2II.1 THE INDUCTIVE OR 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 — ' — ' — - — , ; — 



° o J > 1 ,000,000,000 +1 + 1 



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



long a period in the future is only -' — ' S°°'°°° "t or almost 

 or ^ 2,000,000,000 -|- I ' 



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



thousand times as long is only about y^jxri- "^^^^ 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,^ " 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 a])proxi- 



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 comi)aratively few cases where our judgment of the 



probability of an event depends entirely upon a few ante- 



1 Essay on Probabilities, p. 12S. 



s 2 



