to confirm this, than a careful examination of such propositions. §. 227. 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.In short, all demonstrations are certain. But a question arises, What is certainty? And what in particular do we understand by that certainty, which is ascribed to the conclusions, to which we are conducted in any process of demonstrative reasoning? §. 228. Of the nature of demonstrative certainty. In proceeding to answer the above inquiry, it is to be observed, that, in demonstrative reasonings, we always begin with certain first principles or truths, either known, or taken for granted; and these hold the first place, or are the foundation of that series of propositions, over which the mind successively passes, until it rests in the conclusion. In mathematicks the first principles, of which we here speak, are the definitions.-We begin, therefore, with what is acknowledged by all to be true or certain. At every step there is an intuitive perception of the agreement or disagreement of the propositions, which are compared together. Consequently, however far we may advance in the comparison of them, there is no possibility of falling short of that degree of assent, with which, it is acknowledged, that the series commenced. So that demonstrative certainty may be judged to amount to this ;-Whenever we arrive at the the last step or the conclusion of a series of propositions, the mind intuitively perceives the relation existing, whether it be the agreement or disagreement, coincidence or want of coincidence, between that last step or the conclusion, and the conditions involved in the propositions at the commencement of the series ;-and therefore, demonstrative certainty is in effect the same as the certainty of intuition. §. 229. Of the use of diagrams in demonstrations. Mr. Locke has advanced the opinion, that moral subjects are no less susceptible of demonstration, than mathematical. However this may be, we are certainly more frequently required to practice this species of reasoning in the mathematicks, than any where else; and in conducting the process, nothing is more common, than to make use of various kinds of figures or diagrams.The proper use of diagrams, of a square, circle, triangle, or other figure, which we delineate before us, is to assist the mind in keeping its ideas distinct, and to help in comparing them together with readiness and correctness. They are a sort of auxiliaries, brought in to the help of our intellectual infirmities, but are not absolutely necessary; since demonstrative reasoning, wherever it may be found, resembles any other kind of reasoning in this most important respect, viz. in being a comparison of our ideas. In proof that artificial diagrams are only auxiliaries, and not essentially necessary in demonstrations, it may be remarked, that they are necessarily all of them imperfect, owing to the imperfection of our senses. Our reasonings, therefore, and our conclusions will not apply to the figures before us, but merely to an imagined perfect figure. And a verbal statement of the properties of this imagined perfect figure is what we understand by a DEFINITION, the use of which in this kind of reasoning in particular has already been mentioned. §. 230. Influence of demonstrative reasoning on the mental character. A considerable skill in demonstrative reasoning is on a number of accounts desirable, although it cannot be denied, that very frequent practice and great readiness in it §. 368. Of fear. FEAR is an emotion of pain, caused by an object, which we anticipate will be injurious to us, attended with a desire of avoiding such object or its injurious effects.Here, as in other cases, there is a simple emotion, that of pain; and, in respect to this particular emotion, it does not differ from certain other of the passions. But it dif fers in some other things, viz. in always having the object or cause of the painful emotion in the future, and also in the particular form of the attendant desire.-Having made desire a part of the passion of fear, and also of other complex states of the mind, which involve emotions, of the passions of love, hatred, sympathy, anger, gratitude, and pride, it may have occurred, ere this, to ask, What is meant by that term? -In answer, it must be acknowledged, that it is difficult to give a satisfactory explanation of it. We can, indeed, say, that desire is preceded by the idea of something, which is the object of it; and also that it is preceded by an emotion of pain or of delight. But on the examination of one's own feelings, it will be readily perceived, that both of these are different from the state of mind in question. "With the mere feelings [of desire,] says Brown, I may suppose you to be fully acquainted; and any attempt to define them, as feelings, must involve the use of some word exactly synonymous, or will convey no meaning whatever." But to return to the passion under consideration. The strength or intensity of fear will be in proportion to the apprehended evil. There is a difference of original susceptibility of this passion in different persons; and the amount of apprehended evil will, consequently, vary with the quickness of such susceptibility. But whatever causes may increase or diminish the opinion of the degree of evil, which threatens, there will be a correspondence between the opinion, which is formed of it, and the fearful passion. When this passion is extreme, it prevents the due exercise of the moral susceptibility, and interrupts correct judgment of any kind whatever. It is a feeling of great power, and one, which will not bear to be trifled with. §. 369. Of hope. Such is the extensive influence of that state of the mind, to which we give the name of HOPE, that it deserves a separate consideration, although it cannot be reckoned, as a distinct passion. It is truly nothing more than a modification or form of desire. We desire a thing;if there be but little probability of obtaining it, it is what is termed a wish; when there is an increase of probability, the wish becomes hope; and when the probability is still further increased, the hope becomes expectation, and expectation itself may be distinguished as weak or strong.Consequently, HOPE may be predicated of every thing of whatever kind, where there is desire, whether it be a desire of good or of evil, for ourselves, or for others. When the desire is attended with so little probability as to be a mere wish, it is languid; when there is hope, it assumes a more vivid and enlivening aspect. We, accordingly, speak of 'gay' hope, of 'cheering,' or 'bright' hope, and regard it as spreading a sort of rapturous light over the distant objects, which it contemplates. "With thee, sweet Hope! resides the heavenly light, "That pours remotest rapture on the sight; "Thine is the charm of life's bewildered way, "That calls each slumbering passion into play. The influence of that vividness and pleasure of desire, which we term hope, is very great. It is feit, more or less, in all the duties and situations of life. The school-boy is encouraged in his tasks by some hope of reward; and when grown up to manhood, he cheers himself after a thousand disappointments, with some good in prospect. ľ The poor peasant, who laboriously cultivates his few sterile acres, sees them in his anticipation, rich, and blooming, and prodigal of wealth. It proffers its aid in the chambers of the sick and suffering; and the victim of oppressive tyranny, the captive in the dungeon, is encouraged to summon up the fortitude, necessary to prolong his existence, by the hope, however poorly founded, of future deliverance. §. 370. Of jealousy. JEALOUSY is a painful emotion, caused by some object of love, and attended with a desire of evil towards that object. The circumstance, which characterizes this passion and constitutes its peculiar trait, is, that all its bitterness and hostility are inflicted on some one, whom the jealous person loves. The feeling of suspicious rivalship, which often exists between candidates for fame and power, is sometimes called jealousy on account of its analogy to this passion.―――There are various degrees of jealousy from the forms of mere distrust and of watchful suspicion to its highest paroxysms. In general the strength of the passion will be found to be in proportion to the value, which is attached to the object of it; and is perhaps more frequently found in persons, who have a large share of pride, than in others. Such, in consequence of the habitual belief of their own superiority, are likely to notice many trifling inadvertencies, and to treasure them up as proof of intended negleet, which would not have been observed by others, and certainly were exempt from any evil intention. The person under the influence of this passion is incapable of forming a correct judgment of the conduct of the individual, who is the object of it; he observes every thing, and gives it the worst interpretation; and circumstances, which, in another state of the mind, would have been tokens of innocence, are converted into proof of guilt. Although poetry, it is no fiction; Hence it it justly said to be the monster, that 'makes the meat it feeds on.'--This passion is at times exceeding |