BOOK II, 



NUMBER, VARIETY, AND PROBABILITY. 



CHAPTER VIII. 



PRINCIPLES OF NUMBER. 



NOT without much reason did Pythagoras represent the 

 world as ruled by number. Into almost all our acts of 

 clear thought number enters, and in proportion as we can 

 define numerically we enjoy exact and useful knowledge 

 of the Universe. The science of numbers, too, the study of 

 the principles and methods of reasoning in number, has 

 hitherto presented the widest and most practicable train- 

 ing in logic. So free and energetic has been the study of 

 mathematical forms, compared with the forms and laws of 

 logic, that mathematicians have passed far in advance of 

 any pure logicians. Occasionally, in recent times, they have 

 condescended to apply their great algebraic instruments 

 to a reflex advancement of the primary logical science. It 

 is thus that we chiefly owe to profound mathematicians, 

 such as Sir John Herschel, Dr. W he well, Professor De 

 Morgan or Dr. Boole, the regeneration of logic in the 

 present century, and I entertain no doubt that it is in 

 maintaining a close alliance with the extensive branches of 

 quantitative reasoning that we must look for still further 

 progress in our comprehension of qualitative inference. 



I cannot assent, indeed, to the common notion that 



