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ESSAYS, &c.

ESSAY I.

ON THE CARDINAL IMPORTANCE OF THE STUDY OF MATHEMATICAL SCIENCE, AS A BRANCH OF LIBERAL EDUCATION, AND AS CONNECTED WITH THE ATTAINMENT OF SUPERIOR ABILITY AND SKILL, IN THE EXERCISE OF ORATORY.

THE trains of ideas that pervade the human mind, are reducible to three classes: trains connected by reasoning, trains connected by memory, and trains connected by imagination. The author is perfectly aware, that these trains are often intermixed; and that in the trains that fall under each of these heads; reason, memory, and imagination, predominate merely. He is aware too, that a distribution, modelled with greater logical accuracy, might have been proposed: but it is sufficiently accurate to answer the purposes of this essay.

Reasoning is of three sorts:-demonstrative, certain, and probable.

Reasoning is demonstrative, where the conclusion is established, with such clearness and force of evidence, as to banish from the minds of all who comprehend it, the shadow or possibility of doubt, and to render a different or a contrary conclusion, incredible and even inconceivable, and impossible.

Reasoning is certain, when the conclusion which the reasoner endeavours to establish, is unhesitatingly embraced and confidently acted on, by a vast majority of the intelligent persons who comprehend the evidence, although a different and even a contrary conclusion, may be conceived without incongruity, and expressed without contradiction, and is therefore possible, and being possible, is within the immense range, although on the very verge of credibility.

Reasoning is probable, when the conclusion which the reasoner labours to establish, exhibits greater verisimilitude than any other, in the judgment of those who are best qualified to comprehend the subject to which the conclusion relates: and it is more or less verisimilar, according to the confidence or hesitation with which persons thus qualified, embrace it, although other and perhaps opposite conclusions may be conscientiously embraced, by persons of unquestioned intelligence and unsuspected veracity, and supported by arguments which it demands the utmost ingenuity and the most extensive information, to refute.

Demonstrative reasoning, has its foundation in definitions that suggest ideas perfectly precise, and are re-excited identically by the terms of the definition, in the mind of every human being who possesses a competent faculty of think

ing, resolves itself at every advancing step, (from the simplest and most obvious, to the most complicated and stupendous truths,) into axioms or self-evident propositions, in other words, resolves itself into propositions, nothing contrary to or different from which, can be conceived. Demonstrative reasoning is exclusively conversant with relations subsisting amongst ideas, originally suggested doubtless by impressions made by external objects on the organs of sense, but made at so early a stage of human existence and so universally, that they may be regarded as constituting a part of the essential nature, of the necessary furniture, of human thought.

Certain and probable reasoning have a common foundation in the relation of cause and effect, and differ merely in degree, as will afterwards be shown. Both, however, differ in several important respects, speculative as well as practical, from demonstrative reasoning, the farther consideration of which will occupy the remainder of this essay.

Demonstrative reasoning has relation exclusively to quantity, and constitutes what is denominated mathematical science. Being deduced from definitions that suggest to every mind combinations of ideas perfectly invariable, (provided the terms are distinctly understood,) no one combination is ever confounded with another, how numerous soever the points of resemblance or coincidence may be.

The minutest difference is as plainly distinguishable, as the most striking contrariety. An equilateral triangle is as readily distinguished from, and as little liable to be, confounded with an isosceles, as with a scalene triangle:

such reasoning too, resolvable at every step into self-evident propositions, is necessarily, a portion of immutable truth.

On this foundation, rest the inviolable and incommunicable privileges of mathematical science. Mathematical science is the only kind of human knowledge which may be regarded as a portion of divine truth. It is conceivable, that every existing system or speculation, physical, metaphysical, and moral, (however imposing its pretensions, numerous and enlightened its disciples, and strong its verisimilitude,) may be hereafter refuted, and give place to more congruous explanations of the phenomena of material and intellectual nature, nearer approximations to the truth of things: but it is inconceivable and impossible, that the time will ever arrive, ever did, or can exist, when any mathematical theorem, (the Pythagorean for instance,) will be, has been, or can be refuted.

Were every order of created intelligences, from the most glorious seraphim and cherubim, down to the humblest human intellect capable of comprehending its evidence, contemplating this theorem at the same moment, it is inconceivable that it should not appear in the same light, to every individual mind, in this stupendous congregation of intelligent beings.

Respecting mathematical truth, the ideas of Adam, before the fall, must have corresponded with those of the celestial visitants of Paradise, and with those also of the most corrupted and irreclaimable of his descendants. Even in the infernal regions, where the glorious faculties of one

of the highest orders of created intelligences, are in the utmost possible degree perverted and maligned, where God is detested, evil pursued as good, and truth abhorred, mathematical truth sheds its "increate" and irrefrangible light, on the minds of demons and damned spirits, as clearly, as on the orignally less, but now perhaps more glorious faculties, of Newton or of Pascal. We may even dare to believe, that in regard to every theorem supported by mathematical demonstration, science and omniscience coincide; that the evidence is beheld in the same light, by the Almighty mind, by the Creator himself, and by the humblest and most fallible of his intelligent creatures.

Mathematical science may be therefore viewed, as a portion of divine truth, revealed not by inspiration but by intuition.

Physical science, founded on the relations which external objects bear to each other, (as those relations are manifested to our minds through our senses,) is possibly in its essence, relative and mutable.

In the innumerable orbs that revolve though the immensity of space, which the attributes of God, the discoveries and the analogies of science, warrant us in believing to be habitable, and inhabited probably by beings ascending in capacity and intelligence, immeasurably above the utmost height that can ever be reached by man; it is not impossible, nor even improbable, that the mutual action and influence of material objects, as it is manifested to their intelligent inhabitants by the exercise of their senses, varies with their organization; with the number, perfection, and peculiar

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