PHILOSOPHY OF INDUCTIVE INFERENCE. 263 



which tended, in the creation of things, to associate these 

 properties together, and I expect to find them associated 

 in the next instance. But there always is the possibility 

 that some unknown change may take place between past 

 and future cases. The clock may run down, or be subject 

 to any one of a hundred accidents altering its condition. 

 There is no reason in the nature of things, so far as known 

 to us, why yellow colour, ductility, high specific gravity, 

 and incorrodibility, should always be associated together ; 

 and in other like cases, if not in this, men s expectations 

 have been deceived. Our inferences, therefore, always 

 retain more or less of a hypothetical character, and are so 

 far open to doubt. Only in proportion as our induction 

 approximates to the character of perfect induction, does 

 it approximate to certainty. The amount of uncertainty 

 corresponds to the probability that other objects than 

 those examined, may exist and falsify our inferences ; the 

 amount of probability corresponds to the amount of infor 

 mation yielded by our examination ; and the theory of 

 probability will be needed to prevent our over-estimating 

 or under-estimating the knowledge we possess. 



Illustrations of the Inductive Process. 



To illustrate the passage from the known to the ap 

 parently unknown, let us suppose that the phenomena 

 under investigation consist of numbers, and that the 

 following six numbers being exhibited to us, we are 

 required to infer the character of the next in the 

 series : 



5, 15, 35, 45, 65, 95. 



The question first of all arises, How may we describe this 

 series of numbers ? What is uniformly true of them ? 

 The reader cannot fail to perceive at the first glance that 

 they all end in five, and the problem is, from the proper- 



