the material world around him. Accordingly he strives onward till he reaches the palpable,―till he can apply his abstractions to what passes independent of him. The metaphysician, on the contrary, cannot travel out of his own mind, he has nothing extrinsic with which he can test the justice of his conclusions, his is the fruitless endeavour of the eye striving to contemplate itself without something to reflect its image.

"Mixed mathematics are primarily dependent on the extent and accuracy of our scrutiny into nature, after which their further advancement is limited only by the degree of perfection to which the pure are carried. But to a very moderate progress in the former a very perfect knowledge of the latter is requisite. The laws of nature are, for the most part, simple in themselves, but the circumstances under which they act, induce a complication in their agencies which calls at once for the most powerful exertions of natural reason, and the most refined artifices of practised ingenuity to develop. Combinations are perpetually presenting themselves when the principles are satisfactorily known, the general laws placed beyond a doubt,—the mode of applying mathematical investigation thoroughly understood,-yet which, by the mere complication of the pure mathematical inquiries they involve, defy the utmost powers of calculation. The restless activity of Nature surrounds us with minute phenomena of this kind; the motions and equilibrium of fluids, their capillary attractions, the vibrations of the atmosphere of solid bodies, every breath of wind that blows, every mote that sparkles in the sunbeam, supplies us with an instance in point. On a wider scale, the law of gravitation, modified by the consideration of three gravitating bodies in motion, produces a problem which has resisted every effort of ingenuity and industry, stimulated by the strongest motives which can excite men to exertion.-(Sir John Herschel, art. MATHEMATICS in Brewster's Encyclopædia.)

It is to celebrated mathematicians accordingly that we are principally indebted for our extended knowledge of the material world. Young, Herschel, Arago, Fresnel, and many others whom we could name, have, by maturing the theory of light alone, done as much towards enlarging our minds, and instilling new and imposing ideas, as was ever accomplished by the metaphysician in his endeavours to illustrate our mental operations; that mind must indeed be obscured and prejudiced by the scholastic discipline of exclusive universities, which can underrate the moral effect of the recent researches on heat, magnetism, &c., as instituted by Leslie, Barlow, Melloni, &c., in short, there is not a modern discovery in physics which we do not owe to a mind necessarily trained in mathematical reasoning. The characteristic of mathematical reasoning,-that of being a successive chain of deductions from assumed principles, forces itself so constantly, and so obtrusively on the mind, that we confidently assert, mathematicians, better than most others, can appreciate and understand the force of moral evidence and probability; since it must be allowed that he who can institute a comparison between two species of conceptions, is more likely to rectify both, than he who has only one present to his mind. The learner, when for the first time he comprehends the demonstration of a problem in Euclid, attains a conception of the limit, to use a mathematical phrase, to the "infinite chain of probability," and can appreciate the force of any link, by at once perceiving its relation to that limit. The politician, or the man of the world, who knows no other than moral probability as a ground for conviction, is more liable to

appreciate at an equal value different evidence of this nature, unless he is convinced, like the geometrician, that there are "empirical facts" and 66 necessary matter."

"The study of mathematics would show them the necessity there is in reasoning, to separate all the distinct ideas, and see the habitudes that all those concerned in the present inquiry have to one another, and to lay by those which relate not to the proposition in hand, and wholly leave them out of the reckoning. This is that which in other subjects besides quantity, is what is absolutely requisite to just reasoning, though in them it is not so easily observed nor so carefully practised."-(Conduct of the Understanding, sec. 7.)

We have now to consider the charge made against mathematical study, "that it disposes the mind to one of two opposite extremes, credulity and scepticism."

"Alienated by the opposite character of their studies from those habits of caution and confidence, of skill and sagacity, which the pursuit of knowledge in the universe of probability requires and induces, they (mathematicians) are constrained, when they venture to speculate beyond their diagrams and calculations, on the one hand to accept their facts, either on authority or on imagination; or, on the other, to repudiate altogether as unreal what they are themselves incapable of verifying."-(Review, p. 441.)

To substantiate this view the writer quotes this passage from a living German metaphysician, (J. Sulat). "In so far as the mathematician is accustomed to his own mode of thinking, and ignorant of any other, applies, or does not apply, it to the supersensible, what must follow? In the former case the supersensible world is denied, inasmuch as it cannot be mathematically demonstrated; and in the latter, affirmed only on the ground of feeling and imagination. Thus on the one alternative, the mathematician becomes necessarily a materialist; on the other, a mystic."

