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 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:

Rule.—Most of the beans in this bag are white.

Case.—This handful of beans are from this bag.

Result.—Probably, most of this handful of beans are white.

Now, deny the result, but accept the rule:

Denial of Result.—Few beans of this handful are white.

Rule.—Most beans in this bag are white.

Denial of Case.—Probably, these beans were taken from another bag.

This is an hypothetical inference. Next, deny the result, but accept the case:

Denial of Result.—Few beans of this handful are white.

Case.—These beans came from this bag.