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SCIENTIFIC THOUGHT. 



15. 



Laplace. 



So far as the formal part of the subject was con- 

 cerned, it was left to Laplace to place it on the founda- 

 tion upon which it has ever since rested. He brought 

 together the ideas of his predecessors, notably of 

 De Moivre, the two Bernoullis, Sterling, Bayes, and 

 Lagrange, as well as his own extensive researches, in 

 his great analytical theory of Probability, which ap- 

 peared in 1812, and, with several additions and an 

 elaborate introduction, in two subsequent editions during 

 his lifetime. This work has been justly considered a 

 monument of human genius, and stands worthily beside 

 the great ' Mecanique Celeste ' of its author. The 



ities founded on the data in their 

 previous state of inferiority. The 

 neglect of this obvious reflection 

 has given rise to misapplications of 

 the calculus of probabilities which 

 have made it the real opprobrium 

 of mathematics. It is sufficient to 

 refer to the applications made of it 

 to the credibility of witnesses, and 

 to the correctness of the verdicts of 

 juries." I have already referred to 

 the position which Comte took up. 

 De Morgan, with his usual clearness 

 and wisdom, at the end of his 

 "Theory of Probabilities" ('Ency. 

 Metrop.,' vol. ii. p. 470), whilst re- 

 ducing to a very narrow province 

 these applications of the calculus of 

 probabilities, says : " There are cir- 

 cumstances connected with the 

 mathemathical theory of independ- 

 ent evidence which it maj" be useful 

 to examine. In this, as in several 

 other preceding investigations, it is 

 not so much our wish to deduce 

 and impose results, as to inquire 

 whether these results really coincide 

 with the methods of judging which 

 our reason, unassisted by exact 

 comparison, has already made us 

 adopt. The use of the process is, 

 that both our theory and our pre- 



conceptions thus either assist or 

 destroy each other : in the former 

 case we feel able to trust this 

 science for further directions ; in 

 the latter, a useful new inquiry is 

 opened. For when we consider the 

 very imposing character of the first 

 principles of the science of proba- 

 bilities, and the mathematical 

 necessity which connects those 

 simple first principles with their 

 results, we feel convinced that, 

 even on the supposition that the 

 main conclusions of the present 

 treatise are altogether fallacious, 

 there must arise a necessity for 

 investigating the reason why a 

 methodical treatment of certain 

 notions should lead to results in- 

 consistent with the vuxjue applica- 

 tion of them on which we are ac- 

 customed to rely. For it must not 

 be imagined that opposition to the 

 principles laid down in this treatise 

 is always conducted on other 

 principles : on the contrary, it 

 frequently happens that it is only 

 a result of themselves obtained 

 without calculation, which is ar- 

 rayed against arithmetical deduc- 

 tion." 