It is impossible to avoid the semblance of repetition in an endeavour to confute a series of assumptions based on the same fallacy. Having denied the confined nature of mathematical pursuits, and having shown that they necessarily imply an acquaintance with, and study of, the phenomena of the material world, there exists no à priori reason for assuming that they have that prejudicial effect on the mental faculties which it has been asserted they have, by those who took an erroneous or partial view of their domains. This science has no peculiar tendency to produce that defect in the faculty of judgment which is implied by credulity, since its cultivation does not, necessarily, exclude that of other modes of reasoning, or other intellectual pursuits, by which the judgment may be strengthened and habituated to the exercise of caution, skill, and sagacity. If by scepticism is meant only the suspension of the judgment till more evidence is brought forward by which it may be formed, this cannot be surely imputed as a defect in the reasoning faculty; and we trust that no other meaning was covertly intended,— that recourse has not been had to that worst of controversial weapons, never employed by one capable of wielding better,-the endeavour to overwhelm an opponent by exciting popular prejudice against him.

"Again, with respect to the danger of scepticism arising from the use

of mathematical reasoning, the distinction has been beautifully pointed out between the effects of deductive and inductive habits of thought*. Deductive habits, those acquired in drawing consequences from ascertained laws, have in themselves no tendency to direct the mind towards the contemplation of a Supreme intelligence. Whereas inductive habits, those which are matured by ascending from effects towards their causes, by discovering laws previously unknown, have ever been found in union with a disposition to view the great phenomena of the universe, in connexion with one Supreme intelligence and will.

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The seat of unbelief is usually, indeed, not the understanding, but the heart. It is unhappily true, that the highest attainments in all branches of philosophy and literature have not been incompatible with vague or false views of religion. But surely it is not necessary seriously to confute an argument, which would discourage the study of anatomy, because some distinguished anatomists have been suspected of materialism; which would proscribe natural history, because some of the most attentive observers have weakly regarded all the phenomena of life as the results of unconscious organization; and banish mathematics, because some of those who have cultivated them with success have reasoned ill, or decided falsely upon questions of the highest importance.

"All the sciences may be made the hand-maids of religion. And of these the severe science of mathematics, as applied to investigate the phenomena of the natural world, has ever occupied an honourable and prominent place." (Chevallier, pp. 34, 35.)

Whatever may have been the reviewer's intention, it is obvious to all impartial persons, that his zeal has hurried him into a violation of sound reasoning; the tendency of one pursuit cannot be to generate two opposite defects in minds similarly constituted: if both these defects be generated in minds pursuing the same study, it is to the result of the constitution of the minds engaged on that pursuit, and not to the pursuit itself, that the evil is to be attributed. From what we have already urged it may be conceded, that if a mind, not naturally endowed with a sound faculty of judgment, be by circumstances trained to mathematical studies, the result may be credulity. The fact is, credulity and scepticism ought not to have been brought into opposition; they are not results of different degrees of one intellectual faculty,-imagination is always, more or less, at the bottom of the former. A person is not credulous because he is incapable of weighing moral evidence, and deciding from the balance; but he is credulous because his fancy interferes and prevents his judgment alone from acting. Mr. Dugald Stewart's assertion, that "in those who have confined their studies to mathematics alone, there has often been observed a proneness to that species of religious enthusiasm, in which imagination is the predominant element, and which, like contagion, is propagated in a crowd," should have been considered better, before it was cited in favour of the tendency of mathematics to generate credulity. The temporary prevalence of Simeonism at Cambridge, alluded to by that gentleman, is not a sufficiently decided case in point to have much weight; it was not, we believe, any new creed in religion and morals, hastily embraced, and propagated with that fanaticism and intemperance that characterize those moral epidemics, which seem to Whewell's Bridgewater Treatise, book iii., c. 5, 6.

indicate especial weakness of judgment among the converts. Mr. Simeon only advocated a more strict observance of Gospel-ordinances and certain modifications of church government, concerning which men of equally sound minds and liberal education may differ in opinion: if most of those who embraced his doctrines were mathematicians, that was the necessary consequence of the majority of students at that university being such. It should have been stated what was the proportion between those who did, and those who did not, become converts to them; and again, of these two numbers, what proportion of each was to be allotted to those who studied mathematics, and to those who pursued classical literature. Unless this statement were made, the assertion is but a vague generality, of no value in such an argument.

We think the tenour of the following passage from Mr. Stewart's "Dissertation on the progress of Philosophy," (Supplement to Edinburgh Encyclopædia,) is not exactly consistent with the conclusion intended to be drawn by the reviewer from those he has adduced.

