PHILOSOPHY OF INDUCTIVE INFERENCE. 271 



Discrimination of Certainty and Probability in the 

 Inductive Process. 



We can never recur too often to the truth that our 

 knowledge of the laws and future events of the external 

 world is only probable. The mind itself is quite capable 

 of possessing certain knowledge, and it is well to discri- 

 minate carefully between what we can and cannot know 

 with certainty. In the first place, whatever feeling is 

 actually present to the mind is certainly known to that 

 mind. If I see blue sky, I may be quite sure that I 

 do experience the sensation of blueness. Whatever I do 

 feel, I do feel beyond all doubt. We are indeed very 

 likely to confuse what we really feel with what we are 

 inclined to associate with it, or infer inductively from 

 it; but the whole of our consciousness, as far as it is 

 the result of pure intuition and free from inference, is 

 certain knowledge beyond all doubt. 



In the second place, we may have certainty of inference ; 

 the first axiom of Euclid, the fundamental laws of thought, 

 and the rule of substitution (p. n), are certainly true; 

 and if my senses could inform me that A was indistin- 

 guishable in colour from B, and B from C, then I should 

 be equally certain that A was indistinguishable from C. 

 In short, whatever truth there is in the premises, I can 

 certainly embody in their correct logical result. But 

 practically the certainty generally assumes a hypothetical 

 character. I never can be quite sure that two colours 

 are exactly alike, that two magnitudes are exactly equal, 

 or that two bodies whatsoever are identical even in their 

 apparent qualities. Almost all our judgments involve 

 quantitative relations, and, as will be shown in succeeding 

 chapters, we can never attain exactness and certainty 

 where continuous quantity enters. Judgments concerning 



