242 THE PRINCIPLES OF SCIENCE. 



or to the supposed laws of nature, and every reasoner may 

 be assumed to be dealing plainly, and putting forward the 

 whole force of evidence which he possesses in its favour. 

 If he brings but one argument, and its probability a is 

 small, then in the formula i (i a)(i c) both a and c 

 are small, and the whole expression has but little value. 

 The whole effect of an argument thus turns upon the 

 question whether other arguments remain so that we can 

 introduce other factors (i 6), (i c), &c., into the above 

 expression. In a court of justice, in a publication having 

 an express purpose, and in many other cases, it is doubtless 

 right to assume that the whole evidence considered to 

 have any value as regards the conclusion asserted, is 

 put forward. 



To assign the antecedent probability of any proposi 

 tion, may be a matter of great difficulty or impos 

 sibility, and one with which logic and the theory of pro 

 bability has little concern. From the general body of 

 science or evidence in our possession, we must in each 

 case make the best judgment we can. But in the absence 

 of all knowledge the probability should be considered = ^, 

 for if we make it less than this we incline to believe it 

 false rather than true. Thus before we possessed any 

 means of estimating the magnitudes of the fixed stars, the 

 statement that Sirius was greater than the sun had 

 a probability of exactly ^ ; for it was as likely that it 

 would be greater as that it would be smaller ; and so of 

 any other star. This indeed was the assumption which 

 Michell made in his admirable speculations. It might 

 seem indeed that as every proposition expresses an agree 

 ment, and the agreements or resemblances between phe 

 nomena are infinitely fewer than the differences (p. 52), 

 eveiy proposition should in the absence of other informa 

 tion be infinitely improbable, or c o. But in our logical 



Philosophical Transactions (1767). Abridg. vol. xii. p. 435. 



