individual cases not been carried so far as in the former case when the
generalization was made, but there were found no inherent causes residing in
cloven-footed animals which make it necessary for them to chew their cud. That
is, cloven feet and cud-chewing do not of necessity go together, and the case of
the pig disproves the generalization.
In practically no instance, however, is it possible for us to examine every case
upon which a generalization is based; after examining a sufficient number of
cases, and particularly if there are supporting causes, we are warranted in
making the "inductive leap," or in proceeding at once to state our generalization
as a working hypothesis. Of course it is easy to see that if we have a wrong
generalization, if our major premise is invalid, all that follows in our chain of
reasoning will be worthless. This fact should render us careful in making
generalizations on too narrow a basis of induction. We may have observed that
certain red-haired people of our acquaintance are quick-tempered, but we are not
justified from this in making the general statement that all red-haired people are
quick-tempered. Not only have we not examined a sufficient number of cases to
warrant such a conclusion, but we have found in the red hair not even a cause of
quick temper, but only an occasional concomitant.
The Interrelation of Induction and Deduction.—Induction and deduction
must go hand in hand in building up our world of knowledge. Induction gives us
the particular facts out of which our system of knowledge is built, furnishes us
with the data out of which general truths are formed; deduction allows us to start
with the generalization furnished us by induction, and from this vantage ground
to organize and systematize our knowledge and, through the discovery of its
relations, to unify it and make it usable. Deduction starts with a general truth and
asks the question, "What new relations are made necessary among particular
facts by this truth?" Induction starts with particulars, and asks the question, "To
what general truth do these separate facts lead?" Each method of reasoning needs
the other. Deduction must have induction to furnish the facts for its premises;
induction must have deduction to organize these separate facts into a unified
body of knowledge. "He only sees well who sees the whole in the parts, and the
parts in the whole."
7. PROBLEMS IN OBSERVATION AND INTROSPECTION
- Watch your own thinking for examples of each of the four types described.
Observe a class of children in a recitation or at study and try to decide which