judgment depends. These functions, as we have seen, have been called forth in the grammatical studies of the pupil; but henceforth they must appear in their proper character and be wielded with conscious ability.

It has been received almost as an axiom on the authority of Locke, though probably founded on a misconception of the meaning of Bacon, that Mathematics may be a substitute for Logic: but the position will be found unsupported, if we consider the different purposes of these two great factors of the human intellect.

The first, or the science of Mathematics,as unfolding the necessary relations of all the forms of sensible experience to Space, Time and Number-is one the great value and comprehensive utility of which are so obvious, that it is universally admitted to be not only essential to a liberal education, but more or less an indispensable element of the preparation required for all the ordinary concerns of life.

In the application of mathematical science to nature, as the sphere of our sensible experience, "we have a most assured knowledge, which, vast even to astonishment in its present extent, promises to enlarge itself without limit in the future-a science, of which it may with severest truth be said, that it

"Hath made earth's reasoning animal her Lord,"

hath enabled man to behold the ends of the earth, and to survey what is beneath the heavens. He measureth the sea, and appointeth laws to the flowing thereof: he unravelleth the maze of the moon: he foretelleth the course of the stars-yea, he weigheth them out, and doth compass them as with a line.' And this too by a science in the pure and most perfect sense, which carries with it throughout demonstrative certainty, an absolute necessity of truth. The science of mathematics rests therefore on no grounds of experience, which could at best only give us the knowledge that It is so, not the clear insight and irresistible sense that So it must be.† Consequently it can be only a pure product of the intellect acting by its own powers on its own wealth;-it is the work, indeed, of the Reason, acting on the Pure Sense; for where except in the Reason can necessity and universality be found?

Were the value of mathematical knowledge comprised, however, in the splendid achievements, which the sciences of figure and number have wrought, in bringing the natural world under the power, intellectual and manual, of man,-it would still want the inducement to its study, which its important aid in intellectual training and discipline supplies. Well hath Plato said : οὐδεὶς εἰσίτω ἀγεωμέτρητος, “Let

* Coleridge. Compare Aids to Reflection. Fifth edition, p. 175. + See Appendix C.

no man enter the schools of philosophy, who has not previously disciplined his mind by Geometry. He considered this science as the first purification of the soul by abstracting the attention from the accidents of the senses; "# and a poet of our own age has told us :

“Such is the throne, which man for Truth, amid
The paths of mutability, hath built,-

Secure, unshaken still; and whence he views,
In matter's mouldering structures, the pure forms
Of circle or triangle, cube or cone-
Impassive all; whose attributes nor Force,
Nor Fate, can alter. There he first conceives
True being, and the intellectual world,-

The same this hour and ever. Thence he deems
Of his own lot :-above the painted shapes,
That fleeting move o'er this terrestrial scene,
Looks up;-beyond the adamantine gates
Of death expatiates ;-as his birthright claims
Inheritance of all the works of God ;-
Prepares for endless time his plan of life,
And counts the Universe itself his home."-

AKENSIDE.

Dry and even repulsive as the very name of Logic may sound in an age, in which the immediately useful, in the knowledges that relate to material objects and interests, is predominantly and almost exclusively regarded, it may yet be well to pause—in considering whether the science possesses no other claim to our attention than its admitted abuse by the Schoolmen. You need be under no appre

* Coleridge. Second Lay Sermon, p. 364. Second edition.

hension however that I am about to undertake the difficult, and perhaps distasteful, task of solving the intricacies or of explaining the subtleties of Logic. But if, as may be truly affirmed, the results of experience would want the combinations of thought and the stamp of truth, were they not submitted to a process of Reasoning-then a competent acquaintance with the rules and methods of conclusive discourse cannot be deemed a matter of indifference to any one desirous of securing the privileges of a rational being.

Without the all-important functions of Abstraction and Generalization, implying Comparison and Judgment, and their results expressed in Terms and Propositions,—the impressions on the senses, the influences that continually excite our notice, the appearances around and about us would be but a diffluent chaos; they could not be substantiated as facts, retained as experience, reasoned upon as truths, or made the means of foresight and of extended knowledge. The proper province of Logic, however, is Reasoning or Discoursethe process by which we deduce from known truths all that they legitimately comprehend, by which we apply general rules to particular cases, by which we infer from some less comprehensive truth one of more comprehensive generality;—it is the process by which we weigh evidence, infer and prove by argument, and draw universal and necessary conclusions;

-while in every judgment the presence of Reason is attested by the claim, which it asserts and vindicates to the unavoidable conviction of all rational beings. And the results are the Rules, Maxims and Judgments, which constitute our generalized Experience.

It is not therefore the art of one

"Profoundly skill'd in analytic ;
Who can distinguish and divide

A hair 'twixt south and south-west side;

On either which who can dispute,

Confute, change hands, and still confute:"

BUTLER.

Reasoning is the daily and hourly business of our lives, and, whatever our worldly calling -in the pulpit, at the bar, or at the bedside of the patient-we are unceasingly occupied in inferring or proving a something from what is already ascertained or taken for granted. And in the words of an eminent writer on Logic, "To learn to do that well, which every one will and must do, whether well or ill, may surely be considered as an essential part of a liberal education."*

Nor should we forget, in obtaining the mastery of the art of discoursing conclusively, the various causes, which interfere with sound reasoning, and against which we must be perpetually on our guard, as tending to vitiate our

* Whately's Logic. Preface.