384 INDUCTION. 



non-occurrence will depend, and form an estimate of the comparative fre- 

 quency of the causes favorable and of those unfavorable to the occurrence. 

 These are data of a higher order, by which the empirical law derived from 

 a mere numerical comparison of affirmative and negative instances will be 

 either corrected or confirmed, and in either case we shall obtain a more 

 correct measure of probability than is given by that numerical comparison. 

 It has been well remarked that in the kind of examples by which the doc- 

 trine of chances is usually illustrated, that of balls in a box, the estimate 

 of probabilities is supported by reasons of causation, stronger than specific 

 experience. " What is the reason that in a box where there are nine black 

 balls and one white, we expect to draw a black ball nine times as much (in 

 other words, nine times as often, frequency being the gauge of intensity in 

 expectation) as a white ? Obviously because the local conditions are nine 

 times as favorable ; because the hand may alight in nine places and get a 

 black ball, while it can only alight in one place and find a white ball; just 

 for the same reason that we do not expect to succeed in finding a friend 

 in a crowd, the conditions in order that we and he should come together 

 being many and difficult. This of course would not hold to the same ex- 

 tent were the white balls of smaller size than the black, neither would the 

 probability remain the same ; the larger ball would be much more likely 

 to meet the hand."* 



It is, in fact, evident that when once causation is admitted as a universal 

 law, our expectation of events can only be rationally grounded on that law. 

 To a person who recognizes that every event depends on causes, a thing's 

 having happened once is a reason for expecting it to happen again, only be- 

 cause proving that there exists, or is liable to exist, a cause adequate to 

 produce it.f The frequency of the particular event, apart from all surmise 

 respecting its cause, can give rise to no other induction than that per enu- 

 merationem simplicem/ and the precarious inferences derived from this are 

 superseded, and disappear from the field as soon as the principle of causa- 

 tion makes its appearance there. 



Notwithstanding, however, the abstract superiority of an estimate of 

 probability grounded on causes, it is a fact that in almost all cases in 

 which chances admit of estimation sufficiently precise to render their 

 numerical appreciation of any practical value, the numerical data are not 

 drawn from knowledge of the causes, but fi'om experience of the events 



* Prospective Review for February, 1850. 



t "If this be not so, why do we feel so much more probability added by the first instance 

 than by any single subsequent instance ? Why, except that the first instance gives us its pos- 

 sibility (a cause adequate to it), while every other only gives us the frequency of its conditions ? 

 If no reference to a cause be supposed, possibility would have no meaning ; yet it is clear that, 

 antecedent to its happening, we might have supposed the event impossible, i. e., have believed 

 that there was no physical energy really existing in the world equal to producing it Af- 

 ter the first time of happening, which is, then, more important to the whole probability than 

 any other single instance (because proA'ing the possibility), the number of times becomes im- 

 portant as an index to the intensity or extent of the cause, and its independence of any par- 

 ticular time. If we took the case of a tremendous leap, for instance, and wished to form an 

 estimate of the probability of its succeeding a certain number of times ; the first instance, by 

 showing its possibility (before doubtful) is of the most importance ; but every succeeding leap 

 shows the power to be more perfectly under control, greater and more invariable, and so in- 

 creases the probability ; and no one would think of reasoning in this case straight from one 

 instance to the next, without referring to the physical energy which each leap indicated. Is 

 it not, then, clear that we do not ever " (let us rather say, that we do not in an advanced state 

 of our knowledge) " conclude directly from the happening of an event to the probability of its 

 happening again ; but that we refer to the cause, regarding the past cases as an index to the 

 cause, and the cause as our guide to the future?" — Ibid. 



