380 INDUCTION. 



Probabilities, has been led to give Lis sanction ; the effect in both cases 

 being, entirely to confound the doctrine of the Grounds of Disbelief. 

 The mistake consists in overlooking the distinction between (what may- 

 be called) improbability before the fact, and improbability after it; two 

 different properties, the latter of which is always a' gi-ound of disbelief; 

 the fonner is so or not, as it may happen. 



. Many events are altogether improbable to us, before they have 

 happened, or before we are informed of their happening, which are 

 not in the least incredible when we are informed of them, because not 

 contrary to any, even approximate, induction. In the cast of a per- 

 fectly fair die, the chances are five to one against throwing ace, that is, 

 ace will be thrown on an average only once in six throws. But -this 

 is no reason against believing that ace was thrown on a given occasion, 

 if any credible witness asserts it ; since although 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 improba- 

 bility, then, or in other words, the uruisualness, 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. If we disbelieved all facts which had the chances against 

 them beforehand, we should believe hardly anything. 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 thou- 

 sand to one ; but since he was certain to die at some time or other, 

 and when he died must necessarily die on some particular day, while 

 the chances are innumerable against every day in particular, experi- 

 ence affords no ground whatever for discrediting any testimony 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 com- 

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

 contrary to the unifoim course of experience), that we do not disbe- 

 lieve, merely because the chances were against them, things in strict 

 conformity to the unifonn course of experience ; that we do not dis- 

 believe an alleged fact merely because the combination of causes upon 

 which it depends occurs only once in a certain number of times. It is 

 evident that whatever is shown by experience to occur in a certain 

 proportion (however small) of the whole number of possible cases, is 

 not contraiy to experience ; (though we are right in disbelieving it, if 

 some other supposition respecting the matter in question would be ti"ue 

 in a greater proportion of the whole number of cases.) What would 

 really be contrary to experience, would be the assertion that the event 

 had happened more frequently in some large number of times, than 

 the same combination had ever been known to occur in that number 

 of times; and. this alone it is which is improbable, in the sense of in- 

 credibility, or, as we have called it, improbability after the fact. 



§ 5. While the defenders of Christianity against Hume have thus 

 confounded two different meanings of the word improbability, con- 

 tending that because improbability of the one kind is not necessarily a 

 ground of disbelief, neither therefore is the other, and that nothing 

 supported by credible testimony ought ever to be disbelieved ; La- 

 place, again, falling into the same confusion between the two meanings, 

 contends, on the contrary, that because improbability of the one kind 



