hension of it. These two classes, which comprehend all objects of knowledge, are distinguished from each other, not merely by the broad and obvious lines of distinction inherent in their nature, which have been already explained, but by radical differences in the modes of inquiry and reasoning which are respectively applicable to them. The relations of ideas—that is, of abstractions, or pure ideas are made known to us by intuition or reflection; and reasoning about them proceeds by the demonstrative method, the conclusions at which we arrive being absolutely certain. According to the absolute laws of the human understanding, I speak it reverently, it is not within the power of Omnipotence to disprove these results, or even to render them doubtful. Their falsity would involve a contradiction; to maintain that they are untrue is to say that it is possible for a thing to be and not to be at one and the same moment. All the truths of pure mathematics, pure logic, and pure reason are metaphysical truths, and we can no more doubt them than we can question the accuracy of the multiplication-table. Their falsity is inconceivable. This attribute of logical certainty proceeds from the pure, abstract, and perfectly simple or uncompounded nature of the ideas which enter into such reasoning. These ideas are pure creations of the intellect; in their uncompounded and abstract character they are not derived from observation, and are therefore not perverted by that great source of error, the imperfection of our senses, or the limitations of our power of perception. When we entertain these ideas, or reason about them, the mind is closed to all outward impressions, and freed even from the memory of their former occurrence. The ideas that are contemplated then are contemplated in their entireness; for, being uncompounded, if they are apprehended at all, they must be perfectly apprehended, and consequently the relations between them are discerned at once, or by intuition. Demonstrative reasoning proceeds by a series of such intuitions, and hence the absolute character of its results. If the chain of such reasoning be too far extended, indeed, without a system of notation, the imperfections of memory may come in, some steps may be forgotten,

and mistakes will be committed.

But this cause of error never

affects a simple intuition, or a step in the process when taken by itself. Here the certainty is absolute.

Now what is the method of inquiry or procedure for the other class of objects of knowledge, -for matters of fact? We enter upon totally different ground here. Instead of abstractions, we have realities; instead of shutting out sensible evidence altogether, we are obliged to rely upon it exclusively; instead of intuitions, we have observations and experiments; instead of demonstration, we have induction; instead of the objects of inquiry being perfectly simple and uncompounded, they are made up of an unknown and unknowable number of elements and qualities; and instead of arriving at conclusions which are absolutely true, we gain those only which are morally certain. I speak now of both kinds of matters of fact, both of things which exist, and of events which take place. The imperfections of the senses come in here to their full extent, as causes of possible error. The objects of physical science must always be imperfectly known; we never can be sure that our analysis of them is complete, or that our observation has taken in all their outward qualities. The attractive power of the loadstone was known for ages before its attribute of polarity was discovered; yet what is apparently more simple and obvious than this quality, which can be detected at once by floating a magnet on a piece of cork in a basin of water? Down to the times of Watt and Cavendish, water was supposed to be a simple element, and it figures as such in some of the most remarkable of the ancient theories of cosmogony; these chemists, about a century ago, discovered that it was compounded of two gases. But it is useless to multiply instances. The chemist will tell you that it is not impossible, that it is even probable, that every one of the sixty substances now counted as elementary will ultimately be decomposed. Of course, the vast number of compounded objects of which natural history takes cognizance are still more imperfectly known in their qualities and relations than those substances which as yet are reckoned elementary. This limited acquaintance

with the subjects of investigation must lead only to qualified, and, in the logical meaning of the term, uncertain, conclusions respecting them.

If this is the case with things which exist, it holds still more obviously true of events which take place. Our knowledge of past events depends either on memory, with its acknowledged manifold defects, or on the testimony of others, with the multiplied causes which bring either their intelligence or their veracity into doubt. As to future occurrences, the field of positive science is yet more limited; the truth of every proposition respecting them depends on the axiom, that the course of nature is uniform, and under similar circumstances we may look for similar effects. Now, in the first place, we never can be sure that the circumstances are perfectly similar; and, secondly, the truth of the axiom itself depends wholly on empirical evidence. It is possible, that is, it is conceivable, that the sun may not rise to-morrow; but it is not conceivable that two and two should make five, or that a straight line should not be the shortest distance between two points. The laws of motion are instances of the highest generalization and of the most cautious and rigid induction which the whole field of physical science can afford; but what assurance have we that these laws will hold good for one moment beyond the present time? Obviously, we can have only a moral certainty of their future operation; intuition or demonstration is here out of the question.

