SECT. 21.] Modality. 315 



limitation, and mathematically certain. Many other divi 

 sions might doubtless be mentioned, but, as every mathema 

 tician will recognize, the attempt to secure any general 

 agreement in such a matter of arrangement is quite hopeless. 

 It is here that the beneficial influence of the mathematical 

 theory of Probability is to be gratefully acknowledged. As 

 soon as this came to be studied it must have been perceived 

 that in attempting to mark off clearly from one another 

 certain gradations of belief, we should be seeking for breaches, 

 in a continuous magnitude. In the advance from a slight 

 presumption to a strong presumption, and from that to moral 

 certainty, we are making a gradual ascent, in the course of 

 which there are no natural halting-places. The proof of this 

 continuity need not be entered upon here, for the materials 

 for it will have been gathered from almost every chapter of 

 this work. The reader need merely be reminded that the 

 grounds of our belief, in all cases which admit of number and 

 measurement, are clearly seen to be of this description ; and 

 that therefore unless the belief itself is to be divorced from 

 the grounds on which it rests, what thus holds as to their 

 characteristics must hold also as to its own. 



It follows, therefore, that modality in the old sense of the 

 word, wherein an attempt was made to obtain certain natural 

 divisions in the scale of conviction, must be finally abandoned. 

 All that it endeavoured to do can now be done incomparably 

 better by the theory of Probability, with its numerical scale 

 which admits of indefinite subdivision. None of the old sys 

 tems of division can be regarded as a really natural one ; 

 those which admit but few divisions being found to leave the 

 whole range of the probable in one unbroken class, and those 

 which adopt many divisions lapsing into unavoidable vague 

 ness and uncertainty. 



21. Corresponding to the distinction between pure 



