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power, even where it is the strongest, may lie dead for want of the means of improvement: a favage may have been born with as good faculties as a Bacon or a Newton: but his talent was buried, being never put to ufe; while theirs was cultivated to the best advantage.
It may likewife be obferved, that the chief mean of improving our rational power, is the vigorous exercise of it, in various ways and in different fubjects, by which the habit is acquired of exercifing it properly. Without fuch exercise, and good fenfe over and above, a man who has studied logic all his life, may after all be only a petulant wrangler, without true judgement or fkill of reafoning in any science.
I take this to be Locke's meaning, when in his Thoughts on Education he says, " If you would have your fon to reafon "well, let him read Chillingworth." The ftate of things is much altered fince Locke wrote. Logic has been much improved, chiefly by his writings; and yet much lefs stress is laid upon it, and less time confumed in it. His counfel, therefore, was judicious and feasonable; to wit,
That the improvement of our reasoning power is to be expected much more from an intimate acquaintance with the authors who reafon the beft, than from studying voluminous systems of logic. But if he had meant, that the ftudy of logic was of no ufe nor deferved any attention, he furely would not have taken the pains to have made fo confiderable an addition to it, by his Effay on the Human Understanding, and by his Thoughts on the Conduct of the Understanding. Nor would he have remitted his pupil to Chillingworth, the acutest logician as well as the best reafoner of his age; and one who, in innumerable places of his excellent book, without pedantry even in that pedantic age, makes the happiest application of the rules of logic, for unravelling the sophistical reasoning of his antagonist.
Our reasoning power makes no appearance in infancy; but as we grow up, it unfolds itself by degrees, like the bud of a tree. When a child firft draws an inference, or perceives the force of an inference drawn by another, we may call this the birth of his reafon : but it is yet like a new-born babe, weak and tender; it must
be cherished, carried in arms, and have food of eafy digeftion, till it gather strength.
I believe no man remembers the birth of his reafon: but it is probable that his decifions are at first weak and wavering; and, compared with that steady conviction which he acquires in ripe years, are like the dawn of the morning compared with noon-day. We fee that the reafon of children yields to authority, as a reed to the wind; nay, that it clings to it, and leans upon it, as if conscious of its own weaknefs.
When reafon acquires fuch ftrength as to stand on its own bottom, without the aid of authority or even in oppofition to authority, this may be called its manly age. But in most men, it hardly ever arrives at this period. Many, by their fituation in life, have not the opportunity of cultivating their rational powers. Many, from the habit they have acquired of fubmitting their opinions to the authority of others, or from fome other principle which operates more powerfully than the love of truth, suffer their judgement to be carried along to the end of their days, either by
the authority of a leader, or of a party, or of the multitude, or by their own paffions. Such perfons, however learned, however acute, may be faid to be all their days children in understanding. They reason, they difpute, and perhaps write: but it is not that they may find the truth; but that they may defend opinions which have defcended to them by inheritance, or into which they have fallen by accident, or been led by affection.
I agree with Mr Locke, that there is no study better fitted to exercise and strengthen the reasoning powers, than that of the mathematical fciences; for two reasons; firft, Because there is no other branch of science which gives such scope to long and accurate trains of reafoning; and, fecondly, Because in mathematics there is no room for authority, nor for prejudice of any kind, which may give a falfe bias to the judgement.
When a youth of moderate parts begins to study Euclid, every thing at first is new to him. His apprehenfion is unfteady: his judgement is feeble; and refts partly upon the evidence of the thing, and partly upon the authority of his teacher. But
every time he goes over the definitions, the axioms, the elementary propofitions, more light breaks in upon him: the language becomes familiar, and conveys clear and fteady conceptions; the judgement is con→ firmed he begins to fee what demonstration is; and it is impoffible to see it without being charmed with it. He perceives it to be a kind of evidence that has no need of authority to ftrengthen it. He finds himself emancipated from that bondage; and exults fo much in this new state of independence, that he spurns at authority, and would have demonstration for every thing; until experience teaches him, that this is a kind of evidence that cannot be had in most things; and that in his most important concerns, he must rest contented with probability.
As he goes on in mathematics, the road of demonftration becomes smooth and easy; he can walk in it firmly, and take wider steps and at last he acquires the habit, not only of understanding a demonstration, but of discovering and demonftrating mathematical truths.
Thus, a man, without rules of logic, may acquire a habit of reafoning juftly in VOL. III. 3 G mathematics;