We shall close this the very important remarks on evidence, given by Hartley, in proposition 87 ; referring to the original those readers, who wish to see how he illustrates or proves them by the employment of simple mathematical expressions, and who are disposed to en ter into his important observations re specting the ascertainment of truth and the advancement of km;wledge.
1. If the evidences for any proposition, fact, &c. be dependent on each other, so that the first is required to support the second, the second the third, and so on ; that is, if a failure of any one of the eviden, ces renders all the rest of no value, the separate probability ()reach evidence must be very great in order to make the pro._ position credible ; and this holds so much the more, as the dependent evidences are more numerous.
2. If the evidences for any proposition, fact, &c. be independent on each other ; that is, ifthey be not necessary to support each other, but concur, and can each of them, when established upon its own pro per evidences, be applied directly to esta blish the proposition, fact, Etc. in question, the deficiency in the probability of each must be very great, in order to render the proposition perceptibly doubtful, and this holds so much the more, as the evidences are more numerous.
3. The resulting probability may be sufficiently strong in dependent evidences, and of little value in independent ones, according as the separate probability of each evidence is greater or less. ThstS the principal facts of ancient history are not less probable practically now, than ten or fifteen centuries ago; nor less so then than in the times immediately suc ceeding, because the diminution of evi dence in each century is imperceptible.
And for the same reason a large number of weak arguments prove little.
4. It appears likewise, that the inequali ty of the separate evidences does not pro duce much alteration in these remarks. In like manner, if the number of evidences, dependent or independent, be great, we may make great" concessions as to the va lue of each. Again, a strong evidence in dependent ones can add nothing, but must weaken a little ; and after a point is well settled by a number of independent all that come afterwards are in one sense useless, because they do no more than remove the imperceptible remaining deficiency ; on the other hand, however, as evidence produces different effects on different minds; it is of great moment in all points of general importance, to have as many satisfactory independent eviden ces as possible brought into view ; that if one fail in its effects, from peculiar cir cumstances, another may supply its place. And it will be of great use to pursue these and such like deductions, both mathe matically, and by applying them to pro per instances selected from the sciences, and from common life, in order to remove certain prejudices, which the use ofgeneral terms and ways of speaking, with the va rious associations with them, is apt to in troduce and fix upon the mind. It can not but assist us, in the art of reasoning, thus to analyze, recompose, and ascer tain our evidences.