CAUSE AND EFFECT— PROBABILITY 141 



of perceptions are things which have hitherto repeated 

 themselves without fail. Thus there is past experience 

 of repetition in the class, as well as in the individual, 

 strengthening the probability of a future recurrence of the 

 same sequence. The probability that the sun will rise 

 to-morrow is not only conditioned by men's past ex- 

 perience of the sun's motion, but by their past experience 

 of the uniform order in natural phenomena. There is no 

 need to repeat a cautiously conducted experiment a great 

 number of times to prove — that is, to establish an over- 

 whelming probability in favour of — a certain sequence of 

 perceptions. The overwhelming probability drawn from 

 past experience in favour of all sequences repeating 

 themselves at once embraces the new sequence. Suppose 

 the solidification of hydrogen to have been once accom- 

 plished by an experimenter of known probity and caution, 

 and with a method in which criticism fails to detect any 

 flaw. What is the probability that on repetition of the 

 same process the solidification of hydrogen will follow? 

 Now Laplace has asserted that the probability that an 

 ■event which has occurred / times and has not hitherto 

 failed will occur again, is represented by the fraction ^• 

 Hence in the case of hydrogen the probability of repeti- 

 tion would only be |, or, as we popularly say, the odds 

 would be two to one in its favour. On the other hand, if 

 the sun has risen without fail a million times, the odds in 

 favour of its rising to-morrow would be 1,000,001 to i. 

 It is clear that on this hypothesis there would be practical 

 •certainty with regard to the rising of the sun being 

 repeated, but only some likelihood with regard to the 

 solidification of hydrogen being repeated. The numbers, 

 in fact, do not in the least represent the degrees of 

 belief of the scientist regarding the repetition of the two 

 phenomena. We ought rather to put the problem in 

 this manner : p different sequences of perception have 

 been found to follow the same routine, however often 

 repeated, and none have been found to fail, what is the 

 probability that the (/-f- i)th sequence of perceptions will 

 have a routine ? Laplace's theorem shows us that the 



