362 



INDUCTION. 



compatible with the supposition that 

 their effects, after accumulating so 

 slowly as to be imperceptible for five 

 thousand years, should start into im- 

 mensity in a single day. No mathe- 

 matical law of proportion between an 

 effect and the quantity or relations of 

 its cause could produce such contra- 

 dictory results. The sudden develop- 

 ment of an effect of which there was 

 no previous trace always arises from 

 the coming together of several distinct 

 causes not previously conjoined ; but 

 if such sudden conjunction is destined 

 to take place, the causes, or their 

 causes, must have existed during the 

 entire five thousand years ; and their 

 not having once come together during 

 that period shows how rare that par- 

 ticular combination is. We have, 

 therefore, the warrant of a rigid in- 

 duction for considering it probable, 

 in a degree un distinguishable from 

 certainty that the known conditions 

 requisite for the sun's rising will exist 

 to-morrow. 



§ 3. But this extension of deriva- 

 tive laws, not causative, beyond the 

 limits of observation, can only be to 

 adjacent cases. If instead of to-mor- 

 row, we had said this day twenty 

 thousand years, the inductions would 

 have been anything but conclusive. 

 That a cause which, in opposition to 

 very powerful causes, produced no 

 perceptible effect during five thousand 

 years, should produce a very con- 

 siderable one by the end of twenty 

 thousand, has nothing in it which is 

 not in conformity with our experience 

 of causes. We know many agents, 

 the effect of which in a short period 

 does not amount to a perceptible 

 quantity, but by accumulating for a 

 much longer period becomes con- 

 siderable. Besides, looking at the im- 

 mense multitude of the heavenly 

 bodies, their vast distances, and the 

 rapidity of the motion of such of them 

 as are known to move, it is a supposi- 

 tion not at all contradictory to ex- 

 perience that some body may be in 

 motion towards us, or we towards it, 



within the limits of whose influence 

 we have not come during five thousand 

 years, but which in twenty thousand 

 more may be producing effects upon 

 us of the most extraordinary kind. 

 Or the fact which is capable of pre- 

 venting sunrise may be, not the cumu- 

 lative effect of one cause, but some 

 new combination of causes ; and the 

 chances favourable to that combina- 

 tion, though they have not produced 

 it once in five thousand years, may 

 produce it once in twenty thousand. So 

 that the inductions which authorise us 

 to expect future events grow weaker 

 and weaker the farther we look into 

 the future, and at length become in- 

 appreciable. 



We have considered the probabili- 

 ties of the sun's rising to-morrow, 

 as derived from the real laws, that is, 

 from the laws of the causes on which 

 that uniformity is dependent. Let us 

 now consider how the matter would 

 have stood if the uniformity had been 

 known only as an empirical law ; if 

 we had not been aware that the sun's 

 light and the earth's rotation (or the 

 sun's motion) were the causes on 

 which the periodical occurrence of 

 daylight depends. We could have- 

 extended this empirical law to cases 

 adjacent in time, though not so great 

 a distance of time as we can now. 

 Having evidence that the effects had 

 remained unaltered, and been punc- 

 tually conjoined for five thousand 

 years, we could infer that the un- 

 known causes on which the conjunc- 

 tion is dependent had existed undi- 

 minished and uncounteracted during 

 the same period. The same conclu- 

 sions, therefore, would follow as in the 

 preceding case ; except that we should 

 only know that during five thousand 

 years nothing had occurred to defeat 

 perceptibly this particular effect ; 

 while, when we know the causes, we 

 have the additional assurance that 

 during that interval no such change 

 has been noticeable in the causes 

 themselves as by any degree of mul- 

 tiplication or length of continuance 

 could defeat the effect. 



