302 THE PRINCIPLES OF SCIENCE. 



The grand object of seeking to estimate the probability 

 of future events from past experience, seems to have been 

 entertained by James Bernoulli! and De Moivre, at lea,st 

 such was the opinion of Condorcet ; and Bernouilli may be 

 said to have solved one case of the problem? . The English 

 writers Bayes and Price are, however, undoubtedly the 

 first who put forward any distinct rules on the subject 11 . 

 Condorcet and several other eminent mathematicians ad 

 vanced the mathematical theory of the subject; but it was 

 reserved to the immortal Laplace to bring to the subject 

 the full power of his genius, and carry the solution of the 

 problem almost to perfection. It is instructive to observe 

 that a theory which arose from the consideration of the 

 most petty games of chance, the rules and the very names 

 of which are in many cases forgotten, gradually advanced, 

 until it embraced the most sublime problems of science, 

 and finally undertook to measure the value and certainty 

 of all our inductions. 



Fortuitous Coincidences. 



We should have studied the theory of probability to 

 very little purpose, if we thought that it would furnish 

 us with an infallible guide. The theory itself points out 

 the possibility, or rather the approximate certainty, that 

 we shall sometimes be deceived by extraordinary, but 

 fortuitous coincidences. There is no run of luck so ex 

 treme that it may not happen, and it may happen to us, 

 or in our time, as well as to other persons or in other 

 times. We may be forced by all correct calculation to 

 refer such coincidences to some necessary cause, and yet 

 we may be deceived. AH that the calculus of probability 



s Todlnmter s History, pp. 378, 79. 



11 Philosophical Transactions [1763], vol. liii. p. 370, and [1764], 

 vol. liv. p. 296. Todhunter, pp. 294-300. 



