212 THE PRINCIPLES OF SCIENCE. [CHAP. 



with which logic and the theory of probability have little 

 concern. From the general body of science in our posses- 

 sion, 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 | ; it was as likely that 

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

 of any other star. This was the assumption which Michell 

 made in his admirable speculations. 1 It might seem, 

 indeed, that as every proposition expresses an agreement, 

 and the agreements or resemblances between phenomena 

 are infinitely fewer than the differences (p. 44), every pro- 

 position should in the absence of other information be 

 infinitely improbable. But in our logical system every 

 term may be indifferently positive or negative, so that we 

 express under the same form as many differences as agree- 

 ments. It is impossible therefore that we should have 

 any reason to disbelieve rather than to believe a statement 

 about things of which we know nothing. We can hardly 

 indeed invent a proposition concerning the truth of which 

 we are absolutely ignorant, except when we are entirely 

 ignorant of the terms used. If I ask the reader to assign 

 the odds that a " Platythliptic Coefficient is positive " he 

 will hardly see his way to doing so, unless he regard them 

 as even. 



The assumption that complete doubt is properly ex- 

 pressed by | has been called in question by Bishop Terrot, 2 

 who proposes instead the indefinite symbol ; and he 

 considers that "the a priori probability derived from 

 absolute ignorance has no effect upon the force of a 

 subsequently admitted probability." But if we grant that 

 the probability may have any value between o and I, and 

 that every separate value is equally likely, then n and 

 i n are equally likely, and the average is always |. Or 

 we may take p . dp to express the probability that our 



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

 * Transactions of the Edinburgh Philosophical Society, vol. xxi. 

 P- 375- 



