xi.j PHILOSOPHY OF INDUCTIVE INFERENCE. 229 



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

 and incorrodibility, should always be associated together, 

 and in other 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 us from over-esti- 

 mating 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- 

 ties of these six numbers, to infer the properties of the 

 next number ending in five. If we test their properties 

 by the process of perfect induction, we soon perceive that 

 they have another common property, namely that of being 

 divisible by five without remainder. May we then assert that 

 the next number ending in five is also divisible by five, 

 and, if so, upon what grounds ? Or extending the question, 

 Ts every number ending in five divisible by five ? Does it 

 follow that because six numbers obey a supposed law, 

 therefore 376,685,975 or any other number, however large, 

 obeys the law ? I answer certainly not. The law in ques- 

 tion is undoubtedly true ; but its truth is not proved by 

 any finite number of examples. All that these six numbers 

 can do is to suggest to my mind the possible existence of 



