The beans in the bag are two-thirds white.
But, because all inference may be reduced in some way to Barbara, it does not follow that this is the most appropriate form in which to represent every kind of inference. On the contrary, to show the distinctive characters of different sorts of inference, they must clearly be exhibited in different forms peculiar to each. Barbara particularly typifies deductive reasoning; and so long as the is is taken literally, no inductive reasoning can be put into this form. Barbara is, in fact, nothing but the application of a rule. The so-called major premise lays down this rule; as, for example, All men are mortal. The other or minor premise states a case under the rule; as, Enoch was a man. The conclusion applies the rule to the case and states the result: Enoch is mortal. All deduction is of this character; it is merely the application of general rules to particular cases. Sometimes this is not very evident, as in the following:
All quadrangles are figures,
But no triangle is a quadrangle;
Therefore, some figures are not triangles.
But here the reasoning is really this:
Rule.—Every quadrangle is other than a triangle.
Case.—Some figures are quadrangles.
Result.—Some figures are not triangles.
Inductive or synthetic reasoning, being something more than the mere application of a general rule to a particular case, can never be reduced to this form.
If, from a bag of beans of which we know that 2/3 are white, we take one at random, it is a deductive inference
