144 THE GRAMMAR OF SCIENCE 



it an equal number of black and white balls. The prob- 

 ability of a random drawing resulting in a white ball 

 will now be ^, and this will at each drawing, provided the 

 balls be returned to the bag, be the probability in favour 

 of a white ball. Now let us look upon the world of per- 

 ceptions as a bag containing white and black balls, a 

 white ball representing a routine-order, and a black ball 

 an anomy or breach of routine. Then, since we see no 

 reason why perceptions should have a routine or should 

 not have a routine, may we not assert that each are 

 equally likely, or that there will be the same number of 

 black and white balls in our bag ? If this be so, then 

 obviously the odds are seven to one against a routine- 

 order occurring even three times without a single anomy, 

 and are overwhelming against no breach of routine 

 occurring at all. Yet the only supposition that we 

 appear to have made is this : that, knowing nothing of 

 nature, routine and anomy are to be considered as equally 

 likely to occur. Now we were not really justified in 

 making even this assumption, for it involves a knowledge 

 that we do not possess regarding nature. We use our 

 experience of the constitution and action of coins in 

 general to assert that heads and tails are equally probable, 

 but we have no right to assert before experience that, as 

 we know nothing of nature, routine and breach of routine 

 are equally probable. In our ignorance we ought to con- 

 sider before experience that nature may consist of all 

 routines, all anomies, or a mixture of the two in any 

 proportion whatever, and that all such are equally prob- 

 able. Which of these constitutions after experience is 

 the most probable must clearly depend on what that ex- 

 perience has been like. 



To return to the case of the coin, we must suppose all 

 experience of the action of coins withdrawn from us ; it 

 must be unknown to us, whether coins are so constituted 

 as to have a head on both faces, a tail on both faces, or a 

 head on one and a tail on the other. The probability of 

 any one of these three equally probable constitutions 

 would before experience be -J. Now suppose we had the 



