INDUCTION. 171 



great logical domain. I venture to assert that number is 

 wholly logical, both in its fundamental nature and in all 

 its complex developments. Quantity in all its forms is but 

 a development of number. That which is mathematical 

 is not the less logical ; if anything it is the more logical, 

 in the sense that it presents logical results in the highest 

 degree of complexity and variety. 



Before proceeding then from Perfect to Imperfect In 

 duction I break off in some degree the course of the work, 

 to treat of the logical conditions of number. I shall then 

 employ number to estimate the variety of combinations 

 in which natural phenomena may present themselves, and 

 the probability or improbability of their occurrence under 

 definite circumstances. It is in later parts of the work 

 that I must endeavour to establish, in a complete manner, 

 the notions which I have set forth upon the subject of 

 Imperfect Induction, as applied in the investigation of 

 Nature, which notions may be thus briefly stated: 



1. Imperfect Induction entirely rests upon Perfect In 



duction for its materials. 



2. The logical process by which we seem to pass directly 



from examined to unexamined cases consists in an 

 inverse and complex application of deductive in 

 ference, so that all reasoning may be said to be 

 either directly or inversely deductive. 



3. The result is always of a hypothetical character, and 



is never more than probable. 



4. No nett addition is ever made to our knowledge by 



reasoning ; what we know of future events or unex 

 amined objects is only the unfolded contents of 

 our previous knowledge, and it becomes less and 

 less probable as it is more boldly extended to re 

 mote cases. 



