Volume 1

Observations on man, his frame, his duty, and his expectations. In two parts / By David Hartley.

  • Hartley, David, 1705-1757.
Date:
1749
Catalogue details

Licence: Public Domain Mark

Credit: Observations on man, his frame, his duty, and his expectations. In two parts / By David Hartley. Source: Wellcome Collection.

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367/552 (page 335)
33 f PROP. 87. To deduce Rules for the Afceriainment of Truth, and Advancement of Knowlege, from the ma¬ thematical Methods of confidering Quantity. T^HI S is done in the Dodrine of Chances, with A refped to the Events there confidered. And though we feldom have fuch precife Data in mixed Sciences as are there affumed, yet there are two Re¬ marks of very general Ufe and Application, deducibfe from the Dodrine of Chances. Thus, Firft, If the Evidences brought for any Pro¬ portion, Fad, &c. be dependent on each other, fo that the Firfl is required to fupport the fecond, the fecond to fupport the third, &c. i. e. if a Failure of any one of the Evidences renders all the reft of no Value, the leparate Probability of each Evidence muft be very great, in order to make the Propofition cre¬ dible ; and this holds fo much the more, as the de¬ pendent Evidences are more numerous. For In- ftance, If the Value of each Evidence be f and the a Number of Evidences be n, then will the refulting Probability be —. I here fuppofe abfolute Certainty to be denoted by 1; and confequently, that a can ne¬ ver be lefs than 1. Now it is evident, that 1 de- an creafes with every Increafe both of a and n. Secondly, If the Evidences brought for any Pro¬ pofition, Fa (ft, &c. be independent on each other, i. e> if they be not neceffary to fupport each other, but concur, and can, each of them, when eftablifhed upon its own proper Evidences, be applied diredly to efta- blifh the Propofition, Fad, &V. in Queftion, the De¬ ficiency in the Probability of each muft be very great.