174 THE PRINCIPLES OF SCIENCE. [CHAP. 



may be formed from them, if there be no conditions but 

 those of logic. This number, it need hardly be said, 

 increases after the first few terms, in an extraordinary 

 manner, so that it would require 302 figures to express 

 the number of combinations in which 1,000 qualities 

 might conceivably present themselves. 



If all the combinations allowed by the Laws of Thought 

 occurred indifferently in nature, then science would begin 

 and end with those laws. To observe nature would give 

 us no additional 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, presents a far different and much more 

 interesting problem. The most superficial observation 

 shows that some things are constantly 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 con- 

 ditions and fixed laws. Thus the combinations of events 

 which can really occur are found to be comparatively 

 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 Logical Alphabet, 

 excluding one for the case in which all the letters 

 would be absent. But the formation of our vocal 

 organs prevents us from using the far greater part of 

 these conjunctions of letters. At least one vowel must be 

 present in each word ; more than two consonants cannot 

 usually be brought together ; and to produce words capable 

 of smooth utterance a number of other rules must be 



