be cherished, carried in arms, and have food of eafy digeftion, till it gather ftrength. I believe no man remembers the birth of his reafon : but it is probable that his decifions are at firft 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 confcious of its own weaknefs. When reafon acquires fuch ftrength as to ftand 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,, fuffer their judgement to be carried along to the end of their days, either by 3 F 2 the 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 ftudy better fitted to exercife and strengthen the reasoning powers, than that of the mathematical fciences; for two reafons; firft, Because there is no other branch of fcience which gives fuch fcope 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 false 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 rests 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 confirmed: he begins to fee what demonstration is; and it is impoffible to fee 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 ftate 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 moft things; and that in his most important concerns, he must rest contented with probability. As he goes on in mathematics, the road of demonstration becomes finooth and eafy he can walk in it firmly, and take wider fteps and at laft he acquires the habit, not only of understanding a demonftration, but of difcovering and demonftrating mathematical truths. : Thus, a man, without rules of logic, may acquire a habit of reafoning justly in mathematics; mathematics; and, I believe, he may, by like means, acquire a habit of reafoning justly in mechanics, in jurifprudence, in politics, or in any other fcience. Good fenfe, good examples, and affiduous exercise, may bring a man to reafon juftly and acutely in his own profeffion, without rules. But if any man think, that from this conceffion he may infer the inutility of logic, he betrays a great want of that art by this inference: for it is no better reafoning than this, That because a man may go from Edinburgh to London by the way of Paris, therefore any other road is ufelefs. There is perhaps no practical art which may not be acquired, in a very confiderable degree, by example and practice, without reducing it to rules. But practice, joined with rules, may carry a man on in his art farther and more quickly, than practice without rules. Every ingenious artist knows the utility of having his art reduced to rules, and by that means made a fcience. He is thereby enlightened in his practice, and works with more affurance. By rules, he fometimes corrects his own errors, and often detects the errors of others: he finds them of great use to confirm his judgement, to justify what is right, and to condemn what is wrong. Is it of no use in reasoning, to be well acquainted with the various powers of the human understanding, by which we reafon? Is it of no ufe, to refolve the various kinds of reasoning into their fimple elements; and to discover, as far as we are able, the rules by which these elements are combined in judging and in reafoning? Is it of no ufe, to mark the various fallacies in reasoning, by which even the most ingenious men have been led into error? It must furely betray great want of understanding, to think thefe things ufelefs or unimportant. These are the things which logicians have attempted; and which they have executed; not indeed fo completely as to leave no room for improvement, but in fuch a manner as to give very confiderable aid to our reafoning powers. That the principles laid down with regard to definition and divifion, with regard to the converfion and oppofition of propofitions and the general rules of reafoning, are not without ufe, is fuffi ciently |