we know that either our hypothesis is wrong and that _some_ magnets
do _not_ attract iron; or else that our _judgment_ regarding that
particular "thing" being a magnet is at fault and that it is _not_ a
magnet. In either case, further examination, observation and experiment
is necessary. In case the particular magnet _does_ attract iron, we feel
that we have verified our hypothesis and our judgment.