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Nothing is more interesting and instructive than to remark the astonishing combinations in the same mind, of the highest intellectual endowments with the most deplorable aberrations of the understanding, and even in numberless instances, with the most childish superstitions of the multitude. . . . . . . Nor was the study of the severer sciences on all occasions an effectual remedy against such illusions of the imagination."

As the examples of these deplorable aberrations are taken from divines, jurists, and metaphysicians*, the inference is, that Mr. Stewart, by "the severer," alluded to physical and mathematical sciences, and that he considered them, generally, as an effectual remedy for keeping down the illusions of imagination by strengthening the faculty of judgment.

Though we do not allow much weight to the opinion of individuals, as to the effects on the intellect of any study in which they either do or do not excel; we admit the full force of the evidence deduced, both from the moral conduct and intellectual cultivation of those celebrated for any particular line of study, as to the effect of that study on the mind. We bow not to the authority of Germans deciding on the inferiority of mathematical to classical, or metaphysical studies, for forming the moral constitution, because the nation is eminently unmathematical; and yet that which could give birth to, and adopt, the speculative systems of Oken, Schelling, Goldbeck, Fries, Nees Von Esenbeck, and others,-the land of mesmerism and phrenology,-the country notorious beyond every other for the universal diffusion of scepticism, for which they arrogate the term rationalism, cannot, we suppose, be cited by the anti-mathematical party as having attained that healthy state of intellectual cultivation, which the line of studies pursued ought to have engendered,

* The reviewer observes, triumphantly, that there are four super-eminent metaphysicians, Descartes, Leibnitz, Malebranche, and Locke; that the last was the only one who was not a mathematician, and yet how superior he was to the other three. Malebranche was so little of a mathematician, that his acquirements in that science are unknown to all

the world but the reviewer. Leibnitz did not become a mathematician till he was twenty-three years of age, and his mind, it may be supposed, had nearly attained its full vigour. Descartes was a genius, like Pascal, and though inferior to Locke, yet he was only so in having been born considerably before him.

according to its advocates. The fact is, imagination is the national characteristic faculty of the Germans, and it will be admitted that, when not duly restrained, this faculty is the source of every moral obliquity; if Germany has produced poets, artists, musicians, metaphysicians, antiquarians, and philologists of a higher rank than other contemporary nations in recent times, it has also given birth to more credulity, fanaticism, folly, and crime.

The French, as a nation, cannot be adduced in evidence on the other side, because there was till lately no general intellectual cultivation in that country: but the most inveterate enemy of abstract science as a study, must admit that, as individuals, the Sçavans of Paris are preeminent for their high moral and intellectual excellence. D'Alembert's virtues are universally allowed; and his contemporaries and successors in cultivating mathematical studies are, almost without exception, exempt from any stain on their character. M. Arago, in the present day, is not more distinguished for his profound mathematical and physical knowledge, than for the political influence which his firmness and rectitude have obtained for him in a country torn by factions. The late Carnot offered to defend an important fortress at a critical juncture, and Napoleon would have accepted his services. Condorcet, whose literary decisions have been pronounced by a competent authority as entitled to the highest deference, was a distinguished mathematician at sixteen. The striking and nearly single exception presented by the two Bernouillis*, to what we consider the general rule, is fully admitted; but it has such an abundance of parallels among philologists, jurists, metaphysicians, and divines, that we think no one can assert equanimity of temper, and exemption from envy, malice, and all uncharitableness, to be the usual result of philosophical studies, as they are termed.

We will not, for obvious reasons, cite examples of moral excellence from among our living countrymen distinguished for their scientific attainments; yet we cannot refrain from alluding to one, because the attainment of profound knowledge in abstract science being rare in an individual of her sex, such an example naturally presents itself in a discussion on the beneficial effects on the moral character of such studies. If, then, to a knowledge rarely equalled by men, be united every quality that can adorn a woman, that knowledge being enhanced by the possession of extensive acquirements in other studies-we may at least be allowed to quote her opinions, her pursuits, and her example on our side, in contrast to those of the culpable De Staël.

Let any one recall to his mind all the quarrels which have distracted the world of literature, from the earliest ages to the present moment, let him reflect on the bitter, relentless, bloody hostilities, excited by purely speculative matters of opinion, such as those between the Nominalists and Realists, between the Roman and Canon jurists, the Jansenists and Molinists, with numberless others to which we will not allude; and then let him decide whether the cultivators of abstract and

*We say nearly single, for the unfortunate differences between Newton and Flamsteed, which have lately been brought to light, are venial, compared to the

unnatural hostility of the Swiss brothers; and the exact proportion of blame to be imputed to Flamsteed or his great opponent, is still a matter of discussion.