tianity, it seems but equal justice to make Christianity a test of the correctness of metaphysics. Sometimes a compromise is proposed, which is no less shocking to the feelings of the believer than a contumelious rejection of his faith. Philosophy is represented as candid and liberal; as superseding religion, it is true, in the minds of the cultivated and reflecting classes, but continuing to respect it as an imperfect likeness of itself in the bulk of mankind. According to this theory, there are many stages of progress for the human intellect, and men pass on from religion to philosophy as they do from barbarism to civilization.

Now, before conflicting claims like these can be reconciled, it is necessary to get clearer ideas of the subjects of dispute, to determine their respective boundaries, to see how far, if at all, they encroach upon each other, and, if possible, to settle the logic of the inquiry. Perhaps it will be found, after all, that the provinces of Philosophy and Theology are entirely distinct, so that there is no proper interference, and no cause for controversy between them. To establish this point is the object of the present lecture. We must begin with definitions, and if these appear somewhat abstruse at first, I hope they will become clearer as

we go on.

The simplest as well as the most comprehensive classification of all objects of knowledge is that which separates them into relations of ideas and matters of fact. I borrow the language of him who was at once the most subtile logician and the most consistent skeptic of modern times :-"All the objects of human reason or inquiry," says Hume, "may naturally be divided into two kinds, to wit, Relations of Ideas and Matters of Fact." This coincides very nearly with the familiar distinction between physics and metaphysics, except that the meaning of the latter must be so far extended as to embrace the cognate sciences of ⚫ grammar, logic, and mathematics. Stating the proposition in other words, we say that all science may be reduced to two branches-1. The study of things physical, or those which exist distinct from our thoughts; 2. The study of things metaphysical, or those which do not exist apart from our thoughts.

No one can fail to see an essential difference between a fact and an abstraction, or a pure idea, like that of cause, goodness, power, existence, and the like. The former is an object of sense, something which can be seen, heard, felt, or touched, whether we have had sensible evidence of it ourselves, or rely upon the testimony of others who have had such evidence, or infer its existence from inductive reasoning, or from the presence of its effects. The latter is a pure mental conception, which has no existence except in relation to the mind which forms it. Such conceptions are called realities only by a figure of speech; they are so called to mark our strong sense of the correctness with which a certain quality is attributed to a substance or an action. Thus, virtue is said, figuratively, to be a reality, only to mark our firm belief that there are such things as virtuous actions. In this class must be ranked all the abstractions of the geometer and the algebraist. There are no such things in nature as circles and triangles; the only proper realities are circular objects and triangular objects.

But the nature of these abstractions may be most clearly apprehended by considering, in the first place, what we mean by matters of fact. These may be distinguished into things which exist and events which take place. All the objects of natural history and physical science-stones, shells, plants, and animals are ranked in the former class; all the laws, so called, of physical science, the laws of motion, for instance, — all the habits observed by the naturalist, such as the modes of growth and reproduction of plants and animals, are comprehended in the latter. Both alike are matters of fact. It is a fact that the earth exists, or is; it is equally a fact that the earth moves. That there is a sun in the heavens is a fact of one order; that this sun illumines objects on the earth is a fact of a different order, — it is an event which takes place. We have sensible evidence of both.

I am dwelling too long, perhaps, on a very familiar distinction; but it is one that is fundamental to the present inquiry, which cannot proceed without the fullest and clearest compre

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 fectly 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,

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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