36 SCIENTIFIC METHOD IN PHILOSOPHY 



an inverse ratio to the largeness of the generalisation. 

 The process is delusive and insufficient, exactly in 

 proportion as the subject-matter of the observation is 

 special and limited in extent. As the sphere widens, this 

 unscientific method becomes less and less liable to 

 mislead ; and the most universal class of truths, the law 

 of causation for instance, and the principles of number 

 and of geometry, are duly and satisfactorily proved by 

 that method alone, nor are they susceptible of any other 

 proof." x 



In the above statement, there are two obvious lacunae : 

 (i) How is the method of simple enumeration itself 

 justified ? (2) What logical principle, if any, covers the 

 same ground as this method, without being liable to its 

 failures ? Let us take the second question first. 



A method of proof which, when used as directed, gives 

 sometimes truth and sometimes falsehood as the method 

 of simple enumeration does is obviously not a valid 

 method, for validity demands invariable truth. Thus, if 

 simple enumeration is to be rendered valid, it must not 

 be stated as Mill states it. We shall have to say, at 

 most, that the data render the result probable. Causation 

 holds, we shall say, in every instance we have been able 

 to test ; therefore it probably holds in untested instances. 

 There are terrible difficulties in the notion of probability, 

 but we may ignore them at present. We thus have what 

 at least may be a logical principle, since it is without 

 exception. If a proposition is true in every instance that 

 we happen to know of, and if the instances are very 

 numerous, then, we shall say, it becomes very probable, 

 on the data, that it will be true in any further instance. 

 This is not refuted by the fact that what we declare to be 

 probable does not always happen, for an event may be 



1 Book iii., chapter xxi., 3. 



