12. Induction.
The form of conclusion previously discussed, because it has been so, I expect it will continue to be so in the future, is the form through which each science has arisen and has won its real content, that is, its value for the judgment of the future. It is called inference by induction, and the sciences in which it is preponderatingly applied are called inductive sciences. They are also called experiential or empirical sciences. At the basis of this nomenclature is the notion that there are other sciences, the deductive or rational sciences, in which a reverse logical procedure is applied, whereby from general principles admitted to be valid in advance, according to an absolutely sure logical process, conclusions of like absolute validity are drawn. At the present time people are beginning to recognize the fact that the deductive sciences must give up these claims one by one, and that they already have given them up to a certain extent; partly because on closer study they prove to be inductive sciences, and partly because they must forego the title and rank of a science altogether. The latter alternative applies especially to those provinces of knowledge which have not been used in prophesying the future or cannot be so used.
To return to the inductive method—it is to be noted that Aristotle, who was the first to describe it, proposed two kinds of induction, the complete and the incomplete. The first has this form: since all things of a certain kind are so, each individual thing is so. While the incomplete induction merely says: since many things of a certain kind are so, presumably all things of this kind are so. One instantly perceives that the two conclusions are essentially different. The first lays claim to afford an absolutely certain result. But it rests upon the assumption that all the things of the kind in question are known and have been tested as to their behavior. This hypothesis is generally impossible of fulfilment, since we can never prove that there are not more things of the same kind other than those known to us or tested by us. Moreover, the conclusion is superfluous, as it merely repeats knowledge that we have already directly acquired, since we have tested all the things of the one kind, hence the special thing to which the predication refers.
On the other hand, the incomplete induction affirms something that has not yet been tested, and therefore involves as a condition an extension of our knowledge, sometimes an extremely important extension. To be sure, it must give up the claim to unqualified or absolute validity, but, to compensate, it acquires the irreplaceable advantage of lending itself to practical application. Indeed, in accordance with the scientific practice justified by experience, described on [p. 29], the scientific inductive conclusion assumes the form: because it has once been found to be so, it will always be so. From this appears the significance of this method for the enlargement of science, which, without it, would have had to proceed at an incomparably slower pace.