356 



INDUCTION. 



once causation is admitted as an uni- 

 versal law, our expectation of events 

 can only be rationally grounded on 

 that law. To a person who recog- 

 nises that every event depends on 

 causes, a thing's having happened 

 once is a reason for expecting it to 

 happen again, only because proving 

 that there exists, or is liable to exist, 

 a cause adequate to produce it.* The 

 frequency of the particular event, 

 apart from all surmise respecting 

 its cause, can give rise to no other 

 induction than that^je?* enumerationem 

 simplicem ; and the precarious infer- 

 ences derived from this are super- 

 seded and disappear from the field, 

 as soon as the principle of causation 

 makes its appearance there. 



Notwithstanding, however, the ab- 



* " 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 in- 

 stance gives us its possibility, (a cause 

 adequate to it,) while every other only gives 

 us the frequency of its conditions ? If no 

 reference to a cause be supposed, possi- 

 bility would have no meaning ; yet it is 

 clear that, antecedent to its happening, 

 we might have supposed the event impos- 

 sible, i.e., have believed that there was no 

 physical energy really existing in the world 

 equal to producing it. . . . After the first 

 time of happening, which is, then, more 

 important to the whole probability than 

 any other single instance, (because proving 

 the possibility,) the number of times be- 

 comes important as an index to the inten- 

 sity or extent of the cause, and its inde- 

 pendence of any particular time. If we 

 took the case of a tremendous leap, for 

 instance, und 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 suc- 

 ceeding leap shows the power to be more 

 perfectly under control, greater and more 

 invariable, and so increases 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 pro- 

 bability 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?"— Pro- 

 apective Review for February 1850. 



stract superiority of an estimate of 

 probability grounded on causes, it is 

 a fact that in almost all cases in which 

 chances admit of estimation suflB- 

 ciently precise to render their nume- 

 rical appreciation of any practical 

 value, the numerical data are not 

 drawn from knowledge of the causes, 

 but from experience of the events 

 themselves. The probabilities of life 

 at different ages or in different cli- 

 mates ; the probabilities of recovery 

 from a particular disease ; the chances 

 of the birth of male or female off- 

 spring ; the chances of the destruc- 

 tion of houses or other property by 

 fire ; the chances of the loss of a ship 

 in a particular voyage — are deduced 

 from bills of mortality, returns from 

 hospitals, registers of births, of ship- 

 wrecks, (fee, that is, from the observed 

 frequency not of the causes, but of 

 the effects. The reason is, that in all 

 these classes of facts, the causes are 

 either not amenable to direct obser- 

 vation at all, or not with the requisite 

 precision, and we have no means of 

 judging of their frequency except 

 from the empirical law afforded by 

 the frequency of the effects. The in- 

 ference does not the less depend on 

 causation alone. We reason from an 

 effect to a similar effect by passing 

 through the cause. If the actuary 

 of an insurance office infers from 

 his tables that among a hundred 

 persons now living, of a particular 

 age, five on the average will attain 

 the age of seventy, his inference is 

 legitimate, not for the simple reason 

 that this is the proportion who have 

 lived till seventy in times past, but 

 because the fact of their having so 

 lived shows that this is the proportion 

 existing, at that place and time, be- 

 tween the causes which prolong life 

 to the age of sevent}', and those tend- 

 ing to bring it to an earlier close.* 



* The writer last quoted says that the 

 valuation of chances by comparing the 

 number of cases in which the event occuis 

 with the number in which it does not occur 

 "would generally be wholly erroneous," 

 and " is not the true theory of probability." 

 It is a^ least that which fornis the fovmd^- 



