CHAPTER X. 



THEORY OF PROBABILITY. 



% THE subject upon which we now enter must not be 

 regarded as an isolated and curious branch of speculation. 

 It is the necessary basis of nearly all the judgments 

 and decisions we make in the prosecution of science, or 

 the conduct of ordinary affairs. As Butler truly said, 

 'Probability is the very guide of life.' Had the science of 

 numbers been developed for no other purposes, it must 

 have been developed for the calculation of probabilities. 

 All our inferences concerning the future are merely pro- 

 bable, and a due appreciation of the degree of probability 

 depends entirely upon a due comprehension of the prin- 

 ciples of the subject. I conceive that it is impossible 

 even to expound the principles and methods of induction 

 as applied to natural phenomena, in a sound manner, with- 

 out resting them upon the theory of probability. Perfect 

 knowledge alone can give certainty, and in nature perfect 

 knowledge would be infinite knowledge, which is clearly 

 beyond our capacities. We have, therefore, to content our- 

 selves with partial knowledge knowledge mingled witli 

 ignorance, producing doubt. 



Almost the greatest difficulty in this subject consists in 

 acquiring a precise notion of the matter treated. What 

 is it that we number, and measure, and calculate in the 

 theory of probabilities \ Is it belief, or opinion, or doubt, 

 or knowledge, or chance, or necessity, or want of art ? 



