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proof. This, for order's fake, I have diftri. buted into three classes, the truths of pure intelleftion, of consciousness, and of common sense. The first may be denominated metaphysical, the second physical, the third moral ; all of them natural, original, and unaccountable.

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SECTION 11.

Of deductive evidence. PART I. Division of the subject into scientific and moral, with the principal distinctions :

between them.

" All rational or deductive evidence is derived from one or other of these two sources.; from the invariable properties or relations of general ideas; or from the actual, though perhaps, variable connexions, subfifting among things. The former we call demonstrative, the latter moral. Demonstration is built on pure intellection, and confifteth in an uninterrupted series of axioms. · That propositions formerly demonstrated are taken into the series, doth not in the least invalidate this account; inasmuch as these propofitions are all resolvable into axioms, and are admitted as links in the chain ;

not not because neceffary, but merely to ayoid the useless prolixity which frequent and tedious re. petitions of proofs formerly given would occa fion. Moral evidence is founded on the principles we have from consciousness and common sense, improved by experience; and as it proceeds on this general presumption or moral axiom, that the course of nature in time to come, will be similar to what it hath been hitherto, it decides, in regard to particulars, concerning the future from the past, and concerning things unknown, from things familiar to us. The first is solely conversant about number and extension, and about those other qualities which are measurable by these. Such are duration, velocity, and weight. With regard to such qualities as pleasure and pain, virtue and vice, wisdom and folly, beauty and deformity, though they ad. mit degrees, yet, as there is no standard or common measure, by which their differences and proportions can be ascertained and expressed in numbers, they can never become the subject of demonstrative reasoning. Here rhetoric, it must be acknowledged, hath little to do. Simplicity of diction, and precision in arrangement, whence results perspicuity, are, as was observed already*, • Chap. I. Part 1.

all

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all the requisites. The proper province of rhetoric is the second, or moral evidence; for to the second belong all decisions concerning fact, and things without us.

But that the nature of moral evidence may be better understood, it will not be amiss to re; · mark a few of the most eminent differences bę, tween this and the demonstrative.

Tạe first difference that occurs is in their fub jects. The subject of the one is, aş hath been observa ed, abstract independent truth, or the unchangeable and necessary relations of ideas; that of the other, the real, but often changeable and contingent connexions that subfift among things actually exifting. Abstract truths, as the properties of quan; tity, have no respect to time or to place, no dependence on the volition of any being, or on any cause whatever, but are eternally and immutably the fame. The very reyerse of all this generally obtains with regard to fact. In consequence of what has been now advanced, affertions opposite to truths of the former kind, are not only falsę, but absurd. They are not only not true, but it is impossible they should be true, whilst the meanings of the words (and consequently the ideas compared) remain the same. This dgth not hold com,

monly

monly in any other kind of evidence. Take, for instance, of the first kind, the following af. firmations, The cube of two is the half of fix. ! teen.' •The square of the hypotenuse is equal to ! the sum of the squares of the fides.' ? If equal

things be taken from equal things, the remainders • will be equal.' Contrary propofitions, as, : The ? cube of two is more than the half of fixteen.'"The 4 square ofthe hypotenufe is lessthanthesum of the ! squares of the sides.' • If equal things be taken

from equal things, the remainders will be un! equal,' are chargeable, not only with falfity, but with absurdity, being inconceivable and contradictory. Whereas, to these truths which we acquire by moral evidence, · Cæfar overcame

Pompey.' • The fun will rise to-morrow.' ! All men will die,' the opposite affertions, though untrue, are easily conceivable without changing, in the least, the import of the words, and therefore do not imply a contradiction,

The second difference I shall remark is, that moral evidence admits degrees, demonstration doth not. This is a plain consequence of the preceding difference. Essential or neceffary truth, the fole object of the latter, is incompatible with degree. And though actual truth, or matter of

fact, fact, be the ultimate aim of the former, likeli, hood alone, which is susceptible of degree, is usually the utmost attainment. Whatever is exhibited as demonstration, is either mere illusion, and so no evidence at all, or absolutely perfect. There is no medium. In moral reasoning we afcend from possibility, by an insensible gradation, to probability, and thence, in the same manner, to the summit of moral certainty. On this summit, or on any of the steps leading to it, the conclusion of the argument may reft. Hence the result of that is, by way of eminence, denominated science; and the evidence itself is termed scientific; the result of this is frequently (not always) intitled to no higher denomination than opinion. Now, in the mathematical sciencés, no mention is ever made of opinions.

The third difference is, that in the one there never can be any contrariety of proofs ; in the other, there not only may be, but almost always is. If one demonstration were ever capable of being refuted, it could be folely by another demonstration, this being the only sort of evidence adapted to the subject, and the only fort by which the former could be matched. But, to fuppose that contraries are demonstrable,

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