388 INDUCTION. 



in the die, however small in itself, must be greater than that of a casual 

 coincidence ; and on this ground, a practical decision can generally be come 

 to without much hesitation, if there be the power of repeating the experi- 

 ment. 



When, however, the coincidence is one which can not be accounted for 

 by any known cause, and the connection between the two phenomena, if 

 produced by causation, must be the result of some law of nature hitherto 

 unknown; which is the case we had in view in the last chapter; then, 

 though the probability of a casual coincidence may be capable of apprecia- 

 tion, that of the counter-supposition, the existence of an undiscovered law 

 of nature, is clearly unsusceptible of even an approximate valuation. In 

 order to have the data which such a case would require, it would be neces- 

 sary to know what proportion of all the individual sequences or co-exist- 

 ences occurring in nature are the result of law, and what proportion are 

 mere casual coincidences. It being evident that we can not form any 

 plausible conjecture as to this proportion, much less appreciate it numer- 

 ically, we can not attempt any precise estimation of the comparitive proba- 

 bilities. But of this we are sure, that the detection of an unknown law of 

 nature — of some previously unrecognized constancy of conjunction among 

 phenomena — is no uncommon event. If, therefore, the number of instances 

 in which a coincidence is observed, over and above that which would arise 

 on the average from the mere concurrence of chances, be such that so great 

 an amount of coincidences from accident alone would be an extremely un- 

 common event ; we have reason to conclude that the coincidence is the ef- 

 fect of causation, and may be received (subject to correction from further 

 experience) as an empirical law. Further than this, in point of precision, 

 we can not go ; nor, in most cases, is greater precision required, for the 

 solution of any practical doubt.* 



CHAPTER XIX. 



OF THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES. 



§ 1. We have had frequent occasion to notice the inferior generality of 

 derivative laws, compared with the ultimate laws from which they are de- 

 rived. This inferiority, which affects not only the extent of the proposi- 

 tions themselves, but their degree of certainty within that extent, is most 

 conspicuous in the uniformities of co-existence and sequence obtaining be- 

 tween effects which depend ultimately on different primeval causes. Such 

 uniformities will only obtain where there exists the same collocation of 

 those primeval causes. If the collocation varies, though the laws them- 

 selves remain the same, a totally different set of derivative uniformities 

 may, and generally will, be the result. 



Even where the derivative uniformity is between different effects of the 

 same cause, it Avill by no means obtain as universally as the law of the 



* For a fuller treatment of the many interesting questions raised by the theorj- of probabili- 

 ties, I may now refer to a recent work by Mr. Venn, Fellow of Caius College, Cambridge, 

 "The Logic of Chance;" one of the most thoughtful and philosophical treatises on any sub- 

 ject connected with Logic and Evidence which have been produced, to my knowledge, for 

 many years. Some criticisms contained in it have been very useful to me in revising the cor- 

 responding chapters of the present work. In several of Mr. Venn's opinions, however, I do 

 not agree. What these are will be obvious to any reader of Mr. Venn's work who is also a 

 reader of this. 



