| 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. | |
|
|
Denial of Rule.—Probably, few beans in the bag are white. |
This is an induction.
The relation thus exhibited between synthetic and deductive reasoning is not without its importance. When we adopt a certain hypothesis, it is not alone because it will explain the observed facts, but also because the contrary hypothesis would probably lead to results contrary to those observed. So, when we make an induction, it is drawn not only because it explains the distribution of characters in the sample, but also because a different rule would probably have led to the sample being other than it is.
But the advantage of this way of considering the subject might easily be overrated. An induction is really the inference of a rule, and to consider it as the denial of a rule is an artificial conception, only admissible because, when statistical or proportional propositions are considered as rules, the denial of a rule is itself a rule. So, an hypothesis is really a subsumption of a case under a class and not the denial of it, except for this, that to deny a subsumption under one class is to admit a subsumption under another.
Bocardo may be considered as an induction, so timid as to lose its amplifiative character entirely. Enoch and Elijah are specimens of a certain kind of men. All that kind of men are shown by these instances to be immortal. But instead of boldly concluding that all very pious men, or all men favorites of the Almighty, etc., are immortal, we refrain from specifying the description of men, and rest in the merely explicative inference that some men are immortal. So Baroco might be considered as a very timid hypothesis. Enoch and Elijah are not mortal. Now, we might boldly suppose them to be gods or something of that sort, but instead of that we limit ourselves to the inference that they are of some nature different from that of man.
But, after all, there is an immense difference between the relation of Baroco and Bocardo to Barbara and that of Induction and Hypothe-
