THE ART OF LOGICAL THINKING/PART 11
CHAPTER XI.
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.
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