LOGIC AS THE ESSENCE OF PHILOSOPHY 37 



probable on the data and yet not occur. It is, however, 

 obviously capable of further analysis, and of more exact 

 statement. We shall have to say something like this : 

 that every instance of a proposition * being true increases 

 the probability of its being true in a fresh instance, and 

 that a sufficient number of favourable instances will, in 

 the absence of instances to the contrary, make the proba- 

 bility of the truth of a fresh instance approach indefinitely 

 near to certainty. Some such principle as this is required 

 if the method of simple enumeration is to be valid. 



But this brings us to our other question, namely, how 

 is our principle known to be true ? Obviously, since it 

 is required to justify induction, it cannot be proved by 

 induction ; since it goes beyond the empirical data, it 

 cannot be proved by them alone ; since it is required to 

 justify all inferences from empirical data to what goes 

 beyond them, it cannot itself be even rendered in any 

 degree probable by such data. Hence, if it is known, 

 it is not known by experience, but independently of 

 experience. I do not say that any such principle is 

 known : I only say that it is required to justify the 

 inferences from experience which empiricists allow, and 

 that it cannot itself be justified empirically. 2 



A similar conclusion can be proved by similar 

 arguments concerning any other logical principle. Thus 

 logical knowledge is not derivable from experience alone, 

 and the empiricist's philosophy can therefore not be 

 accepted in its entirety, in spite of its excellence in many 

 matters which lie outside logic. 



Hegel and his followers widened the scope of logic in 

 quite a different way a way which I believe to be 



1 Or rather a propositional function. 



2 The subject of causality and induction will be discussed again in 

 Lecture VIII. 



