THE THEORY OF PROBABILITY. 243 



system every term may be indifferently positive or nega- 

 tive, so that we express under the form A is B or A = AB 

 as many differences as agreements. It is impossible 

 therefore that we should have any reason to disbelieve 

 rather than to believe it. We can hardly indeed invent 

 a proposition concerning the truth of which we are 

 absolutely ignorant, except when we are absolutely ignorant 

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

 odds that a ' Platythliptic Coefficient is positive ' P 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,^ 

 who proposes instead the indefinite symbol ; and he 

 considers that 'the d priori probability derived from 

 absolute ignorance has no effect upon the force of a 

 subsequently admitted probability.' But a writer of far 

 greater power, the late Professor Donkin, has strongly 

 defended the commonly adopted expression of complete 

 doubt. 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 estimate concerning 

 any proposition should lie between p and p + dp. The 

 complete probability of the proposition is then the in- 

 tegral taken between the limits i and o, or again ^ r . 



Difficulties of the Theory. 



The doctrine of probability, though undoubtedly true, 

 requires very careful application. Not only is it a branch 



P 'Philosophical Transactions,' vol. 146. part i. p, 273. 



q ' Transactions of the Edinburgh Philosophical Society,' vol. xxi. p. 375, 



r 'Philosophical Magazine/ 4th Series, vol. i. p. 361. 



B 2 



