THE THEORY OF PROBABILITY. 227 



well said that the quantity of belief is ' always relative 

 to a particular state of knowledge or ignorance ; but 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.' c Dr. Boole, too, 

 seemed to entertain a like view, when he described the 

 theory as engaged with ' the equal distribution of ignor- 

 ance,' d 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 as professing to evolve 

 knowledge out of ignorance ; but as Professor Donkin has 

 admirably remarked, it is really ' a method of avoiding 

 the erection of belief upon ignorance/ e It defines rational 

 expectation by measuring the comparative amounts of 

 knowledge and ignorance, and teaches us to regulate our 

 action with regard to future events in a way which will, 

 in the long run, lead to the least amount of disappointment 

 and injury. It is, as Laplace as happily expressed it, good 

 sense reduced to calculation. 



This theory appears to me the noblest creation of 

 human intellect, and it passes my conception how two 

 men possessing such high intelligence as Auguste Comte 

 and J. S. Mill, could have been found depreciating it, 

 or even vainly attempting to question its validity. To 



c 'Philosophical Magazine,' 4th Series, vol. i. p. 355. 



d ' Transactions of the Royal Society of Edinburgh,' vol. xxi. part iv. 



e 'Philosophical Magazine,' 4th Series, vol i. p. 355. 



