Page:Popular Science Monthly Volume 13.djvu/489

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ILLUSTRATIONS OF THE LOGIC OF SCIENCE.

not explain what we have seen, namely, all these documents and monuments, without supposing that he really existed. Hypothesis again.

As a general rule, hypothesis is a weak kind of argument. It often inclines our judgment so slightly toward its conclusion that we cannot say that we believe the latter to be true; we only surmise that it may be so. But there is no difference except one of degree between such an inference and that by which we are led to believe that we remember the occurrences of yesterday from our feeling as if we did so.

 
II.

Besides the way just pointed out of inverting a deductive syllogism to produce an induction or hypothesis, there is another. If from the truth of a certain premise the truth of a certain conclusion would necessarily follow, then from the falsity of the conclusion the falsity of the premise would follow. Thus, take the following syllogism in Barbara:

Rule.—All men are mortal.
Case.—Enoch and Elijah were men.
ThreeDots.svg Result.—Enoch and Elijah were mortal.

Now, a person who denies this result may admit the rule, and, in that case, he must deny the case. Thus:

Denial of Result.—Enoch and Elijah were not mortal.
Rule.—All men are mortal.
ThreeDots.svg Denial of Case.—Enoch and Elijah were not men.
 

This kind of syllogism is called Baroco, which is the typical mood of the second figure. On the other hand, the person who denies the result may admit the case, and in that case he must deny the rule. Thus:

Denial of the Result.—Enoch and Elijah were not mortal.
Case.—Enoch and Elijah were men.
ThreeDots.svg Denial of the Rule.—Some men are not mortal.

This kind of syllogism is called Bocardo, which is the typical mood of the third figure.

Baroco and Bocardo are, of course, deductive syllogisms; but of a very peculiar kind. They are called by logicians indirect moods, because they need some transformation to appear as the application of a rule to a particular case. But if, instead of setting out as we have here done with a necessary deduction in Barbara, we take a probable deduction of similar form, the indirect moods which we shall obtain will be—

Corresponding to Baroco, an hypothesis;

and, Corresponding to Bocardo, an induction.

For example, let us begin with this probable deduction in Barbara: