LAWS OF NATURE. 859 



become mutually each other's test, showing that one or other 

 must be given up, or at least more guardedly expressed. In 

 the case of inductions which confirm each other, the one which 

 becomes a conclusion from ratiocination rises to at least the 

 level of certainty of the weakest of those from which it is 

 deduced ; while in general all are more or less increased in 

 certainty. Thus the Torricellian experiment, though a mere 

 case of three more general laws, not only strengthened greatly 

 the evidence on which those laws rested*, but converted one of 

 them (the weight of the atmosphere) from a doubtful gene- 

 ralization into a completely established doctrine. 



If, then, a survey of the uniformities which have been 

 ascertained to exist in nature, should point out some which, 

 as far as any human purpose requires certainty, may be con- 

 sidered quite certain and quite universal ; then by means of 

 these uniformities we may be able to raise multitudes of other 

 inductions to the same point in the scale. For if we can show, 

 with respect to any inductive inference, that either it must be 

 true, or one of these certain and universal inductions must admit 

 of an exception ; the former generalization will attain the same 

 certainty, and indefeasibleness within the bounds assigned to it, 

 which are the attributes of the latter. It will be proved to be 

 a law ; and if not a result of other and simpler laws, it will be 

 a law of nature. 



There are such certain and universal inductions ; and it is 

 because there are such, that a Logic of Induction is possible. 



