§ 5. It has even been held by some writers, that all ratiocination rests in the last resort on a _reductio ad absurdum_; since the way to enforce assent to it, in case of obscurity, would be to show that if the conclusion be denied we must deny some one at least of the premisses, which, as they are all supposed true, would be a contradiction. And in accordance with this, many have thought that the peculiar nature of the evidence of ratiocination consisted in the impossibility of admitting the premisses and rejecting the conclusion without a contradiction in terms. This theory, however is inadmissible as an explanation of the grounds on which ratiocination itself rests. If any one denies the conclusion notwithstanding his admission of the premisses, he is not involved in any direct and express contradiction until he is compelled to deny some premiss; and he can only be forced to do this by a _reductio ad absurdum_, that is, by another ratiocination: now, if he denies the validity of the reasoning process itself, he can no more be forced to assent to the second syllogism than to the first. In truth, therefore, no one is ever forced to a contradiction in terms: he can only be forced to a contradiction (or rather an infringement) of the fundamental maxim of ratiocination, namely, that whatever has a mark, has what it is a mark of; or, (in the case of universal propositions,) that whatever is a mark of anything, is a mark of whatever else that thing is a mark of. For in the case of every correct argument, as soon as thrown into the syllogistic form, it is evident without the aid of any other syllogism, that he who, admitting the premisses, fails to draw the conclusion, does not conform to the above axiom. 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.