SECT. 12.] Chance, Causation, and Design. 249 



12. For the theoretic solution of such a question we 

 require the two following data : 



(1) The relative frequency of the two classes of agencies, 

 viz. that which is to act in a chance way and that which 

 is to act designedly. 



(2) The probability that each of these agencies, if it 

 were ^the really operative one, would produce the event in 

 question. 



The latter of these data can generally be secured without 

 any difficulty. The determination of the various contin 

 gencies on the chance hypothesis ought not, if the example 

 were a suitable one, to offer any other than arithmetical 

 difficulties. And as regards the design alternative, it is 

 generally taken for granted that if this had been operative 

 it would certainly have produced the result aimed at. For 

 instance, if ten pence are found on a table, all with head 

 uppermost, and it be asked whether chance or design had 

 been at work here ; we feel no difficulty up to a certain 

 point. Had the pence been tossed we should have got ten 

 heads only once in 1024 throws; but had they been placed 

 designedly the result would have been achieved with cer 

 tainty. 



But the other postulate, viz. that of the relative preva 

 lence of these two classes of agencies, opens up a far more 

 serious class of difficulties. Cases can be found no doubt, 

 though they are not very frequent, in which this question 

 can be answered approximately, and then there is no further 

 trouble. For instance, if in a school class-list I were to see 

 the four names Brown, Jones, Robinson, Smith, standing 

 in this order, it might occur to me to enquire whether this 

 arrangement were alphabetical or one of merit. In our 

 enlarged sense of the terms this is equivalent to chance 

 and design as the alternatives ; for, since the initial letter of 



