222 SCIENTIFIC METHOD IN PHILOSOPHY 



If inferences as to the future are valid, what principle 

 must be involved in making them ? 



The principle involved is the principle of induction, 

 which, if it is true, must be an a priori logical law, not 

 capable of being proved or disproved by experience. It 

 is a difficult question how this principle ought to be 

 formulated ; but if it is to warrant the inferences which 

 we wish to make by its means, it must lead to the follow- 

 ing proposition : " If, in a great number of instances, a 

 thing of a certain kind is associated in a certain way with 

 a thing of a certain other kind, it is probable that a thing 

 of the one kind is always similarly associated with a thing 

 of the other kind ; and as the number of instances 

 increases, the probability approaches indefinitely near to 

 certainty." It may well be questioned whether this 

 proposition is true ; but if we admit it, we can infer that 

 any characteristic of the whole, of the observed past is 

 likely to apply to the future and to the unobserved past. 

 This proposition, therefore, if it is true, will warrant the 

 inference that causal laws probably hold at all times, future 

 as well as past ; but without this principle, the observed 

 cases of the truth of causal laws afford no presumption as 

 to the unobserved cases, and therefore the existence of a 

 thing not directly observed can never be validly inferred. 



It is thus the principle of induction, rather than the 

 law of causality, which is at the bottom of all inferences 

 as to the existence of things not immediately given. 

 With the principle of induction, all that is wanted for 

 such inferences can be proved ; without it, all such 

 inferences are invalid. This principle has not received 

 the attention which its great importance deserves. Those 

 who were interested in deductive logic naturally enough 

 ignored it, while those who emphasised the scope of 

 induction wished to maintain that all logic is empirical, 