There is, then, a radical difference, or a difference in kind, between the two methods of investigation which are applicable respectively to physical and to metaphysical science. But so far as the truth of the conclusions, in either case, is concerned, this difference is not one of degree; our conviction is just as firm in the one case as in the other. No one complains of the insufficiency of the evidence on which rest all the truths of physical science and all the facts of history. Our persuasion of the reality of our past experience, and of the truths which depend on that experience, would not be affected, certainly would not be increased in the slightest degree, by a technical demonstration

of that reality or of those truths. In fact, the theorems of geometry are received, and practically applied, by multitudes who are incapable of demonstrating them. The carpenter, for instance, makes almost daily use of the forty-fifth proposition of Euclid, though he is not usually able to supply the steps of its logical proof; he knows that it is correct by the results of his application of it, and because he is told that others have demonstrated it, and that he could easily follow out the demonstration himself, if he were to give the requisite time and attention to the process. The mariner, also, steers his ship by the aid of his Practical Navigator and Nautical Almanac, though he cannot give the rationale of one of his own calculations. Instruct him in this respect, teach him trigonometry enough to demonstrate the rules of plain sailing, and you will enlarge the sphere of his ideas and add to his sources of intellectual enjoyment; but you will not increase by one iota the strength of his belief in the correctness of the processes. The moral evidence on which it formerly rested in his mind was sufficient; the strength of the conviction produced by it could not be increased.

It is more pertinent to my present object to remark, that the conduct of human beings is governed exclusively by the evidence and the reasoning which are applicable to matters of fact, or, in other words, by experience. It is the only proof they have that food will nourish, fire burn, or water drown them, — that any place exists which they have never visited, or that any person lives with whom they have not conversed. These contingent truths enter into all our inferences from the past, and all our calculations for the future; man's life is guided by them, from the cradle to the grave. If it be objected to this view, that our convictions of duty are intuitive, and therefore absolute, I answer, that duty relates only to motives and a choice of ends; action is always a use of means, and the selection of means is the work of experience. The moral law, for instance, bids me cultivate honest and humane intentions towards my fellow-man ; how those intentions shall be most properly manifested in outward conduct is a question for the intellect, and one that can be

answered only by the lessons of experience. The sense of obligation stops short with the active intent.

Here, then, we rest the basis of our inquiry. All objects of human knowledge are divided into two classes, perfectly distinguishable from each other; a distinct method of investigation, and a peculiar logic, or reasoning process, being appropriate to each. The conclusions at which we arrive in the two cases are equally well-founded, equally deserving of confidence; but they differ widely in the kind or character of the conviction on which they rest, and in the nature of the process by which they were obtained.

My next proposition is, that these two modes of inquiry are not interchangeable, but confusion, uncertainty, and error invariably result from mistaking one for the other, or from attempting to extend the limits of either beyond its proper province. Matters of fact cannot be demonstrated; the attempt at a demonstration leads directly to that insane skepticism which teaches us to distrust or reject all experience. The relations of pure ideas cannot be ascertained by the inductive method; they can neither be proved by testimony, nor learned from experiment and observation. The trial of these inadequate media of proof will tend only to deprive the soul of its highest convictions, and will terminate in a mean and shallow empiricism. The history of science, from the earliest period down to the present day, affords numberless illustrations of the evil of confounding these two methods. The physical inquiries of the ancients were all fruitless, because their false notions of the dignity of science made them despise particulars and begin with general ideas, from which, by logical deduction, they hoped to obtain all special truths; that is, from abstractions they sought to infer matters of fact, and thus to change the labor of the inquirer from observation to reflection. Their physics were all metaphysics. "The early philosophers of Greece," says Mr. Whewell, “entered upon the work of physical speculation in a manner which showed the vigor and confidence of the questioning spirit, as yet untamed by labors and reverses. It was for later ages to learn that man