﻿Measurement of Chance. 11 



problem, then it will be found by examination of the use of 

 such propositions that their importance depends simply on 

 the value of that chauce. If that chance is greater than a 

 certain value, the proposition will be true for the purposes 

 concerned ; if it is less, it will be false. I cannot myself ever 

 find in such propositions any meaning which is not contained 

 in the proposition : — The chance that the die will turn up 

 six is greater or less than some other chance. Accordingly 

 again, there seems no room for a probability which is distinct 

 from chance. 



11. Of the second kind of proposition an answer to the 

 following question may be taken as typical : — I have two 

 dice, of which the chances of turning up six are unequal. 

 I throw one, but I do not know which. It turns up six. 

 Which oE the two dice have I thrown? 



Here again (P. pp. 185-192), if the question is asked 

 of a single throw, it seems to me that the only possible 

 answer is simply, I do not know ; except, as before, if the 

 throw would be a ei coincidence " with one die and not with 

 the other. For, once more, if the events concerned are 

 really characterized by chances, it is inconsistent with the 

 statement that they are so characterized to assert that, at a 

 single trial, the result, if compatible with either of the two 

 " causes/' may not happen as the result of either of them. 

 If, on the other hand, the throws are repeated (while it is 

 certain that the same die is always used), and if they deter- 

 mine the chance of one die rather than that of the other, it 

 is clearly certain that this die, and not the other, is being- 

 used ; a die can be identified by its chance as certainly as 

 by its resistance or any other physical property. But 

 intermediate between these extremes, there certainly seem 

 to be cases in which, though the evidence is not sufficient 

 to enable us to assert definitely which die is being thrown, 

 we begin to suspect that it is one and not the other. The 

 possibility of such a state of mind arises from the fact that 

 there is necessarily a finite period during which the 

 evidence is accumulating ; it does not arise when, as in 

 the usual determination of resistance, the evidence is obtained 

 all at the same time. And our suspicion will increase 

 generally with the " probability " as estimated by the well- 

 known Bayes's formula for the probability of causes. In 

 this case it appears to me that there is such a thing as 

 probability, determined by but distinguishable from chance, 

 and applying to a proposition, and not to an event. But 

 I can find no reason to believe that this probability is 



