In fact, the theorems of geom

of that reality or of those truths. etry 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 proThe moral evidence on which it formerly rested in his mind was sufficient; the strength of the conviction produced by it could not be increased.

cesses.

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

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

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, con

sists 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.

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 by the labors of more than two thousand years. This statement is perhaps too strong; for something was undoubtedly accomplished in astronomy by Hipparchus and Ptolemy, something in natural history by such observers as Aristotle, Theophrastus, and Pliny, while the medical profession, even at the present day, does not wholly repudiate the authority of Hippocrates and Galen. But how little real progress the human mind had made during this long lapse of centuries may be correctly inferred from the round of studies pursued at the universities; the course of seven sciences, included under the fantastic names of the trivium and the quadrivium, comprised grammar, logic, and rhetoric, together with arithmetic, geometry, music, and astronomy. Of these, only the last can be ranked among the physical sciences, as music was then only an art which had not been reduced to its scientific principles. The others are all metaphysical in character, and the only organon, or method of investigation, which was then in use, being appropriate to these, the success with which they were cultivated affords a striking contrast to the barrenness of physical inquiry. Logic came almost perfect from the hands of him who may be called its inventor. Sir William Hamilton, the most accomplished logician of our own day, asserts distinctly, that there has been, "in fact, no progress made in the general development of the syllogism since the time of Aristotle." The case of mathematics is nearly

as strong, the geometry of Euclid and Archimedes being still the boast of the science. These were the results of applying the appropriate mode of reasoning to the metaphysical sciences, or those which are concerned exclusively with the relations of ideas; while the inappropriateness of this same mode of reasoning to physical science, that is, to matters of fact, is proved by the almost total failure of all attempts in this department for more than twenty centuries.

It is not necessary to dwell here on so familiar a history as that of the sudden rise and extraordinary development of physical science at the close of the sixteenth century. The rapid succession of brilliant discoveries made by Galileo, Stevinus, and Gilbert, was in itself a proof that they had at length hit upon the true method of physical investigation, just before the illustrious Englishman- himself hardly capable of reducing any one of his own rules successfully to practice, but gifted with an intellect no less clear and penetrating than comprehensive and profound, and with a sagacity and hopefulness which unrolled before him the history of the future triumphs of science almost as distinctly as the record of its past defeats-supplied the rationale of this method, reduced it to a complete system, and evolved and stated with wonderful precision the rules for its successful use, in those immortal works which have gained for him the deserved title of Father of the Inductive Philosophy. To say that the inductive method was practised in some cases before the time of Bacon is about as idle as to assert that men sometimes reasoned correctly before Aristotle wrote his Logic; though the assertion in the former case is not true to the same extent as in the latter, since the latter half of the century in which Bacon was born, though not that in which his principal works were published, witnessed the first successful application of this method to physical science. The merit of these two great men is of the same order; each wrought out with scientific precision and completeness the logic of discovery and proof in one of the two great departments of human knowledge. The one taught us the theory of reasoning syllogistically, or to a demonstration, about the