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INDUCTION. 



or that they, or we ourselves, if we 

 were the direct percipients, w»re mis- 

 taken. 



That there are such cases, no one 

 is likely to dispute. Assertions for 

 which there is abundant positive evi- 

 dence are often disbelieved, on account 

 of what is called their improbability, 

 or impossibility. And the question 

 for consideration is what, in the pre- 

 sent case, these words mean, and how 

 far and in what circumstances the 

 properties which they express are suffi- 

 cient grounds for disbelief. 



§ 2. It is to be remarked in the 

 first place, that the positive evidence 

 produced in support of an assertion 

 which is nevertheless rejected on the 

 score of impossibility or improbability, 

 is never such as amounts to full proof. 

 It is always grounded on some ap- 

 proximate generalisation. The fact 

 may have been asserted by a hundred 

 witnesses ; but there are many ex- 

 ceptions to the universality of the 

 generalisation 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 approxi- 

 mate generalisation, all will depend 

 on what the evidence in the negative 

 is. If that also rests on an approxi- 

 mate generalisation, it is a case for 

 comparison of probabilities. If the 

 approximate generalisations leading 

 to the affirmative are, when added 

 together, less strong, or in other 

 words, farther from being universal, 

 than the approximate generalisations 

 which support the negative side of 

 the question, the proposition is said 

 to be improbable, and is to be disbe- 

 lieved provisionally. If, however, an 

 alleged fact be in contradiction, not 

 to any number of approximate gene- 

 ralisations, but to a completed gene- 



ralisation grounded on a rigorous in- 

 duction, it is said to be impossible, 

 and is to be disbelieved totally. 



This last principle, simple and evi- 

 dent 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 vio- 

 lent 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 contra- 

 dictory to a complete induction is in- 

 credible. That such a maxim as this 

 should either be accounted a danger- 

 ous' heresy, or mistaken for a great 

 and recondite truth, speaks ill for the 

 state of philosophical speculation on 

 such subjects. 



But does not (it may be asked) the 

 very statement of the proposition 

 imply a contradiction? An alleged 

 fact, according to this theory, is not 

 to be believed if it contradict a com- 

 plete induction. But it is essential 

 to the completeness of an induction 

 that it shall not contradict any known 

 fact. It is not then a petitio principii 

 to say, that the fact ought to be dis- 

 believed because the induction op- 

 posed to it is complete ? How can 

 we have a right to declare the induc- 

 tion complete, while facts, supported 

 by credible evidence, present them- 

 selves in opposition to it ? 



I answer, we have that right when- 

 ever the scientific canons of induction 

 give it to us ; that is, whenever the 

 induction can be complete. We have 

 it, for example, in a case of causation 

 in which there has been an experi- 

 mentum crucis. If an antecedent A, 

 superadded to a set of antecedents in 

 all other respects unaltered, is fol- 

 lowed by an effect B which did not 

 exist before, A is, in that instance at 

 least, the cause of B, or an indispen- 

 sable part of its cause ; and if A be 

 tried again with many totally different 

 sets of antecedents and B still follows, 

 then it is the whole cause. If these 

 observations or experiments have been 



