The Philosophical Review/Volume 1/Summary: Hobhouse - Induction and Deduction
H.'s question is whether deduction involves something quite different from generalization, or is the same thing under a different aspect, or a particular species of the same thing; in any case can it be found to imply any single axiom, and if so, what is the relation of that axiom to the axiom of induction? Taking first syllogism as deduction, he finds that the conclusion of a syllogism is implicit in the premises on no further condition than that these premises have meaning. If we regard syllogism as employing a universal premise, it presupposes the axiom of induction, under which a universal truth is asserted and applied on the round of a particular observation. Taking next deduction to be the combination of several universals in a chain of reasoning, we here assert a relation between two universals on the ground of the relation of each to one or more intermediate universals, i.e. out of several relations we construct a resultant relation, or a whole in which the resultant relation appears as a part. This reasoning depends in the end on generalization, for it implies some such axiom as: If, when two terms are related to a third, a relation between the two is observed, then other terms similarly related to a third will have a similar relation to each other. All cases, then, tend to show that deduction involves generalization from an observed case on a single axiom; the axioms, therefore, of induction are the axioms of reasoning, and the generalization of particulars is the work of reason.