viii Preface to the First Edition. 



make it their special occupation, but its general principles 

 are sure to be cramped if it is not exposed occasionally to 

 the free criticism of those whose main culture has been of 

 a more general character. Probability has been very much 

 abandoned to mathematicians, who as mathematicians have 

 generally been unwilling to treat it thoroughly. They have 

 worked out its results, it is true, with wonderful acuteness, 

 and the greatest ingenuity has been shown in solving various 

 problems that arose, and deducing subordinate rules. And 

 this was all that they could in fairness be expected to do. 

 Any subject which has been discussed by such men as 

 Laplace and Poisson, and on which they have exhausted all 

 their powers of analysis, could not fail to be profoundly 

 treated, so far as it fell within their province. But from this 

 province the real principles of the science have generally 

 been excluded, or so meagrely discussed that they had better 

 have been omitted altogether. Treating the subject as ma 

 thematicians such writers have naturally taken it up at the 

 point where their mathematics would best come into play, 

 and that of course has not been at the foundations. In the 

 works of most writers upon the subject we should search in 

 vain for anything like a critical discussion of the funda 

 mental principles upon which its rules rest, the class of 

 enquiries to which it is most properly applicable, or the 

 relation it bears to Logic and the general rules of inductive 

 evidence. 



This want of precision as to ultimate principles is per 

 fectly compatible here, as it is in the departments of Morals 

 and Politics, with a general agreement on processes and 

 results. But it is, to say the least, unphilosophical, and 

 denotes a state of things in which positive error is always 

 liable to arise whenever the process of controversy forces us 

 to appeal to the foundations of the science. 



