the Theory of Probabilities. 355 



culty is real, but merely relative to our knowledge and skill ; 

 the latter, if real, would be absolute, and inherent in the subject- 

 matter, which I conceive to be not the case. (See the paper in 

 the Philosophical Magazine for December 1850, arts. 6, 17, 18.) 



4. SecontUy, it is of course familiar to all who have thought 

 or read modern works on the subject, that the " probability " 

 which is estimated numerically means merely " quantity of 

 belief," and is nothing inherent in the hypothesis to which it 

 refers. It is therefore always relative to a particular state of 

 knowledge or ignorance ; but it must be observed that it is ab- 

 solute in the sense of not being relative to any individual mind ; 

 since, the same information being presupposed, all minds ought 

 to distribute their belief in the same way. It is to be regretted 

 that the usual terminology of the subject makes it almost neces- 

 sary to repeat this otherwise superfluous remark at the beginning 

 of every discussion. Thus it is usual to say that "certainty is 

 represented by 1 ;" where what is (or ought to be) meant is that 

 "entire belief" is represented by 1. The word "certainty " 

 naturally suggests the idea of the absolute truth of the thing 

 believed ; whereas people very often " entirely believe " what is 

 not true ; and this state of belief is represented (as to its quan- 

 tity) by 1, just as correctly as where the thing believed is abso- 

 lutely tnie. 



5. Thirdly, it is to be observed that the whole theory may be 

 truly described, in a certain sense, as "knowledge founded upon 

 ignorance;" but I think it might be more adequately designated 

 as " a method of avoiding the erection of belief upon ignorance." 

 I make this obsen'ation with reference to a remark of Mr. Ellis's 

 (Philosophical Magazine for November 1850, p. 325), concerning 

 which I shall have more to say hereafter. At present it will not 

 be out of place to notice briefly the natui'e of the ai'gument com- 

 monly called the " sufiicicnt reason," the true character of which 

 appears to be often misconceived. Its force in all cases depends 

 (as it seems to me) u])on a previous assumption that an intelligible 

 law exists concerning the matter in question. If this assumption 

 be admitted, and if it can be shown that there is only one intel- 

 ligible law, then that must be the actual law. Thus we may 

 argue that the angles at the base of an isosceles triangle are equal 

 (not because there is no reason why one should be greater than 

 the other, but), because, if not, no intelligible statement could be 

 given of ichir.h is the greater. And in like manner, a person who 

 should dispute the propriety of dividing our belief equally 

 amongst hypotheses about which we are equally ignorant, ought 

 to be refuted by asking him to state which is to be preferred. 

 He must either admit the proposed law, or maintain that there 

 is QO law at all. 



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