tally punishing offences of a slight nature. But before considering the cases he has particularly in view, he remarks on the right of capital punishment for murder; and admits, that the principle of self defence gives such a right. He then takes up the case of stealing, and contends, that we have no right to punish the thief with death, because no such right is given by the laws of nature; for, before the formation of the civil cómpact, the institution of property was not known. He then considers the nature of civil society, and contends, that, in the formation of the social compact, no such extraordinary power, as that of putting to death for stealing or other crimes of similar aggravation, could have been implied in that compact, because it never was possessed by those, who formed it; &c.

Here is an argument, made up of a number of propositions, and carried on, as may be supposed, to very consid erable length. And in this argument, as in all others, every proposition is, in the first instance, suggested by the laws of association; it is not at all a matter of arbitrary volition. The disputant first states the inquiry in general terms; he then considers the particular case of murder; the crime of theft is next considered; and this is examined, first, in reference to natural law, and, afterwards, in reference to civil law. And this consecution of proposi tions takes place precisely the same, as when the sight of a stranger in the crowd suggests the image of an old friend, and the friend suggests the village of his residence, and the village suggests an ancient ruin in its neighbourhood, and the ruin suggests heroes and battles of other days.— It is true, that other propositions may have been suggested at the same time, and the disputant may have had his choice between them, but this was all the direct power, which he possessed; and even that in strictness of speech can hardly be called direct. (See §. 213.)

§. 289. Grounds of the selection of propositions. A number of propositions are presented to the mind by the principles of association; the person, who carries on the process of reasoning, makes his selection among

them. But it is reasonable to inquire, How it happens, that there is such a suitableness or agreement in the propositions, as they are successively adopted into the train of reasoning? And this seems to be no other than to inquire into the circumstances, under which the choice of them is made, or the grounds of the selection.

Let it be considered, then, that in all arguments, whether moral or demonstrative, there is some general subject, on which the evidence is made to bear; there is some point in particular to be examined. In reference to these general outlines, we have a prevailing and permanent deire. This desire is not only a great help in giving quickless and strength to the laws of association; but exerises also a very considerable indirect influence in giv ng an appropriate character to the thoughts, which are uggested by those laws. Hence the great body of the ropositions, which are at such times brought up, will be und to have a greater or less reference to the general bject. These are all very rapidly compared by the mind ith those outlines, in regard to which its feelings of dere are exercised, or with what we usually term the point be proved. Here the mind, in the exercise of that susptibility of feelings of relation, which we have already en it to possess, immediately discovers the suitableness want of suitableness, the agreement or want of agreeent of the propositions presented to it, to the general subt. This perception of suitableness, which is one of Ose relative feelings, of which the mind is from its very ture held to be susceptible, exists as an ultimate fact in r mental constitution. All, that can profitably be said relation to it, is the mere statement of the fact, and of : circumstances, under which it is found to exist.-Those positions, which are judged by the mind, in the exercise that capacity which its Creator has given it, to be agreee to the general subject or point to be proved, are perted by it to enter in, as continuous parts of the argunt. And in this way a series of propositions rises up, having reference to one ultimate purpose, regular, appriate, and in their issue laying the foundation of the

different degrees of assent.--This explanation will apply not only to the supposed argument in the last section, which is an instance of moral reasoning, but will hold good essentially of all other instances of whatever kind. The difference in the various kinds of reasoning consists less in the mental process, than in the nature of the subjects compared together, and in the conditions attending them.

§. 290. Of the subjects of demonstrative reasoning.

In order to have a full view of this subject, it is necessary to examine it, under the two prominent heads of Moral and Demonstrative.-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 hereaf ter more particularly, are matters of fact, including their connection with other facts, whether constant or variable. and all attendant circumstances.That the exterior an gle of a triangle is equal to both the interior and opposite angles, is a truth, which comes within the province of dem onstration. That Homer was the author of the Iliad, tha Xerxes invaded Greece, &c. are inquiries, belonging moral reasoning.

§. 291. Use of definitions and axioms in demonstrative reasoning

In every process of reasoning there must be at t commencement of it something to be proved; there me also be some things either known, or taken for granted such, with which the comparison of the propositions

gins. 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 princi ples 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, are equal to one another;" "From equals take away equals, and equals remain." We genrally find a number of them prefixed to treatises of geomtry; and it has been a mistaken supposition, which has ong prevailed, that they are at the foundation of geometical, and of all demonstrative reasoning. But axioms, taen by themselves, lead to no conclusions. With their ssistance alone, it cannot be denied, that the truth, involed in propositions susceptible of demonstration, would ave been beyond our reach.

But axioms are by no means without their use, although heir nature may have been misunderstood. They are roperly and originally intuitive perceptions of the truth, ad whether they be expressed in words, as we generally nd them, or not, is of but little consequence, except as a latter of convenience to beginners, and in giving instrucon. But those intuitive perceptions, which are always aplied in them, are essential helps; and if by their aid one we should be unable to complete a demonstration,

we should be equally unable without them. We begu 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.

§. 292. 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 also to involve an absurdity; that is, are inconsistent with, and contradictory to themselves. Nothing more can be wanted to confirm this, than a careful examination of such propositions.

§. 293. Demonstrative reasonings do not admit of different

degrees of belief.

When our thoughts are employed upon subjects, which come within the province of moral reasoning, we yield different degrees of assent; we form opinions more or less probable. It is different in demonstrations; the assent, which we yield, is at all times of the highest kind, and is never susceptible of being regarded, as more or less.—It short, all demonstrations are certain. But a question first arises, What is certainty? (See . 267.) And again, What in particular do we understand by that certainty which is ascribed to the conclusions, to which we are co ducted in any process of demonstrative reasoning?