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sessed a clear insight into events, and was in no respects 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 readily 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."

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

Many of the most respectable and valuable men in our legislative assemblies are persons, who are rarely heard in debate. While they are known to possess reach of thought and correctness of judgment, they exhibit in public discussion little more than confusion and apparent inability.- -Mr. Jefferson, author of the Declaration of American Independence, is declared by one of his illustrious associates, who knew him well, to have been a silent member of the Continental Congress. And yet he had at that period the reputation of literature and science, and of being a happy writer; and lent great aid by his promptness and decision on committees.A remark of a similar purport is made by Mr. Jefferson in his recently published Memoirs, in respect to Washington and Franklin. (See North American Review, Vol. XXII, p. 386.)

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. Every thing 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 embody all the evanescent processes of thought, appears to others defective and confused.

CHAPTER EIGHTH.

DEMONSTRATIVE REASONING.

§. 12. 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 examine it under the two prominent heads of Moral and Demonstrative.

There are various particulars, in which moral and demonstrative reasoning differ from each other; and 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 or thoughts are called abstract, which are representative 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 connection 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.

§. 13. 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 demonstrations of mathematics. Axioms are certain self-evident propositions, or propositions, the truth of which is discovered by intuition, such as the following; "Things, equal to the same, or 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 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, it cannot be denied, that the truth, involved in propositions susceptible of demonstration, would have been beyond our reach. (See §. 326, Vol. I.)

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 giving 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.

§. 14. The opposites of demonstrative reasonings absurd.

In demonstrations we consider only one side of a question; it is not necessary to do any thing 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 always imply some fallacy. Thus, the proposition, that the three angles of a triangle are not equal to two right angles, and other propositions, which are the opposite of what has been demonstrated, will always be found to be false, and

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