444 INDUCTION. 



asserts it ; since though ace is only thrown once in six times, some number 

 which is only thrown once in six times must have been thrown if the die 

 was thrown at all. The improbability, then, or, in other words, the unusu- 

 alness, of any fact, is no reason for disbelieving it, if the nature of the case 

 renders it certain that either that or something equally improbable, that 

 is, equally unusual, did happen. Nor is this all; for even if the other five 

 sides of the die were all twos, or all threes, yet as ace would still, on the 

 average, come up once in e\'ery six throws, its coming up in a given throw 

 would be not in any way contradictory to experience. If we disbelieved 

 all facts which had the chances against them beforehand, we should believe 

 hardly any thing. We are told that A. B. died yesterday; the moment 

 before we were so told, the chances against his having died on that day 

 may have been ten thousand to one; but since he was certain to die at 

 some time or other, and when he died must necessarily die on some par- 

 ticular day, while the preponderance of chances is very great against every 

 day in particular, experience affords no ground for discrediting any testi- 

 mony which may be produced to the event's having taken place on a given 

 day. 



Yet it has been considered by Dr. Campbell and others, as a complete 

 answer to Hume's doctrine (that things are incredible which are contrary 

 to the uniform course of experience), that we do not disbelieve, merely 

 because the chances were against them, things in strict conformity to the 

 uniform course of experience; that we do not disbelieve an alleged fact 

 merely because the combination of causes on which it depends occurs only 

 once in a certain number of times. It is evident that whatever is shown 

 by observation, or can be proved from laws of nature, to occur in a certain 

 proportion (however small) of the whole number of possible cases, is not 

 contrary to experience; though we are right in disbelieving it, if some 

 other suj)position respecting the matter in question involves, on the whole, 

 a less departure from the ordinary course of events. Yet on such grounds 

 as this have able writers been led to the extraordinary conclusion, that 

 nothing supported by credible testimony ought ever to be disbelieved. 



§ 5. We have considered two species of events, commonly said to be im- 

 probable ; one kind which are in no way extraordinary, but which, having 

 an immense preponderance of chances against them, are improbable until 

 they are affirmed, but no longer ; another kind which, being contrary to 

 some recognized law of nature, are incredible on any amount of testimony 

 except such as would be sufficient to shake our belief in the law^ itself. 

 But between these two classes of events, there is an intermediate class, con- 

 sisting of what are commonly termed Coincidences : in other words, those 

 combinations of chances Avhich present some peculiar and unexpected reg- 

 ularity, assimilating them, in so far, to the results of law. As if, for exam- 

 ple, in a lottery of a thousand tickets, the numbers should be drawn in the 

 exact order of what are called the natural numbers, 1, 2, 3, etc. We have 

 still to consider the principles of evidence applicable to this case : whether 

 there is any difference between coincidences and ordinary events, in the 

 amount of testimony or other evidence necessary to render them credible. 



It is certain that on every rational principle of expectation, a combina- 

 tion of this peculiar sort may be expected quite as often as any other given 

 series of a thousand numbers ; that with perfectly fair dice, sixes will be 

 thrown twice, thrice, or any number of times in succession, quite as often 

 in a thousand or a million throws, as any other succession of numbers fixed 



