XM.] THE INDUCTIVE OB INVERSE METHOD. 259 



When an event has happened a very great number of 

 times, its happening once again approaches nearly to cer- 

 tainty. If we suppose the sun to have risen one thousand 

 million times, the probability that it will rise again, on 



the ground of this knowledge merely, is - - -2^ 

 But then the probability that it will continue to rise for as 

 long a period in the future is only 00,000+ ^ Qr a j mog |. 



exactly \. The probability that it will continue so rising a 

 thousand times as long is only about y^^y. The lesson which 

 we may draw from these figures is quite that which we 

 should adopt on other grounds, namely, that experience 

 never affords certain knowledge, and that it is exceedingly 

 improbable that events will always happen as we observe 

 them. Inferences pushed far beyond their data soon lose 

 any considerable probability. De Morgan has said, 1 " No 

 finite experience whatsoever can justify us in saying that 

 the future shall coincide with the past in all time to come, 

 or that there is any probability for such a conclusion." On 

 the other hand, we gain the assurance that experience 

 sufficiently extended and prolonged will give us the 

 knowledge of future events with an unlimited degree of 

 probability, provided indeed that those events are not 

 subject to arbitrary interference. 



It must be clearly understood that these probabilities are 

 only such as arise from the mere happening of the events, 

 irrespective of any knowledge derived from other sources 

 concerning those events or the general laws of nature. 

 All our knowledge of nature is indeed founded in like 

 manner upon observation, and is therefore only probable. 

 The law of gravitation itself is only probably true. But 

 when a number of different facts, observed under the most 

 diverse circumstances, are found to be harmonized under a 

 supposed law of nature, the probability of the law approxi- 

 mates closely to certainty. Each science rests upon so 

 many observed facts, and derives so much support from 

 analogies or connections with other sciences, that there 

 are comparatively few cases where our judgment of the 

 probability of an event depends entirely upon a few ante- 



Essay on Probabilities, p. 128. 



