can have no sensible evidence of the relations of abstract ideas. There is no question of dignity between the two methods; each is sovereign in its own sphere. There is no superiority of the one kind of evidence over the other, when considered as a foundation of belief; both lead to positive and well-founded convictions.

The latest historian of the Inductive Sciences is not satisfied with this exclusion of metaphysical ideas from the domain of physical investigation; his work upon the Philosophy of these sciences, which is an elaborate attempt to enlarge the inductive method by the doctrines, and to clothe it in the terminology, of Kantian metaphysics, is a virtual restoration of the scholastic method, or the philosophy of the Middle Ages, and must be considered as "a remarkable instance of what has been aptly called the peculiar zest which the reaction against modern tendencies gives to the revival of ancient absurdities." When Mr. Whewell, in his glowing admiration of the brilliant discoveries recently made in natural science, expresses his confident hope that the mere physical inquirer will soon pass on from a determination of the laws of phenomena to a knowledge of the efficient causes of these phenomena, and gives as a reason for this expectation the light that has recently been thrown upon the action of polar forces, one may be permitted to doubt whether he knows the meaning of the words he uses, or is able to distinguish efficient from occasional causes. A far more cautious thinker, Mr. John Stuart Mill, in his zeal for inductive logic, falls into an error of the opposite character, by boldly taking up the doctrine, that even the axioms of the mathematician are but generalizations from experience, that there is no distinction between necessary truths and facts of observation, and, consequently, that the reasonings of the geometer do not differ in kind from the inductions of the optician or the chemist. It is hardly necessary to say, that the common opinion of the scientific world lies. between the extreme doctrines maintained respectively by these two theorists.

The case of the mixed sciences deserves consideration here, as it really corroborates the principles that have been advanced,

though it may appear at first sight to conflict with them. Pure logic and pure mathematics are not so much sciences as methods of scientific inquiry, or organa of investigation and proof. They are modes of reasoning, irrespective of the subjects or facts about which we reason, and therefore applicable to all subjects. In the syllogism, for instance, the conclusion follows with absolute certainty from the premises, the truth of the premises being presupposed; whether this truth rests upon sensible evidence, or intuition, or a previous demonstration, is of no consequence. The principles of the syllogism, then, are pure abstractions; and the letters of the alphabet, or purely arbitrary marks taken as signs of any ideas or facts whatsoever, are the most convenient notation for expressing them. If the premises are matters of fact, or contingent truth, the conclusion will also be a matter of fact, or contingent truth; only the relation between premises and conclusion is a metaphysical truth, and as such is made known by intuition.

The case is precisely similar with mathematics, in which we employ a notation of the same sort. In its pure form, this science proceeds from abstraction to abstraction, the truth developed by it having no foundation in fact, and never being exemplified in the external world. If an event in the physical world, or a proposition founded on experience, be taken as a datum, or point of departure for the inquiry, however long the chain of mathematical reasoning may be which proceeds from it, the result at which we arrive is a truth of the same order with the one which formed the basis of the investigation. It has lost nothing, and it has gained nothing, in point of logical certainty, through the process to which it has been subjected. Take, for instance, the most brilliant achievement that is recorded in the whole history of mathematical science, the recent discovery by Adams and Leverrier of a new orb on the farther verge of our planetary system. Its existence was long before suspected, for it was said that its influence had been felt trembling along the far-extended line of our delicate analysis. But how was this influence detected? It was through repeated observations, made

by the telescope, of certain irregularities in the motion of Uranus, observations so delicate, and irregularities so slight, that many years elapsed before it could be said with certainty that the latter were real, or before they could be measured so nicely as to afford a basis for the calculations which were to reveal the mass and the position of the body that caused them ; —I say the mass and the position, for the general fact of the existence of such a body was inferred at once, by strict induction, from the mere knowledge that there were such irregularities.

