163 INDUCTION. 



what, in the present case, these words mean, and how far and 

 in what circumstances the properties which they express are 

 sufficient grounds for disbelief. 



2. It is to he remarked in the first place, that the posi- 

 tive evidence produced in support of an assertion which is 

 nevertheless rejected on the score of impossibility or improba- 

 bility, is never such as amounts to full proof. It is always 

 grounded on some approximate generalization. The fact may 

 have been asserted by a hundred witnesses ; but there are 

 many exceptions to the universality of the generalization that 

 what a hundred witnesses affirm is true. We may seem to 

 ourselves to have actually seen the fact : but, that we really 

 see what we think we see, is by no means an universal truth ; 

 our organs may have been in a morbid state ; or we may have 

 inferred something, and imagined that we perceived it. The 

 evidence, then, in the affirmative being never more than an 

 approximate generalization, all will depend on what the 

 evidence in the negative is. If that also rests on an approxi- 

 mate generalization, it is a case for comparison of probabilities. 

 If the approximate generalizations leading to the affirmative 

 are, when added together, less strong, or in other words, 

 farther from being universal, than the approximate generali- 

 zations which support the negative side of the question, the 

 proposition is said to be improbable, and is to be disbelieved 

 provisionally. If however an alleged fact be in contradic- 

 tion, not to any number of approximate generalizations, but to 

 a completed generalization grounded on a rigorous induction, 

 it is said to be impossible, and is to be disbelieved totally. 



This last principle, simple and evident as it appears, is 

 the doctrine which, on the occasion of an attempt to apply it 

 to the question of the credibility of miracles, excited so violent 

 a controversy. Hume's celebrated doctrine, that nothing is 

 credible which is contradictory to experience, or at variance 

 with laws of nature, is merely this very plain and harmless 

 proposition, that whatever is contradictory to a complete induc- 

 tion is incredible. That such a maxim as this should either 

 be accounted a dangerous heresy, or mistaken for a great and 



