x.] THE THEORY OF PROBABILITY. 199 



bility we really mean or ought to mean degree of belief." 

 The late Professor Donkin expressed the meaning of 

 probability as " quantity of belief ; " but I have never felt 

 satisfied with such definitions of probability. The nature 

 of belief is not more clear to my mind than the notion 

 which it is used to define. But an all-sufficient objection 

 is, that the theory does not measure what the belief is, but 

 what it ought to be. Few minds think in close accordance 

 with the theory, and there are many cases of evidence in 

 which the belief existing is habitually different from what 

 it ought to be. Even if the state of belief in any mind 

 could be measured and expressed in figures, the results 

 would be worthless. The value of the theory consists in 

 correcting and guiding our belief, and rendering our states 

 of mind and consequent actions harmonious with our 

 knowledge of exterior conditions. 



This objection has been clearly perceived by some of 

 thos'e who still used quantity of belief as a definition of 

 probability. Thus De Morgan adds "Belief is but 

 another name for imperfect knowledge." Donkin has 

 well said that the quantity of belief is " always relative 

 to a particular state of knowledge or ignorance; bat it 

 must be observed that it is absolute in the sense of not 

 being relative to any individual mind; since, the same 

 information being presupposed, all minds ought to dis- 

 tribute their belief in the same way." l Boole seemed to 

 entertain a like view, when he described the theory as 

 engaged with "the equal distribution of ignorance;" 2 

 but we may just as well say that it is engaged with the 

 equal distribution of knowledge. 



I prefer to dispense altogether with this obscure word 

 belief, and to say that the theory of probability deals with 

 quantity of knowledge, an expression of which a precise 

 explanation and measure can presently be given. An 

 event is only probable when our knowledge of it is 

 diluted with ignorance, and exact calculation is needed 

 to discriminate how much we do and do not know. The 

 theory has been described by some writers as professing to 

 evolve knowledge out of ignorance ; but as Donkin admirably 

 remarked, it is really " a method of avoiding the erection 



1 Philosophical Magazine, 4th Series, vol. i. p. 355. 



* Transactions of the Royal Society of Edinburgh, vol. x*i. part 4, 



