we reason about the figure compofed of fuch lines, it is fufficient that these figures have fome appearance of regularity lefs or more is of no importance; because our reafoning is not founded upon them, but upon our ideas. Thus, to demonstrate that the three angles of a triangle are equal to two right angles, a triangle is drawn upon paper, in order to keep the mind steady to its object, and to prevent wandering. After tracing the steps that lead to a conclufion, we are fatisfied that the propofition is true; being confcious that the reasoning is built upon the ideal figure, not upon that which is is drawn upon the paper. And being alfo confcious

that the enquiry is carried on independent of any particular length of the fides, we are fatisfied of the univerfality of the propofition, and of its being applicable to all triangles whatever.

Numbers confidered by themfelves, abftractedly from things, make the fubject of arithmetic. And with refpect both to mathematical and arithmetical reasonings, which frequently confift of many steps, the process is fhortened by the invention of figns, which, by a fingle dafh of the pen, exprefs clearly what would require many words. By that means, a very long chain of reafoning is expreffed by a few fymbols; a method that contributes greatly to readinefs of comprehenfion. If in fuch reafonings words were neceffary, the mind, embarraffed with their multiplicity, would have great difficulty to follow any long chain of reafoning. A line drawn upon paper reprefents an ideal line, and a few fimple characters reprefent the abstract ideas of number.

Arithmetical reafoning, like mathematical, depends entirely upon the relation of equality, which can be afcertained with the greateft certainty among many ideas. Hence, reafonings upon fuch ideas afford the highest degree of conviction. I do not fay, however, that this is always the cafe; for a man who is confcious of his own fallibility, is feldom without fome degree of diffidence, where the reafoning confifts of many fteps. And though on a review no error is difcovered, yet he is confcious there may be errors, though they have efcaped him.

As

As to the other kind of demonstrative reafoning, founded on fome propofition of which we are intuitively certain, I justly call it demonstrative, because it affords the fame conviction that arifes from mathematical reafoning. In both, the means of conviction are the fame, viz. a clear perception of the relation between two ideas; and there are many relations of which we have ideas no less clear than of equality; witness fubftance and quality, the whole and its parts, cause and effect, and many others. From the intuitive propofition, for example, That nothing which begins to exift can exift without a caufe, I can conclude, that fome one being must have existed from all eternity, with no lefs certainty, than that the three angles of a triangle are equal to two right angles.

What falls next in order, is that inferior kind of knowledge which is termed opinion; and which, like knowledge properly fo termed, is founded in fome inftances upon intuition, and in fome upon reafoning.But it differs from knowledge in the following particular, that it produces different degrees of conviction, fometimes approaching to certainty, and fometimes finking toward the verge of improbability. The conftancy and uniformity of natural operations is a fit fubject for illuftrating that difference. The future fucceffive changes of day and night, of winter and fummer, and of other fucceffions which have hitherto been regular and uniform, fall under intuitive knowledge, because of these we have the highest conviction. As the conviction is inferior of fucceffions that hitherto have been varied in any degree, these fall under intuitive opinión. We expect fummer after winter with the utmost confidence; but we have not the faine confidence in expecting a hot fummer or a cold winter. And yet the probability approaches much nearer to certainty than the intuitive opinion we have, that the operations of nature are extremely fimple, a propofition that is very. little relied on.

As to opinion founded on reasoning, it is obvious, that the conviction produced by the reasoning, can never rise above what is produced by the intuitive propo→ fition upon which the reafoning is founded. And that

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it may be weaker, will appear from confidering, that even where the fundamental propofition is certain, it may lead to the conclufive opinion by intermediate propofitions, that are probable only, not certain. In a word, it holds in general with respect to every fort of reafoning, that the conclufive propofition can never rife higher in point of conviction, than the very loweft of the intuitive propofitions employed as steps in the reafoning.

The perception we have of the contingency of future events, opens a wide field to our reafoning about probabilities. That perception involves more or lefs doubt according to its fubject. In fome instances, the event is perceived to be extremely doubtful: in others it is perceived to be lefs doubtful. It appears altogether doubtful, in throwing a dye, which of the fix fides will turn up; and for that reason, we cannot juftly conclude for one rather than another. If one only of the fix fides be marked with a figure, we conclude, that a blank will turn up; and five to one is an equal wager that fuch will be the effect. In judging of the future behaviour of a man who has hitherto been governed by intereft, we may conclude with a probability approaching to certainty, that intereft will continue to prevail.

