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 V 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.

The two methods afford equally safe grounds of belief. — 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 atten tion 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

* Mr. Stewart remarks, that the mathematician himself is obliged to admit the evidence of testimony while engaged in his most abstruse investigations. 'In astronomical calculations, for example, how few are the instances in which the data rest on the evidence of our own senses; and yet our confidence in the result is not, on that account, in the smallest degree weakened. On the contrary, what certainty can be more complete than that with which we look forward to an eclipse of the sun or the moon, on the faith of elements and of computations which we have never verified, and for the accuracy of which we have no ground of assurance whatever, but the scientific reputation of the writers from whom we have borrowed them. An astronomer who should affect any scepticism with respect to an event so predicted, would render himself no less an object of ridicule, than if he were disposed to cavil about the certainty of the sun's rising to-morrow.

"Even in pure mathematics, a similar regard to testimony, accompanied with a similar faith in the faculties of others, is by no means uncommon. Who would scruple, in a geometrical investigation, to adopt as a link in the chain, a theorem of Apollonius or of Archimedes, although he might not have leisure at the moment to satisfy himself, by an actual examination of their demonstrations, that they had been guilty of no paralogism, either from accident or design, in the course of their reasonings?"

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.

The logic of physical and metaphysical inquiry.

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.

Evil of confounding the two methods. 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 tends only to deprive the soul of its highest convictions, and terminates 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 Dr. 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 must acquire, slowly and patiently, letter by letter, the alphabet in which nature writes her answers to such inquiries; the first students wished to divine, at a single glance, the whole import of the book." As their first inquiry, they endeavored to discover the origin and principle of the universe. Thales maintained that it was water; according to another, it was air; while a third considered fire as the origin of all things. This last hypothesis, it may be remarked, has been revived by a popular cosmogonist of our own day, who has found the seminal principle of all things, including the various ranks of animate being, the body, and even the soul, of man, in a primitive fiery mist. These wide and ambitious doctrines, it has been well remarked, are "better suited to the dim magnificence of poetry, than to the purpose of a philosophy which was to bear the sharp scrutiny of reason. When we speak of the principles of things, the term, even now,

*The author of the Vestiges of Creation.

is very ambiguous and indefinite in its import; but how much more was that the case in the first attempts to use such abstractions!"

Error of the Schoolmen. The history of physical science, as it was studied by the schoolmen during the Middle Ages, is quite as unsatisfactory as the record of its treatment by the ancients. Logic, which I have ventured to class with the metaphysical sciences, because it is exclusively concerned with the relations of ideas, or with abstractions of the highest order, now claimed the chief attention in the schools. There were two reasons for giving it this preference: first, because it was held, as before, that all knowledge might be deduced from general ideas, so as to avoid the necessity of studying nature or observing particulars; and secondly, because it was believed that the ancients had already exhausted the inquiry and completed the work, so that all truth might be ascertained, and all controversies terminated, by a right interpretation of the works of Aristotle and his commentators, this interpretation being governed, of course, by the rules of a sound logic. The scholastics held, "that all science may be obtained by the use of reasoning alone, — that by analyzing and combining the notions which common language brings before us, we may learn all that we can know." The fallacy of this, it has been well remarked, consists in mistaking the universality of the theory of language for the generalization of facts. All words, excepting proper names, denote either general conceptions or abstract ideas; and the study of the relations of words is therefore a study of the relations of ideas, and must proceed by the former of the two methods which we have been considering,—that is, by intuition and demonstration.

This method barren of results. We might well expect that physical science, or the study of matters of fact, when pursued by this method, would produce only nugatory or profitless results. It has been stated on high authority, that not one step had really been taken in physical science down to the period of the Revival of Letters; - not a foot of ground had been gained