So that induction is the inference of the rule from the case and result.
But this is not the only way of inverting a deductive syllogism so as to produce a synthetic inference. Suppose I enter a room and there find a number of bags, containing different kinds of beans. On the table there is a handful of white beans; and, after some searching, I find one of the bags contains white beans only. I at once infer as a probability, or as a fair guess, that this handful was taken out of that bag. This sort of inference is called making an hypothesis.[[52]] It is the inference of a case from a rule and result. We have, then—
Deduction.
Rule.—All the beans from this bag are white.
Case.—These beans are from this bag.
∴ Result.—These beans are white.
Induction.
Case.—These beans are from this bag.
Result.—These beans are white.
∴ Rule.—All the beans from this bag are white.