ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 207 



might be, and, for instance, not so much so as a world of pure chance 

 would be. 



But we can never get to the bottom of this question until we take 

 account of a highly -important logical principle 1 which I now proceed to 

 enounce. This principle is that any plurality or lot of objects what- 

 ever have some character in common (no matter how insignificant) 

 which is peculiar to them and not shared by anything else. The word 

 " character " here is taken in such a sense as to include negative char- 

 acters, such as incivility, inequality, etc., as well as their positives, 

 civility, equality, etc. To prove the theorem, I will show what character 

 any two things, A and B, have in common, not shared by anj'thing 

 else. The things, A and B, are each distinguished from all other 

 things by the possession of certain characters which may be named A- 

 ness and B-ness. Corresponding to these positive characters, are the 

 negative characters un-A-ness, which is possessed by everything except 

 A, and un-B-ness, which is possessed by everything except B. These 

 two characters are united in everything except A and B ; and this 

 union of the characters un-A-ness and un-B-ness makes a compound 

 character which may be termed A-B-lessness. This is not possessed 

 by either A or B, but it is possessed by everything else. This charac- 

 ter, like every other, has its corresponding negative un-A-B-lessness, 

 and this last is the character possessed by both A and B, and by noth- 

 ing else. It is obvious that what has thus been shown true of two 

 things is, mutatis mutandis, true of any number of things. Q. E. D. 



In any world whatever, then, there must be a character peculiar to 

 each possible group of objects. If, as a matter of nomenclature, char- 

 acters peculiar to the same group be regarded as only different aspects 

 of the same character, then we may say that there will be precisely one 

 character for each possible group of objects. Thus, suppose a world to 

 contain five things, a, (3, y, d, e. Then it will have a separate character 

 for each of the 31 groups (with non-existence making up 32 or 2 6 ) shown 



a[3yde 



This shows that a contradiction is involved in the very idea of a 

 chance-world, for in a world of 32 things, instead of there being only 3 5 

 1 This principle was, I believe, first stated by Mr. De Morgan. 



