142 THE GRAMMAR OF SCIENCE 



odds are (/+ i) to one in favour of the new sequence 

 having a routine. In other words, since/ represents here 

 the infinite variety of phenomena in which men's past 

 experience has shown that the same causes are on repeti- 

 tion followed by the same effect, there are overwhelming 

 odds that any newly -observed phenomenon may be 

 classified under this law of causation.^ So great and, 

 considering the odds, reasonably great is our belief in 

 this law of causation applying to new phenomena, that 

 when a sequence of perceptions does not appear to repeat 

 itself, we assert with the utmost confidence that the same 

 causes have not been present in the original and in the 

 repeated sequence. 



S 14. — Probability as to Breaches in the Routine 

 of Perceptions 



Laplace has even enabled us to take account of 

 possible " miracles," anomies, or breaches of routine in 

 the sequence of perceptions. He tells us that if an 

 event has happened / times and failed q times, then the 

 probability that it will happen the next time is ^"'"' , or 



the odds in favour of its happening are/-|-i to^+i. 

 Now if we are as generous as we possibly can be to the 

 reporters of the miraculous, we can hardly assert that a 

 well-authenticated breach of the routine of perceptions 

 has happened once in past experience for every looo 

 million cases of routine. In other words, we must take 

 p equal to 1000 million times q, or the odds against a 

 miracle happening in the next sequence of perceptions 

 would be about lOOO millions to one. It is clear from 

 this that any belief that the miraculous will occur in our 

 immediate experience cannot possibly form a factor in the 

 conduct of practical life. Indeed the odds against a 

 miracle occurring are so great, the percentage of per- 

 manently diseased or temporarily disordered perceptive 



1 A somewhat greater probability in favour of a new sequence which has 

 repeated itself r times repeating itself on the (^+i)th trial will be given 

 below. 



