There is an impression shared by many that the relation between the white and black races in this country is becoming less amicable and more and more surcharged with injustice. The basis for this impression is to be found in certain dramatic and sensational events, in particular the riots in Springfield, Illinois, and in Atlanta, Georgia. The memory of those events is becoming faint in many minds; but the impression they created remains. A dramatic event will have an effect upon public opinion which statistics, more significant but less picturesque, will altogether fail to produce. In the horror at the brief work of a mob the diminution in the annual number of lynchings is forgotten.
The fundamental mistake in this is in the picking out of a startling episode or a reckless utterance and regarding it as typical. We do not arrive at the truth in that way. The Black Hand assassin does not furnish a true index to the Italian character. Aaron Burr is not an exhibit of the product of American Puritanism. So, if we wish to find out what American democracy has done with the negro, we do not search, if we are wise, into the chain-gang of Georgia or into the slums of New York. [Footnote: The Outlook, April 4, 1908.]
The value of inductive reasoning depends upon the number of instances observed. Very seldom is it possible to investigate every case of the class under discussion. Of course this can sometimes be done. For instance, one may be able to state that all his brothers are college graduates, since he can speak authoritatively concerning each one of them. But usually an examination of every instance is out of the question, and whenever induction is based on less than all existing cases, it establishes only probable truth.
From the foregoing it is seen that the tests for induction are two:—
(1) Have enough instances of the class under consideration been investigated to establish the existence of a general law?
(2) Have enough instances been investigated to establish the probable existence of a general law?
2. DEDUCTIVE REASONING. Deductive reasoning is the method of demonstrating the truth of a particular statement by showing that some general principle, which has previously been established or which is admitted to be true, applies to it. A stranger on coming to the United States might ask whether our postal system is a success. The answer would perhaps be, "Yes, certainly it is, for it is maintained by the government, and all our government enterprises are successful." When the metal thurium was discovered, a query doubtless arose as to whether it was fusible. It was then reasoned that since all metals hitherto known were fusible, and since thurium was a metal, undoubtedly it was fusible. Stated in clearer form, the reasoning in each case would be:—
A. All our government enterprises are successful.
B. The United States postal system is a government enterprise.
C. Therefore the United States postal system is successful.