[ io8 J 



fol'owins manner i if the firft witnefs gives — — of certainty, 

 ^ a -r c 



and there is wanting of it — — , the fecond atteftcr will add 

 ° a -\- c 



— ' c 



of that ; and confequently leave wanting; only 



a-^c a-Vc ^ " a + c 



2 



of that -f- : — ^^ J . And in like manner, the third attefter 



a^-c a + c^ 



a c^ , , . . c^ 



adds his of that =^,, and leaves wantmg only ^r==, &c. 



a-irC a + c a-\r c 



Hence, he obferves, it follows, that if a fmgle witnefs (hould 

 be only f© far credible as to give me the half of full certainty; a 

 fecond of the fame credibility, joined with the firfl, would give 

 me A*S a third l-'h,, &c. which appears to be falfe ; for we have 

 (hewn above, that no number of fuch reporters could produce an 

 affurance greater than that of an even chance, for the truth or 

 falfhood of the fa£l. 



The fallacy of his argument lies in this, that he fuppofes all the 

 individual concurrent witneffcs to produce unequal degrees of 

 affurance, which is evidently a falfe polition ; fince they are all 

 of equal credibility and equally concurrent, and therefore contri- 

 bute equally in producing our affurance. 



Dr. Waring, whofe folution is effentially the fame with Hallcy's, 

 fays, if there be two different arguments (or witneffcs) entirely 

 independent of each other, in fupport of a fad, whofc probabilities 



let 



