354 Prof. Donkin on certain Questions relating to 



whole theoiy is the following : — JVhen several hypotheses are pre- 

 sented to our mind, which me believe to be mutualhj exclusive and 

 exhamtive, but about which we know nothing further, we distribute 

 our belief equally amongst them. I mean by these expressions to 

 imply, that the hypotheses not only exhaust the whole range of 

 possibility, but also that they exclude one another, so that one 

 nnist be true and all the rest false. If n be the number of such 



hypotheses, and entire belief be denoted by unity, then - is the 



quantity of belief we give to each of them. Moreover, if we 



select a group of m hAjpotheses out of these n, the quantity of 



belief which we give to the complex hypothesis that some one of 



these m is true, is the sum of the quantities which we give to 



m 

 each of them, namely — . 



2. This being admitted as an account of the May in which we 

 actually do distribute our belief in simple cases, the whole of the 

 subseqvient theory follows as a deduction of the way in which 

 we must distribute it in complex cases, if we would be consistent. 

 And as ecpial distribution is the only possible (because the only 

 intelligible) laic in the case of hypotheses about which we have 

 no information, so the laws which are deduced from it as appli- 

 cable to the cases in which we have some information (which con- 

 stitute the complex cases occurring in practice), are also, in those 

 cases, the only possible laws; since any other mode of distribu-' 

 tion would be found, when completely analysed, to rest upon a 

 random preference of one hypothesis to another about which we 

 are equally ignorant. We must therefore either accept the theory 

 of probabilities with all its developments, or we must abandon 

 the idea of getting a rational belief at all in any case where ab- 

 solute knowledge is unattainable. And every attempt to acquire 

 such a rational (as distinct from a random) belief, is an attempt, 

 however unconscious, rude and imperfect, to apply the princi- 

 ples of the mathematical theory. 



3. Several important remarks suggest themselves in reference 

 to what has just been said. And first, I do not see on what 

 ground it can be doubted that every definite state of belief con- 

 cerning a proposed hypothesis is in itself capable of being repre- 

 sented by a numerical expression, however difficult or impracti- 

 cable it may be to ascertain its actual value. It would be very 

 difficult to estimate in numbers the vis viva of all the particles 

 of a human body at any instant ; but no one doubts that it is 

 capable of numerical expression. I mention this point, because 

 I am not sure that Professor Forbes has distinguished the diffi- 

 culty of ascertaining numbers in certain cases from a supposed 

 difficulty of expression by means of numbers. The former diffi- 



