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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

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 guess-work. 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 abstractions are, as it were, ready-made by nature, gravitation being the sole quality that it is necessary to take into view. Friction and a resisting medium-though of this last there may be some doubt are eliminated by the nature of the case; the problem is complicated only by the gravitating effect of different bodies on each other. Our conclusions are very general, then, but also very limited, as they relate exclusively to position and motion. Astronomy, it was remarked many years ago, is a perfect science; and so it is, the theory of it, though the improvement of instruments is daily bringing to light new facts.

Thus it appears, that we approximate the sphere of metaphysical evidence and demonstrative reasoning just in proportion as we leave the world of realities and facts, and abandon the consideration of objects in their entireness, or in all their relations.

LECTURE II.

THIS DISTINCTION APPLIED TO PHILOSOPHY AND THEOLOGY.

In my last Lecture, I endeavoured to define and distinguish the nature and scope of physical and metaphysical inquiry, - -to show that the one was properly confined to matters of fact, and the other to relations of ideas. Demonstrative reasoning, I attempted to prove, belongs exclusively to the latter, and its conclusions are always abstract; the truths of physical science are obtained only by the inductive method, by observation and experiment, and by generalizations extending from individuals to a class. Yet the former method has no superiority over the latter, when considered simply as a foundation of belief. Both alike command our assent on indisputable grounds, though the media of proof are radically unlike. Sensible evidence and inductive reasoning, it is true, admit of degrees, and lead to all shades of belief, from the faintest probability up to what is called moral certainty. Demonstrative reasoning, on the other hand, has no degrees; a proposition is established by it either conclusively or not at all. If successful, it would be contradictory and absurd to deny the conclusion, the proof being then equivalent, but not superior, to that which in the former case renders a fact morally certain. To adopt Locke's distinction between insanity and idiocy, we might say that only a madman can reject a mathematical proof after it has been once explained to him, while to be incapable of governing one's conduct by that sensible evidence which controls the actions of our fellows is simple idiocy.

Such a person is usually said to be incapable of keeping out of fire and water, because he is not able to learn from induction, or repeated experiment, that the former will burn and the latter. will drown him. A very brief glance at the history of science was intended to show, that most of the mistakes, retrogressions, and absurdities which have hindered the progress of it may be traced to ignorance or forgetfulness of the distinction here pointed out, to an attempt to deduce facts from abstract conceptions, or to draw down pure ideas to sensible observation and material tests, to calling for demonstration in physics, or following the guidance of the senses only in metaphysical investigations. Illustrations of this error might easily be multiplied from the whole domain of science and speculation, not less numerous and apt in our own day, perhaps, than they were among the ancients or in the times of the schoolmen; but less conspicuous, affecting a smaller class of minds, and therefore less likely, we may hope, to be chronicled for the mingled amusement and pity of future generations. They are now the follies of a sect, a party, or a clique, usually a small one; while in former days. they were the indications of a universal evil, proceeding from illformed habits of thought, and offering a far-extended and almost insuperable barrier to the progress of knowledge.

Leaving the task of mere illustration, then, I proceed to inquire how far the distinction now pointed out may be made available for one great purpose of these lectures, to determine clearly the respective limits of religion and philosophy. It is obvious that the latter term, which is often applied very generally to the pursuit of all knowledge, must here be used in a restricted sense, and be made synonymous, in fact, with metaphysics. It cannot be defined more clearly without a tedious enumeration of all the questions and problems which it comprehends. It is concerned with the origin and explication of our ideas of cause, power, infinity, knowledge, free-will, identity, substance, and the like, all of which are pure abstractions, so that we must reason about them demonstratively, or not at all. Philosophy, in this narrow meaning of the word, includes precisely that class of sub

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