248 THE PRINCIPLES OF SCIENCE. 



data required for the estimation of probabilities are too 

 complicated and difficult to obtain. But such failures in 

 no way diminish the truth and beauty of the theory itself; 

 for in reality there is no branch of science in which, as we 

 shaU afterwards fully consider, our symbols can cope with 

 the complexity of Nature. As the late Professor Donkin 

 excellently said, 



' I do not see on what ground it can be doubted that 

 every definite state of belief concerning a proposed 

 hypothesis, is in itself capable of being represented 

 by a numerical expression, however difficult or im- 

 practicable it may be to ascertain its actual value. It 

 would be very difficult to estimate in numbers the vis 

 viva of all the particles of a human body at any instant ; 

 but no one doubts that it is capable of numerical ex- 

 pression/ 11 



The difficulty, in short, is merely relative to our know- 

 ledge and skill, and is not absolute or inherent in the 

 subject. We must distinguish between what is theo- 

 retically conceivable and what is practicable with our 

 present mental resources. Provided that our aspirations 

 are pointed in a right direction, we must not allow them 

 to be damped by the consideration that they pass beyond 

 what can now be turned to immediate use. In spite of 

 its immense difficulties of application, and the aspersions 

 which have been mistakenly cast upon it, the theory of 

 probabilities, I repeat, is the noblest, as it will in course 

 of time prove, perhaps the most fruitful branch of mathe- 

 matical science. It is the very guide of life, and hardly 

 can we take a step or make a decision of any kind without 

 correctly or incorrectly making an estimation of proba- 

 bilities. In the next chapter we proceed to consider how 

 the whole cogency of inductive reasoning, as applied to 



h ' Philosophical Magazine,' 4th Series, vol. i. p. 354. 



