178 The Rules of Inference in Probability. [CHAP. vn. 



the question ? I quite admit the psychological fact that we 

 have degrees of belief, more or less corresponding to the 

 frequency of the events to which they refer. In the above ex 

 ample, for instance, we should undoubtedly admit on enquiry 

 that our belief in the man s return was affected by each of 

 the risks in question, so that we had less expectation of it 

 than if he were subject to either risk separately ; that is, we 

 should in some way compound the risks. But what I cannot 

 recognise is that we should be able to perform the process 

 with any approach to accuracy without appeal to the statis 

 tics, or that, even supposing we could do so, we should 

 have any guarantee of the correctness of the result with 

 out similar appeal. It appears to me in fact that but little 

 meaning, and certainly no security, can be attained by so 

 regarding the process of inference. The probabilities ex 

 pressed as degrees of belief, just as those which are expressed 

 as fractions, must, when we are put upon our justification, 

 first be translated into their corresponding facts of statistical 

 frequency of occurrence of the events, and then the in 

 ferences must be drawn and justified there. This part of 

 the operation, as we have already shown, is mostly carried 

 on by the ordinary rules of arithmetic. When we have 

 obtained our conclusion we may, if we please, translate it 

 back again into the subjective form, just as we can and do 

 for convenience into the fractional, but I do not see how the 

 process of inference can be conceived as taking place in that 

 form, and still less how any proof of it can thus be given. If 

 therefore the process of inference be so expressed it must be 

 regarded as a symbolical process, symbolical of such an in 

 ference about things as has been described above, and it 

 therefore seems to me more advisable to state and expound 

 it in this latter form. 



