OF THE CALCULATION OF CHANCES. 65 



as more likely than the rest to surpass the average proportion, 

 it follows that we cannot rationally presume this of any; 

 which we should do, if we were to bet in favour of it, receiving 

 less odds than in the ratio of the number of the other kinds. 

 Even, therefore, in this extreme case of the calculation of 

 probabilities, which does not rest on special experience at all, 

 the logical ground of the process is our knowledge, such 

 knowledge as we then have, of the laws governing the frequency 

 of occurrence of the different cases ; but in this case the 

 knowledge is limited to that which, being universal and axio- 

 matic, does not require reference to specific experience, or to 

 any considerations arising out of the special nature of the 

 problem under discussion. 



Except, however, in such cases as games of chance, where 

 the very purpose in view requires ignorance instead of know- 

 ledge, I can conceive no case in which we ought to be satisfied 

 with such an estimate of chances as this ; an estimate founded 

 on the absolute minimum of knowledge respecting the subject. 

 It is plain that, in the case of the coloured balls, a very slight 

 ground of surmise that the white balls were really more 

 numerous than either of the other colours, would suffice to 

 vitiate the whole of the calculations made in our previous 

 state of indifference. It would place us in that position of 

 more advanced knowledge, in which the probabilities, to us, 

 would be different from what they were before ; and in esti- 

 mating these new probabilities we should have to proceed on 

 a totally different set of data, furnished no longer by mere 

 counting of possible suppositions, but by specific knowledge 

 of facts. Such data it should always be our endeavour to 

 obtain ; and in all inquiries, unless on subjects equally beyond 

 the range of our means of knowledge and our practical uses, 

 they may be obtained, if not good, at least better than none 

 at all.* 



* It even appears to me that the calculation of chances, where there are 

 no data grounded either on special experience or on special inference, must, 

 in an immense majority of cases, break down, from sheer impossibility of 

 assigning any principle by which to be guided in setting out the list of pos- 

 sibilities. In the case of the coloured balls we have no difficulty in making 



VOL. II. 5 



