76 INDUCTION. 



form a conjecture as to the antecedent probability of such a 

 circumstance, from the characters of the parties concerned, or 

 other such evidence ; but it would be impossible to estimate 

 that probability with anything like numerical precision. The 

 counter-probability, however, that of the accidental origin 

 of the coincidence, dwindling so rapidly as it does at each new 

 trial ; the stage is soon reached at which the chance of unfair 

 ness 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 experiment. 



When, however, the coincidence is one which cannot be 

 accounted for by any known cause, and the connexion 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 appre 

 ciation, 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 necessary to know what 

 proportion of all the individual sequences or coexistences 

 occurring in nature are the result of law, and what propor 

 tion are mere casual coincidences. It being evident that we 

 cannot form any plausible conjecture as to this proportion, 

 much less appreciate it numerically, we cannot attempt any 

 precise estimation of the comparative probabilities. But of 

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

 nature of some previously unrecognised constancy of con 

 junction 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 uncommon event ; we have reason to conclude 

 that the coincidence is the effect of causation, and may be re 

 ceived (subject to correction from further experience) as an 

 empirical law. Further than this, in point of precision, we 



