146 THE GRAMMAR OF SCIENCE 



by the late Professor G. Boole.^ We may indeed reason- 

 ably question whether it is possible to draw knowledge 

 out of complete ignorance. But before we can agree 

 with Boole that Laplace's method is nugatory, we must 

 ask whether, after all, his principle is not based on know- 

 ledge, namely, on that derived from the experience that 

 in cases where we are ignorant, there in the long run all 

 constitutions will be found to be equally probable. 



A good example of this has been given by Professor 

 Edgeworth. Suppose we divide 143,678 by 7 and stop 

 at the fourth figure of the quotient, we have 2052 as the 

 result. Now we may be supposed ignorant of what the 

 next figure will turn out to be, and in our ignorance all 

 the digits from o to 9 are equally probable. Why ? 

 Because if we divided a very great quantity of numbers 

 of 6 figures by 7, stopping at the fourth digit in the 

 quotient, we should find that the number of times each of 

 the digits from o to 9 would occur in the fifth place 

 were practically equal. In other words, statistics would 

 Justify the " equal distribution of our ignorance," or 

 experience show us that in our ignorance all constitutions 

 were equally probable. This example may, perhaps, 

 suffice to show that there is an element of human ex- 

 perience at the basis of Laplace's assumption. The 

 reader who wishes to pursue this subject further may be 

 referred in the first place to Professor Edgeworth's 

 article.'^ " I submit," he writes, " the assumption that any 

 probability-constant about which we know nothing in par- 

 ticular is as likely to have one value as another, is 

 grounded upon the rough but solid experience that such 

 constants do as a matter of fact as often have one value 

 as another." 



The reader may, however, ask why may not " nature " 

 change after one set of experiences and before another ? 

 The only answer to this question lies in the views ex- 



1 An Investigation of the Laws of Thought (London, 1854), chap. xx. 

 Problems Relating to the Connexion of Caicses and Effects^ especially pp. 363- 



75- 



- "The Philosophy of Chance," Mitid, vol. ix. pp. 223-35, 1884- 



