196 THE PRINCIPLES OF SCIENCE. 



the number of qualities, 2 n is the number of varieties of 

 things which may be formed from them, if there be no con 

 ditions but those of logic. This number, it need hardly 

 be said, increases after the first few terms, in an extra 

 ordinary manner, so that it would require 302 figures, 

 even to express the number of combinations in which 1000 

 qualities might conceivably present themselves. 



If all the combinations allowed by the Laws of Thought 

 occurred in nature, then science would begin and end with 

 those laws. To observe nature would give us no ad 

 ditional knowledge, because no two qualities would in the 

 long run be oftener associated than any other two. We 

 could never predict events with more certainty than we 

 now predict the throws of dice, and experience would be 

 without use. But the universe, as actually created, pre 

 sents a far different and much more interesting problem. 

 The most superficial observation shows that some things 

 are habitually associated with other things. The more 

 mature our examination, the more we become convinced 

 that each event depends upon the prior occurrence of 

 some other series of events. Action and reaction are 

 gradually discovered to underlie the whole scene, and an 

 independent or casual occurrence does not exist except in 

 appearance. Even dice as they fall are surely determined 

 in their course by prior conditions and fixed laws. Thus 

 the combinations of events which can really occur are 

 found to be very restricted, and it is the work of science 

 to detect these restricting conditions. 



In the English alphabet, for instance, we have twenty- 

 six letters. Were the combinations of such letters per 

 fectly free, so that any letter could be indifferently 

 sounded with any other, the number of words which 

 could be formed without any repetition would be 2 26 - i, 

 or 67,108,863, equal in number to the combinations of 

 the twenty-seventh column of the Abecedarium, excluding 



