are rules empirically discovered for combining relations of a special kind. For combining relations of any other kind analogous rules would have to be discovered.
On the Nature of Induction.1
Any proposition is susceptible to two sorts of proof. We can adduce premises that directly imply it, or we can adduce premises that indirectly imply it because they imply the falsity of its contradictory alternatives. In inductive reasoning we prove universal propositions by adducing as premises the particular propositions furnished by experience. Formal logic tells us that the value of a particular proposition consists in its power to disprove its contradictory universal rather than to prove its subalternate universal. We might naturally suppose that the evidential function of experience as a knowledge of particulars was to disprove universal statements rather than to prove them, and that if a universal conclusion was proved true by appeal to experience, the proof would be based upon the disproof or elimination of alternatives. That induction is actually and always of this indirect type of inference, and that as such it is properly expressed by a disjunctive syllogism in the negative mood (modus tollendo ponens), is what I wish to show.
There is, of course, no novelty in the conception of induction as a process of elimination. Mill's canons are efficacious because they embody implicitly the eliminative principle. In Hobhouse and Aikins, to mention only two of the modern logicians, the principle is explicitly recognized, and the chief problems of induction are treated, especially by Hobhouse, from that point of view. Yet so far as I am aware there has been nowhere an attempt to identify induction in all its phases with the kind of indirect inference known as the reductio ad absurdum, and it has seemed to me worth while to make that attempt for two reasons: First, because the several inductive____________________