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 that this bean is probably white, the probability being 2/3. We have, in effect, the following syllogism:
Rule.—The beans in this bag are 2/3 white.
Case.—This bean has been drawn in such a way that in the long run the relative number of white beans so drawn would be equal to the relative number in the bag.
Result.—This bean has been drawn in such a way that in the long run it would turn out white 2/3 of the time.
If instead of drawing one bean we draw a handful at random and conclude that about 2/3 of the handful are probably white, the reasoning is of the same sort. If, however, not knowing what proportion of white beans there are in the bag, we draw a handful at random and, finding 2/3 of the beans in the handful white, conclude that about 2/3 of those in the bag are white, we are rowing up the current of deductive sequence, and are concluding a rule from the observation of a result in a certain case. This is particularly clear when all the handful turn out one color. The induction then is: