ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 209 



class, but at random. These specimens will agree in a great number 

 of respects. If, now, it were likely that a second lot would agree with 

 the first in the majority of these respects, we might base on this con- 

 sideration an inference in regard to any one of these characters. But 

 such an inference would neither be of the nature of induction, nor 

 would it (except in special cases) be valid, because the vast majority of 

 points of agreement in the first sample drawn would generally be en- 

 tirely accidental, as well as insignificant. To illustrate this, I take the 

 ages at death of the first five poets given in Wheeler's " Biographical 

 Dictionary." They are : 



Aagard, 48. 



Abeille, 70. 



Abulola, 84. 



Abunowas, 48. 



Accords, 45. 



These five ages have the following characters in common : 



1. The difference of the two digits composing the number, divided 

 by three, leaves a remainder of one. 



2. The first digit raised to the power indicated by the second, and 

 divided by three, leaves a remainder of one. 



3. The sum of the prime factors of each age, including one, is divisi- 

 ble by three. 



It is easy to see that the number of accidental agreements of this 

 sort would be quite endless. But suppose that, instead of considering 

 a character because of its prevalence in the sample, we designate a 

 character before taking the sample, selecting it for its importance, ob- 

 viousness, or other point of interest. Then two considerable samples 

 drawn at random are extremely likely to agree approximately in regard 

 to the proportion of occurrences of a character so chosen. The infer- 

 ence that a previously designated character has nearly the same fre- 

 quency of occurrence in the ichole of a class that it has in a sample 

 drawn at random out of that class is induction. If the character be 

 not previously designated, then a sample in which it is found to be 

 prevalent can only serve to suggest that it may be prevalent in the 

 whole class. We may consider this surmise as an inference if we please 

 an inference of possibility ; but a second sample must be drawn to test 

 the question of whether the character actually is prevalent. Instead 

 of designating beforehand a single character in reference to which we 

 will examine a sample, we may designate two, and use the same sample 

 to determine the relative frequencies of both. This will be making two 

 inductive inferences at once ; and, of course, we are less certain that 

 both will yield correct conclusions than we should be that either sep- 

 arately would do so. What is true of two characters is true of any 

 limited number. Now, the number of characters which have any consid- 

 erable interest for us in reference to any class of objects is more moderate 



VOL. XIII. 14 



