CAUSE AND EFFECT— PROBABILITY 147 



pressed partly in earlier chapters of this work, partly in 

 the following chapter on Space and Time. Nature, we 

 have seen, is a construct of the human mind (pp. 41, 

 1 01-6, 107); time and space are not inherent in an 

 outside world, but are modes of discriminating" groups of 

 sense-impressions (pp. 154, 182). Thus "nature" is 

 essentially conditioned by our perceptive faculty, and 

 " change " cannot be thought of as apart from ourselves. 

 That " nature " is identical " before and after experience " 

 will be admitted, as soon as it is recognised as probable 

 that time and change relate to perception, and not to the 

 " beyond " of sense-impressions. The sameness of the 

 perceptive faculty is very likely the key to the sameness 

 of the modes of perception. The conditions for each 

 trial (as in throwing a die or in drawing from a bag) 

 remaining the same, lie according to this view in the 

 identity of the perceptive faculty. 



^ 16. — Nature of Laplace's Investigation 



We are now in a position to return to our bag of 

 white and black balls, but we can no longer suppose an 

 equal number of both kinds, or that routine and breach of 

 routine are equally probable. We must assume our 

 " nature bag " to have every possible constitution or 

 every possible ratio of black to white balls to be equally 

 likely ; to do this we suppose an infinitely great number 

 of balls in all. We may then calculate the probability 

 that with each of these constitutions the observed result, 

 say p white balls and q black balls (or, / cases of routine, 

 and q anomies) would arise in/-f-^ drawings.^ This will 

 determine, by Laplace's principle, the probability that 

 each hypothetical constitution is the real constitution of 

 the bag. Let these probabilities be represented by the 

 letters P^, Po, P3 . . . etc. We may then determine the 

 probabilities on each of these constitutions that a white 

 ball will be drawn in the (/-1-^-f i)th drawing. If these 



1 The reader may suppose the ball returned to the bag after each 

 drawin". 



