SECT. 6.] The Rule of Succession. 195 



to do. We assume our statistical proposition to be true, 

 neglecting the diminution of its value by the process of 

 attainment ; we take it up first at this point and then apply 

 our rules to it. We receive it in fact, if one may use the 

 expression, ready-made, and ask no questions about the pro 

 cess or completeness of its manufacture. 



5. It is not to be supposed, of course, that any writers 

 have seriously attempted to reduce to one system of calcula 

 tion all the causes mentioned above, and to embrace in one 

 formula the diminution of certainty to which the inclusion of 

 them subjects us. But on the other hand, they have been 

 unwilling to restrain themselves from all appeal to them. 

 From an early period in the study of the science attempts 

 have been made to proceed, by the Calculus of Probability, 

 from the observed cases to adjacent and similar cases. In 

 practice, as has been already said, it is not possible to avoid 

 some extension of this kind. But it should be observed, 

 that in these instances the divergence from the strict ground 

 of experience is not in reality recognized, at least not as a 

 part of our logical procedure. We have, it is true, wandered 

 somewhat beyond it, and so obtained a wider proposition 

 than our data strictly necessitated, and therefore one of less 

 certainty. Still we assume the conclusion given by induc 

 tion to be equally certain with the data, or rather omit all 

 notice of the divergence from consideration. It is assumed 

 that the unexamined instances will resemble the examined, 

 an assumption for which abundant warrant may exist ; the 

 theory of the calculation rests upon the supposition that 

 there will be no difference between them, and the practical 

 error is insignificant simply because this difference is small. 



6. But the rule we are now about to discuss, and 

 which may be called the Rule of Succession, is of a very 

 different kind. It not only recognizes the fact that we are 



132 



