OPINION AND PROBABILITY 285 



is \ and f respectively, agree in affirming the occurrence of an event . . . whose 

 antecedent probability is \ . . .&quot; But the whole practical difficulty the 

 practical impossibility, it may be called lies precisely in fixing, with any pre 

 tension to mathematical accuracy, the degree of probability as to their accur 

 acy in such cases. Of course, if that could be done, the value of their combined 

 testimony would be x \ = T \ that the event occurred, and i x 4 = 7 V that 

 it did not occur : the odds are 6 to I in its favour, and its probability is . 

 But how can the accuracy of their testimony be so estimated ? Is it because 

 they have been found to tell the truth three out of four times, and two out of 

 three times, respectively ? But then their carefulness and competence (scientia), 

 no less than their truthfulness (veracitas), must be taken into account. And, 

 furthermore, the general conditions are so variable, the fluctuations to which 

 human character is subject under the influence of strong motives and temp 

 tations are so great and so uncertain, as to render the whole calculation 

 practically worthless (cf. 260, 261). 



To take another instance from the social sciences : A judge delivers a 

 wrong sentence once in ten times on an average ; can he be compared, as 

 Condorcet and Poisson have compared him, to an urn containing nine white 

 balls and one black one ? The comparison is scarcely less inaccurate than 

 uncomplimentary. Bertrand s criticism is unanswerable : &quot; The urn is as passive 

 and indifferent to the influences playing upon it as the balls ; and the general 

 set of conditions remains ever and always the same throughout the repeated 

 drawings. But the judges listen to the evidence, and consult with one another 

 about it ; they hear the same facts, and each bases his sentence, whether it be 

 wrong or right, upon those same facts. And just as one has his reasons for 

 judging rightly, so has the other his reasons for judging in the opposite sense. 

 It is not that he has put his hand, as it were, into the urn of his own mind, 

 and drawn forth by chance an erroneous sentence. No ; the influences that 

 lead up to that sentence are of quite a different order from those that deter 

 mine the drawing of a ball from an urn. He has believed a false witness, or 

 distrusted an honest one, owing to some unfortunate combination of circum 

 stances ; or he has been unduly influenced by the pleading of a clever advo 

 cate ; or he has perhaps been prejudiced by self-interest or some other 

 consideration. The very same objective evidence has elicited just the opposite 

 sentence from his two colleagues ; so that the probability of their pronouncing 

 all three the same sentence is not at all to be compared with the probability 

 of drawing three balls of the same colour by three independent draws.&quot; 1 



269. FUNCTIONS OF STATISTICS AND AVERAGES: THEIR 

 RIGHT AND WRONG INTERPRETATIONS. 2 In the presence of such 

 complex social phenomena as we have referred to already, or of 

 complex natural phenomena like those relating to climate, for 

 example, where unknown causes are interfering, through un 

 discovered laws, with those already known, the compilation of 

 statistics and averages will enable us to lay down highly probable, 

 or morally certain, judgments, not about the happening of an 



1 J. BERTRAND, Calcul des probability, p. 236. 

 2 C/. MBRCIER, Logique, pp. 349-51, 361-70. 