A boat, moored at night by the side of a placid stream, suddenly heaves and oscillates as a few slight ripples move over the surface of the waters; and the watcher in that little boat, though he can descry nothing in the darkness, knows at once that some large object not far off is passing up or down the river, and throwing off those waves which extend obliquely from its wake. Had he instruments nice enough to measure the exact size and force of these ripples, and the aid of an empirical law, like that of Bode, to teach him that the object could move only through a certain channel at a known distance from him, he might calculate the size and exact position of the moving mass, so as to turn his night-glass directly upon it. This is precisely what was done by Adams and Leverrier. The calculation alone was mathematical; the existence of the new planet had previously been made known by induction, and the data used by the computers were all observed facts. And it was not the mathematical process which afforded any new evidence, or added to the convictions of astronomers that a hitherto unobserved planet rolled beyond the path of Uranus. The calculations left this supposed fact precisely where it was before, with the exact measure or kind of certainty which belongs to a truth of induction. The crowning labor of the whole, the real discovery, which, in legal phrase, changed circumstantial to direct evidence, was made when Challis at Cambridge and Galle at Berlin turned their telescopes to the region indicated, and actually saw the new orb which was causing this ripple in the heavens. In what sense, or with what color of reasoning, then, can it be said that moral evidence, the

testimony of the senses, is inferior in degree to mathematical certainty ?

It would not be difficult, in the case of any of the mixed sciences, to separate demonstrative from empirical truths by simply inquiring whether the terms of the proposition express abstract or concrete ideas. Ethical science has this mixed character, quite as much so as mechanics. Casuistry consists in the application of the general and abstract principles of ethics to particular cases; and here, from the difficulty of getting at or expressing all the facts in the case, doubt comes in. If I say that veracity is a duty of paramount obligation, I affirm what no human being, in the full possession of his reason, will dare to deny, any more than to question the conclusions of the geometer. But if informed, on some express occasion, that I am bound to tell the whole truth to a sick person or a madman, I demur; here is a particular case, and all the attendant circumstances must be noted; it seems necessary to inquire what are the motives for giving intelligence to such a person, and what will be the probable consequences of imparting to him the whole truth. I do not undertake to decide the point; moralists differ about it; and this difference is quite enough for my purpose, which is to show, that whenever we come down from the abstract to the concrete, doubts may reasonably and righteously be entertained. We have left the region of abstract truths, of intuition and demonstration, and come down to a practical application, to the world of realities, where a different method must be pursued; we must here observe facts, weigh probabilities, estimate consequences, and bring all the resources of the inductive logic into play. Let it not be said, that this is removing the certainty of moral obligation to a point whence it can never actually guide the conduct of men. In vastly the greater number of instances, the light which observation and experience afford for the application of the rule is quite as clear and convincing as the boasted demonstration which supports the abstract principle; and in the few remaining cases, as the moral law relates exclusively to motives, there is no danger of fatal error.

And herein, as it seems to me, is one great cause of the abuse of general principles in morals, politics, and jurisprudence, and of the intolerable evils which are occasioned by fanaticism of belief and a reckless ultraism. It may be granted that the abstract principle, the grand object in view, is one of awful and imperative obligation, overriding all considerations of personal interest, and needing to be prosecuted with a martyr's zeal perhaps even to a martyr's fate. But this admission does not justify me, on a particular occasion, in shutting my eyes and rushing at that object like a mad bull, careless of the injury or ruin that I may cause, or of the other duties that I may trample down in my path. The question respecting the validity of the principle is totally distinct from that which concerns the choice of means, of the time and manner of carrying it into effect. The former is determined by intuition, by "the inner light," if you will, — by the candle which the Lord hath set up in every unperverted conscience, lighting him on to that clear, absolute, and immediate conviction which knows no doubt, and quails not at any personal sacrifice. The latter is to be settled by careful and anxious observation of the particular circumstances of the case, by a cautious induction of examples illustrating consequences, by examining heedfully and reverently all the other duties that may possibly be violated by our conduct. If this scrutiny be neglected, not even the glory of self-sacrifice will avail to cover up the awful error, except, perhaps, in our own esteem. Omitting this, though the zealot should follow his principles even to the scaffold or the stake, his name shall not be encircled with the glory of a martyr, but it shall be said of him, that he "died as the fool dieth."

Coming back for a moment to the main subject of discussion, it may be observed, that the peculiar clearness and force of demonstrative reasoning seem to depend on that perfect knowledge of the subjects of inquiry which results from their simplicity or uncompounded character. In the science of Medicine, at least in the therapeutical branch of it, we need to know many or all of the qualities and constituents of very complex objects, the medicinal qualities of the drugs, the peculiarities of the patient's