Belief comes laft in order, which, as defined above, is knowledge of the truth of facts that falls below certainty, and involves in its nature fome degree of doubt. It is alfo of two kinds one founded upon ; intuition, and one upon reasoning. Thus, knowledge, opinion, belief, are all of them equally diftinguishable into intuitive and difcurfive. Of intuitive belief, I difcover three different fources or caufes. First, A prefent object. Secondly, An object formerly prefent. Thirdly, The teftimony of others.

To have a clear conception of the first cause, it must be obferved, that among the fimple perceptions that compofe the complex perception of a present object, a perception of real and present existence is one. This perception rifes commonly to certainty; in which cafe it is a branch of knowledge properly fo terined; and is handled as fuch above. But this perception falls

below

below certainty in fome inftances ; as when an object, feen at a great diftance, or in a fog, is perceived to be a horfe, but fo indistinctly as to make it a probability only. The perception in fuch a cafe is termed belief. Both perceptions are fundamentally of the fame nature; being funple perceptions of real exiftence. They differ only in point of accuracy: the perception of reality that inakes a branch of knowledge, is fo clear and distinct as to exclude all doubt or hesitation: the perception of reality that occafions belief, being lefs clear and diftinct, makes not the existence of the object certain to us, but only probable.

With refpect to the fecond caufe; the exiftence of an abfent object, formerly feen, ainounts not to a cer tainty; and therefore is the fubject of belief only, not of knowledge. Things are in a continual flux from production to diffolution; and our fenfes are accommodated to that variable scene: a present object admits no doubt of its existence; but after it is removed, its existence becomes lefs certain, and in time finks down to a flight degree of probability.

Human teftimony, the third caufe, produces belief, more or less strong, according to circumstances. In general, nature leads us to rely upon the veracity of each other; and commonly the degree of reliance is proportioned to the degree of veracity. Sometimes be lief approaches to certainty, as when it is founded on the evidence of perfons above all exception. Sometimes it finks to the loweft degree of probability, as when a fact is told by one who has no great reputation for truth. The nature of the fact, common or uncommon, has likewise an influence: an ordinary incident gains credit upon very flight evidence; but it requires the strongest evidence to overcome the improbability of an event that deviates from the ordinary courfe of nature. At the fame time, it must be observed, that belief is not always founded upon rational principles.There are biaffes and weakneffes in human nature that fometimes disturb the operation, and produce belief without fufficient or proper evidence: we are difpofed to believe on every flight evidence, an interesting event, however rare or fingular, that alarms and agitates the

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mind; because the mind, in agitation is remarkably fufceptible of impreffions: for which reafon, ftories of ghofts and apparitions pass current with the vulgar. Eloquence alfo has great power over the mind; and, by making deep impreffions, enforces the belief of facts upon evidence that would not be regarded in a cool

moment.

The dependence that our perception of real existence, and confequently belief, hath upon oral evidence, enlivens focial intercourfe, and promotes fociety. But the perception of real existence has a still more extenfive influence; for from that perception is derived a great part of the entertainment we find in hiftory, and in hiftorical fables (a). At the fame time, a perception that may be raised by fiction as well as by truth, would often miflead, were we abandoned to its impulfe but the God of nature hath provided a remedy for that evil, by erecting within the mind a tribunal, to which there lies an appeal from the rafh impreflions of fenfe. When the delufion of eloquence or of dread fubfides, the perplexed mind is uncertain what to believe.

A regular procefs commences, counsel is heard, evidence produced, and a final judgment pronounced, fometimes confirming, fometimes varying, the belief 'impreffed upon us by the lively perception of reality. Thus, by a wife appointment of nature, intuitive belief is fubjected to rational difcuffion: when confirmed by reafon, it turns more vigorous and authoritative : when contradicted by reafon, it difappears among fenfible people. In fome inftances, it is too headftrong for reafon; as in the cafe of hobgoblins and apparitions, which pafs current among the vulgar in fpite of rea

fon.

We proceed to the other kind of belief, viz. that which is founded on reafoning, to which, when intuition fails us, we must have recourfe for ascertaining certain facts. Thus, from known effects, we infer the existence of unknown caufes. That an effect must have a caufe, is an intuitive propofition; but to afcertain what particular thing is the cause, requires commonly a procefs

(a) Elements of Criticism, ch. 2. part 1. § 7.