[bowman] fundamental PROCESSES IN HISTORICAL SCIENCE 507 



black and 10 white beans thrown into a box, the probability that a 

 white bean would be touched first by a blindfolded person would be 

 10/15 or 2/3 (=10 chances out of 15, or 2 chances out of 3), while 

 the probability against this event and in favor of the touching of a 

 black bean first would be 5 /1 5 or 1 /3 ( = 5 chances out of 15 or 1 chance 

 out of 3)." 



The Century Dictionary (New York; The Century Company), 

 in a lengthier definition of probability and of the fundamental rules 

 governing it in its logical and mathematical sense, enunciates the 

 following two principles: — 



(1) "Probability has been defined as the degree of belief 

 which ought to be accorded to a problematical judgment; 

 but this conceptualistic probability, as it is termed, is strictly 

 not probability, but a sense of probability. Probability may be 

 measured in different ways. The conceptualistic measure is the 

 degree of confidence to which a reason is entitled ; it is used in the 

 mental process of balancing reasons pro and con. . . . But 

 the measure which is most easily guarded against the fallacies 

 which beset the calculation of probabilities is the ratio of the 

 number of favorable cases to the whole number of equally pos- 

 sible cases, or the ratio of the number of occurrences of the event 

 to the total number of occasions in the course of experience. 

 This ratio is called the probability or chance of an event. Thus 

 the probability that a die will turn up ace is 1 /6." (=1 favorable 

 case or chance out of 6). 



(2) "The chief practical application of probability is to 

 insurance and its only significance lies in an assurance as to the 

 average result in the long run." 



The reference in the 2nd principle here enunciated is not to the 

 inferior conceptualistic measure of probability or "balancing of reasons 

 pro and con," but to the superior measure or ratio described in the 

 1st principle as most easily guarded against fallacies. 



PROBABILITY AS A CRITERION OF HISTORICAL CONCLUSIONS, EXCEPT 



WHERE THEY REPRESENT AVERAGED RESULTS, IS CONDEMNED BY 



IMPARTIAL DEFINITIONS. 



The Century definition is drawn from the stand-point of science 

 in general, therefore it is impartial with respect to any one of its 

 branches, such as historical science, which is here especially under 

 consideration. According to the definition there are two measures 



