follow ary mechanic calling, where we find that what was once done with difficulty comes in time to be done with great ease and readiness. The muscles of such persons seem to move with a kind of instinctive facility and accuracy in the performance of those works to which they have been for a long time addicted.

There is a similar effect of frequent practice in the increase of quickness and facility in our mental operations; and certainly as much so in those which are implied in reasoning as in any others. If, for instance, a person has never been in the habit of going through geometrical demonstrations, he finds his mind very slowly and with difficulty advancing from one step to another; while, on the other hand, a person who has so often practised this species of argumentation as to have formed a habit, advances forward from one part of the train of reasoning to another with great rapidity and delight. And the result is the same in any process of moral reasoning. In the prosecution of any argument of a moral nature, there is necessarily a mental perception of the congruity of its several parts, or of the agreement of the succeeding proposition with that which went before. The degree of readiness in bringing together propositions, and in putting forth such perceptions, will greatly depend on the degree of practice.

There

§ 183. Of reasoning in connexion with language or expression. Language is the great instrument of reasoning. may indeed be a deductive process which is purely mental; but, in point of fact, this is seldom the case. In the use of language, it is worthy of notice, that there is often a want of correspondence between the purely mental pro- · cess in reasoning and the outward verbal expression of it. When persons are called upon to state their arguments suddenly and in public debate, they often commit errors which are at variance with the prevalent opinion of their good sense and mental ability. This is particularly true of men who are chiefly engaged in the ordinary business of life, or are in any situation where there is a constant call for action. The conclusions at which such persons arrive may be supposed to be generally correct, but they

frequently find themselves unable to state clearly and correctly to others the process of reasoning by which they arrived at them.-Oliver Cromwell, the famous English Protector, is said to have been a person to whom this statement would well apply. The complicated incidents of his life, and the perplexities of his situation, and his great success, sufficiently evince that he possessed a clear insight into events, and was in no respect deficient in understanding; but when he attempted to express his opinions in the presence of others, and to explain himself on questions of policy, he was confused and obscure. His mind eadily insinuated itself into the intricacies of a subject; and while he could assert with confidence that he had arrived at a satisfactory conclusion, he could not so readily describe either the direction he had taken, or the involutions of the journey." All accounts," says Mr Hume," agree in ascribing to Cromwell a tiresome, dark, unintelligible elocution, even when he had no intention to disguise his meaning; yet no man's actions were ever, in such a variety of difficult cases, more decisive and judicious."

184. Illustration of the foregoing section.

Such instances are not unfrequent. Mr. Stewart somewhere mentions the case of an English officer, a friend of Lord Mansfield, who had been appointed to the government of Jamaica. The officer expressed some doubts of his competency to preside in the court of chancery. Mansfield assured him that he would not find the difficulty so great as he imagined.-"Trust," said he," to your own good sense in forming your opinions, but beware of stating the grounds of your judgments. The judgments will probably be right; the arguments will infallibly be wrong."

The perplexity, which is so often experienced by men engaged in active life, in giving a prompt and correct verbal expression to the internal trains of thought, is probably owing in part to a want of practice of that kind, and in part to certain mental habits, which they have been led, from their situation, to form and strengthen In a thousand emergencies they have been obliged to act with

quickness, and, at the same time, with caution; in other words, to examine subjects, and to do it with expedition. In this way they have acquired exceeding readiness in all their mental acts. The consequence of this is, that the numerous minute circumstances, involved more or less in all subjects of difficult inquiry, are passed in review with such rapidity, and are made in so very small a degree the objects of separate attention, that they vanish and are forgotten. Hence these persons, although the conclusion to which they have come be satisfactory, are unable to state to others all the subordinate steps in the argument. Everything has once been distinctly and fairly before their own minds, although with that great rapidity which is always implied in a HABIT; but their argument, as stated in words, owing to their inability to arrest and imbody all the evanescent processes of thought, appears to others defective and confused.

CHAPTER X.

