Without attaching exaggerated importance to the distinction now drawn, I think it enables us to characterize in a more accurate manner than is usually done, the nature of demonstrative evidence and of logical necessity. That is necessary, from which to withhold assent would be to violate the above axiom. And since the axiom can only be violated by assenting to premisses and rejecting a legitimate conclusion from them, nothing is necessary, except the connexion between a conclusion and premisses; of which doctrine, the whole of this and the preceding chapter are submitted as the proof.
We have now proceeded as far in the theory of Deduction as we can advance in the present stage of our inquiry. Any further insight into the subject requires that the foundation shall have been laid of the philosophic theory of Induction itself; in which theory that of deduction, as a mode of induction, which we have now shown it to be, will assume spontaneously the place which belongs to it, and will receive its share of whatever light may be thrown upon the great intellectual operation of which it forms so important a part.
We here, therefore, close the Second Book. The theory of Induction, in the most comprehensive sense of the term, will form the subject of the Third.
BOOK III. OF INDUCTION.
“According to the doctrine now stated, the highest, or rather the only proper object of physics, is to ascertain those established conjunctions of successive events, which constitute the order of the universe; to record the phenomena which it exhibits to our observations, or which it discloses to our experiments; and to refer these phenomena to their general laws.”—D. Stewart, Elements of the Philosophy of the Human Mind, vol. ii. chap. iv. sect. 1.