ADDRESS. "Mathematics from the first have been triumphant over the husk; Philosophy is still militant for the kernel." Such is the judgment of Sir William Hamilton, oue of the highest authorities, certainly, in any question which authority can decide; and among all thinkers our age has seen, one of the noblest inheritors of a yet unfulfilled renown. He urges as a leading and fatal objection to the use of Mathematics in education, that they deal only with the husks of truth. He would accordingly proscribe them, where mental culture is the aim. He further objects to this study certain special evil effects upon the mind. It is so true, so absolute and unquestionable in every step and every result, that it loses all the force of truth. It is so reliable in its methods, that it compels belief, and trains the mind to skepticism! So rigid and exacting in its proofs that it makes men credulous and superstitious! If all these sad and opposite results do indeed proceed "from the study of Mathematics, we can wonder no longer that one tree is the tree of the knowledge of both good and evil. We must agree with one of the church fathers who referred this science to a very low, bad source indeed, and join the superstitious Banquo in saying, "'tis strange, And oftentimes to win us to our harm The instruments of darkness tell us truths; But who can believe it? To all who love this science, to all whose eye is not evil through prejudice, Truth as revealed by Mathematics is Truth in her native beauty, with her disguises stript away; and thus seen, led out from the veils of form and matter behind which half her light is quenched, into the clear air of exact knowledge, she is the purest and sweetest "daughter of the voice of God; "—while, the more absolute the Truth, the surer is the signet of the Divine. If then we free Sir William's aphorism, as we may, from the sneer about "husk and kernel," it means simply that "Mathematics have always been triumphant; Philosophy is still militant." Now this occurs in a piece of special pleading against Mathematics. He wishes to drive them out from the course of mental training utterly, reserving only those elementary branches which every educated man needs in daily life; and to substitute a course of metaphysical study. We are justified then in accepting these words as being, in the author's view, what they really are in themselves, an epitome of the history of these two sciences. But what a confession does the special advocate of metaphysics make, in his very plea! He would reject from education a triumphant branch, and would substitute for it a militant branch. He would supplant an established science by that which is only struggling to become a science, He would put away a method which has broken down a thousand barriers, each of which threatened to become the horizon of human knowledge forever, in favor of one which has never yet made one step of real progress, because its starting-point changes with every mind that attempts it; and whose chief contribution to science, an enemy might say, has been the multiplication of the known species of monomania! Glance hastily at the history of the two. You see that Mathematics have been always steadily progressive; metaphysics have been fixedly stationary. The former science has been adding at every step to human knowledge, in all directions, for it is thoroughly trustworthy, and what it does once is done forever. The latter has been actively moving indeed, with an infinite variety of motion, but in an orbit ever returning upon itself. The former accordingly has always been the wonder of the uninitiated; the latter their laughing-stock. You remember the judgment of Varro, Cicero's friend, and the greatest reader, as well as the most voluminous author, of ancient times. He assures us that there is no absurdity, capable of utterance in words, so gross that it has not been advanced and defended by some one of these selfstyled philosophers. If this was true two thousand years since, what shall be said of the multiplied absurdities of modern metaphysics? What would Varro say, could he stand in the metaphysical alcove of a modern public Library? It was impossible that this waste of intellect and labor should take place without remonstrance from the true spirit of science; and in the present age, which exaggerates utility and aims only at a visible goal, it is impossible to keep this reaction and remonstrance within reasonable bounds. Hence modern science tends to ignore metaphysics and even deny their possibility. Indeed, their utter exclusion from the realms of human knowledge is a fundamental principle of the Positive Philosophy, and is being accepted more and more widely, under the vast and growing influence of that system. We may regret this movement, in view of the materializing influences, which, at best, have such power over contemporary thought; yet we cannot altogether blame it. For the method pursued by the metaphysicians can but appear to those whose habits of thought are formed amid the exact scientific methods by which other branches have been advanced, utterly and radically wrong. I confess that they seem so to me. The human mind has but one mode of discovering new truth; induction from particular facts. Yet the failure of the greatest minds which have devoted themselves to Philosophy has not taught their successors to introduce that mode here. Hence the whole science still waits for its new language and its new method. Hence the melancholy spectacle presented by him from whom I first quoted; one of the most critical and brilliant intellects of modern times; who, if ever any man was so endowed, seemed to have burning within him a light to illuminate the whole realm of mental science; but almost shut it in upon itself, and was content to scatter here and there a bright ray in the dark corners of the theme. Hence too the sad fact which he urges on our notice; that while Exact Science has been steadily advancing, with Let there be Light upon her banners, and ever new worlds of daring thought adding their glory to her train, the halls of metaphysics stand to this day, a mere circus for the showy wrestling of mental athletes. The Mathematics have traced in the changeless laws of nature the image and superscription of the Immutable God, while the metaphysics, after so many ages of toil and wrangling, are yet without one general fact, one received doctrine. Now in selecting a science for mental discipline, we need no great Philosopher to tell us that we must have one which has results. That one is most desirable whose methods are most perfect, and whose discoveries are most certain. We wish to accustom the mind to rely with well-grounded confidence on its own movements and its own conclusions. Only thus can the true scientific spirit be awakened. The young mind which learns to seek for truth by metaphysical methods, amid the surer training of this age, is sending his thoughts by a lame footman, while his neighbors use the lightning telegraph. He takes his place for his mental journeys on the old blind nag of Speculation, whom he leaves with loose rein to find her own way across the boundless heath; while the world. is rushing and whistling past him along sure, prepared paths of iron demonstration, with the chained forces of nature as attendants. At the peril of the young mind, its training must be something solid, something trustworthy. The early training of the scholar must teach him to use his energies in seeking firm and reliable truth, not in defending vague, verbal theory. But though metaphysics be too uncertain to afford this training, will not Logic answer? It has often been suggested as a substitute for Mathematics, and as a better discipline for that scientific spirit, which is to be to the young student what his proboscis is to the Elephant; a test which he applies instinctively to his path as he advances, step by step; and which prevents him from passing a bridge of speculation to an island of mere theory. It might have been thought sufficient once; only a few generations ago, before the spirit of '76 awoke in science or in politics, and when all the schools occupied steps below the throne of Aristotle. But since, amid the dusty crowd and stormy wrangling of these latter days, Logic itself seems to have become too uncertain for elementary instruction. I mean, those principles, if any, which it possesses as established beyond controversy, and which may be given to the young as unquestioned truth, are too few, too incomplete, too dimly apprehended, to be employed as an instrument of early mental culture. Considered as the Science of Thought, it is terribly weak as applied to inductive reasoning; which indeed no one has ever yet succeeded in reducing to an acknowledged logical form, except by shutting up the whole difficulty of the argument in the major premiss, by an astonishing petitio principii. Yet take away Inductive reasoning from the domain of Logic, and what is left worth contending for? She may rule her little province as she will; beyond the notice of an inquiring, advancing age; and cut off from the fellowship of the sciences. They who wish to appreciate the uncertainty of Logic in its details may examine the controversy between Professor De Morgan and Sir William Hamilton, on the question whether a judg |