DEMONSTRATIVE REASONING.

185. Of the subjects of demonstrative reasoning.

IN the remarks which have hitherto been made, the subject of reasoning has been taken up in the most general point of view. The considerations that have been proposed are applicable, in the main, to reasoning in all its forms. But it is necessary, in order to possess a more full and satisfactory conception of this subject, to exam. ine it under the two prominent heads of Moral and Demonstrative.

There are various particulars in which moral and demonstrative reasoning differ from each other; the consideration of which will suggest more fully their distinctive nature. Among other things, DEMONSTRATIVE reasoning differs from any other species of reasoning in the subjects about which it is employed. The subjects are abstract ideas, and the necessary relations among them. Those

ideas of thoughts are called abstract which are represent ative of such qualities and properties in objects as can be distinctly examined by the mind separate from other qualities and properties with which they are commonly united. And there may be reckoned, as coming within this class of subjects, the properties of numbers and of geometrical figures; also extension, duration, weight, velocity, forces, &c., so far as they are susceptible of being accurately expressed by numbers or other mathematical signs. But the subjects of moral reasoning, upon which we are to remark hereafter more particularly, are matters of fact, including their connexion with other facts, whether constant or variable, and all attendant circumstances.-That the exterior angle of a triangle is equal to both the interior and opposite angles, is a truth which comes within the province of demonstration. That Homer was the author of the Iliad, that Xerxes invaded Greece, &c., are inquiries belonging to moral reasoning.

186. Use of definitions and axioms in demonstrative reasoning. In every process of reasoning, there must be, at the commencement of it, something to be proved; there must also be some things, either known or taken for granted as such, with which the comparison of the propositions begins. The preliminary truths in demonstrative reasonings are involved in such definitions as are found in all mathematical treatises. It is impossible to give a demonstration of the properties of a circle, parabola, ellipse, or other mathematical figure, without first having given a definition of them. DEFINITIONS, therefore, are the facts assumed, the FIRST PRINCIPLES in demonstrative reasoning, from which, by means of the subsequent steps, the conclusion is derived. We find something entirely similar in respect to subjects which admit of the application of a different form of reasoning. Thus, in Natural Philosophy, the general facts in relation to the gravity and elasticity of the air may be considered as first principles. From these principles in Physics are deduced, as consequences, the suspension of the mercury in the barometer, and its fall when carried up to an eminence. We must not forget here the use of axioms in the dem

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onstrations of mathematics. Axioms are certain self-ev ident propositions, or propositions the truth of which is discovered by intuition, such as the following: "Things equal to the same, are equal to one another;" "From equals take away equals, and equals remain." We generally find a number of them prefixed to treatises of geometry, and other treatises involving geometrical principles; and it has been a mistaken supposition, which has long prevailed, that they are at the foundation of geometrical and of all other demonstrative reasoning. But axioms, taken by themselves, lead to no conclusions. With their assistance alone, the truth, involved in propositions susceptible of demonstration, would have been beyond our reach.

But axioms are by no means without their use, although their nature may have been misunderstood. They are properly and originally intuitive perceptions of the truth; and whether they be expressed in words, as we generally find them, or not, is of but little consequence, except as a matter of convenience to beginners, and in givng instruction. But those intuitive perceptions which are always implied in them are essential helps; and if by their aid alone we should be unable to complete a demonstration, we should be equally unable without them. We begin with definitions; we compare together successively a number of propositions; and these intuitive perceptions of their agreement or disagreement, to which, when expressed in words, we give the name of axioms, attend us at every step.

187. The opposites of demonstrative reasonings absurd.

In demonstrations we consider only one side of a question; it is not necessary to do anything more than this. The first principles in the reasoning are given; they are not only supposed to be certain, but they are assumed as such; these are followed by a number of propositions in succession, all of which are compared together; if the conclusion be a demonstrative one, then there has been a clear perception of certainty at every step in the train. Whatever may be urged against an argument thus conducted is of no consequence; the opposite of it will al