about, 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.

Pure mathematics never lead to a discovery of matters of fact. -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 further 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,

*"Calculation," says Dugald Stewart, "is certainly not an instrument of discovery at all analogous to experiment and observation; it can accomplish nothing in the study of nature till they have supplied the materials; and is indeed only one of the arts by which we are enabled to give a greater degree of accuracy to their results."

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?

Mixed character of ethical science. 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 danof fatal error.

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Ultraism and fanaticism traced to the abuse of abstract principles. 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."

In what proportions demonstrative reasoning is applicable to the various Mixed Sciences. 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 constitution, and the circumstances of the moment, which may greatly modify the action of the former upon the latter. Obviously, this is the business of sheer empiricism, being in many instances no better than guesswork. In Chemistry, we go a step higher, as it is necessary to attend, at most, to the qualities or elements of but one class of objects; still, we never can know that the analysis is complete, or the observation perfect, and are therefore obliged to grope our way by experiment and very limited induction, perhaps never establishing a universal principle by a priori evidence. In the science of Mechanics, we make a great advance, as many abstractions are employed, friction, the rigidity of materials, and the resistance of the air, being generally put aside; mathematical reasoning here comes into play, which had no application in the former sciences, and our conclusions are more abstract, more general, and therefore less practically available. In Celestial Mechanics, it happens curiously, that the

"The evidence on which the physician proceeds," says Dugald Stewart, "so far as it rests on experience, is weakened or destroyed by the uncertain condition of every new case to which his former results are to be applied. Without a peculiar sagacity and discrimination in marking not only the resembling, but the characteristical, feature of disorders classed under the same technical name, his practice cannot be said with propriety to be guided by any one rational principle of decision, but merely by blind and random conjecture."

"That practical science which relates to the strength of materials," for instance, "combines the principles of several sciences. Let the problem be, to determine the necessary breadth and depth of the girder of a floor, that shall sustain a given weight, the length of the span also being given. Now, these dimensions are not to be found without having recourse, first, to the higher mathematics, or those purely abstract truths which are independent of all the laws of the actual world, and which would be what they are, although there were no such principle as gravitation, or no material system. In the next place, this law of gravitation