6 ON THE FOUNDATIONS OF 



clear that expectation never could exist, if we did not believe in 

 the general similarity of the past to the future, i.e. in the 

 regularity of nature, which is here deduced from it. 



A little further on,... "II suit encore de ce theoreme que 

 dans une scrie d'eVenemens inde'finiment prolonged, 1'action des 

 causes r^gulieres et constantes doit 1'emporter a. la'longue, sur 

 celle, des causes irrdgulieres....Ainsi des chances favorables et 

 nombreuses etant constamment attaches a 1'observation des 

 principes eternels de raison de justice et d'humanite, qui fondent 

 et qui maintiennent les societes ; il y a un grand avantage a se 

 conformer & ces principes, et de graves inconveniens a s'en 

 e'carter. Que Ton consulte les histoires, et sa propre experience 

 on y verra tous les faits venir a 1'appui de ce re*sultat du calcul." 

 Without disputing the truth of the conclusion, we may doubt 

 whether it is to be considered as a "resultat du calcul." 



The same expression occurs immediately afterwards in another 

 passage, in which the writer seems to allude to the history of his 

 own times, and to the ambition of the great chieftain whom he 

 at one time served. 



Indeed it would seem as if to Laplace all the lessons of his- 

 tory were merely confirmations of the " r&sultats du calcul." 

 We are tempted to say with Cicero "hie ab artificio suo non 

 recessit." 



11. The results of the theory of probabilities express the 

 number of ways in which a given event can occur, or the pro- 

 portional number of times it will occur on the long run : they 

 are not to be taken as the measure of any mental state ; nor are 

 we entitled to assume that the theory is applicable wherever a 

 presumption exists in favour of a proposition whose truth is 

 uncertain. 



Nevertheless it has been applied to a great variety of induc- 

 tive results ; with what success and in what manner, I shall 

 now attempt to enquire. 



12. Our confidence in any inductive result varies with a 

 variety of circumstances ; one of these is the number of particular 

 cases from which it is deduced. Now the measure of this confi- 

 dence which the theory professes to give, depends on this 

 number exclusively. Yet no one can deny, that the force of the 



