the Theory of Probabilities. 361 



of these a prim probabilities must be, for lue, determinate ; and 

 that the sokition of the problem obtained as in art. 1 1 is, for 

 me, the true solution. Bnt then the question arises. What is the 

 meaning of the well-knowai processes which are applied on the 

 supposition of one or more of the values in question being \vholly 

 or partially vniknown ? It cannot, or at least ought not, to be 

 implied, that any hypothesis has an inherent a priori probability 

 which can be conceived to be known with chfferent degrees of 

 precision. But it is to be observed, that a quantitj^, though de- 

 terminate, may be unknown to a person who either has not per- 

 formed, or has not skill enough to perform, the calculations 

 necessary for ascertaining its value. And in this case his know- 

 ledge of it admits of all degrees, from absolute inability to give 

 a preference to any one of its possible values over any other, to an 

 approximation accompanied by any amount of belief as to its pre- 

 cision. We have, then, this intelligible answer to the question sug- 

 gested above ; namely, that in employing the methods alluded to, 

 we meet the case in which the a priori probabilities involved in the 

 problem have not been actually calculated, by introducing the 

 expression of our belief as to the result of the calculation, sup- 

 posing it performed. But there is also another intelligible 

 answer which I conceive applies to some cases. Although the 

 value of a probability relative to my particular state of informa- 

 tion may be not only determinate (as it always is), but known (as 

 it often is not), I may wish to introduce into the solution of the 

 })roblem the value Avhich it ivould have if I were in some other 

 state of information; and this value may be the subject of belief 

 differing, as in the former case, in any degree from precise 

 knowledge. 



14. With reference to the tirst of the two cases just men- 

 tioned, it must be noticed that the admission that a hypothesis 

 may be presented to my mind, without my therefore calculating 

 (or being able to calculate) its probability, by no means amounts 

 to an admission that I am not put into a definite state of belief 

 respecting it. Take, for instance, the extreme case in which I 

 cannot even guess at what the result of the calculation would be : 

 then the probability that it would tarn out to lie between p and 



p + djj is ,,,-, that is, simply dp; and since the probability of 



the hypothesis proposed would in that case be p, it follows that 

 the quantity of belief which I give to the comjxjund supposition, 

 that the result of the calculation would be as above, a)id that the 

 jK'oposed hypothesiH i.s tr\xe, is re})resented by pdp ; and there- 

 fore the wliole belief which I give to the truth of the hypothesis 



i s J pdp = -, whicti Completely agi'ces with common sense . In 



