the Theory of Probabilities. 359 



" common sense/^ This accordance is nowhere more conspicuous 

 than in those cases in which a numerical result cannot be obtained 

 with certainty, from the difficulty of assigning the actual values 

 of the quantities which appear in the formulae. It becomes 

 apparent in such instances from a consideration of the forms of 

 the expressions, and of the effects of supposed variation in the 

 quantities involved in them, and particularly from an examination 

 of extreme cases. And the comparative conclusions which can 

 be thus arrived at are probably quite as useful and instructive 

 as any absolute result would be, supposing it attainable. 



10. Let us first observe, that though thei'e is no such thing 

 as chance, that is, occurrence of events without any cause, there 

 is such a thing as accident, that is, occurrence of events from causes 

 not connected with some supposed plan or design. If I arrange 

 my books with reference solely to their size, their arrangement 

 as to subjects will be accidental. Not that it will be determined 

 without cause ; but, on the contraiy, by a complex system and 

 sequence of causes. Since, however, we have no means of tra- 

 cing this sequence, we give up the attempt as hopeless, and look 

 upon the supposed occmi-ence of all the possible arrangements 

 as exhaustive hypotheses about which we know nothing more, 

 so long as we do not know what the actual arrangement is. 



11. Now suppose I go into a room and see a number of balls 

 laid on a table, and disposed in some regular figure, say a circle. 

 Somebody must have put them there. But was it part of his 

 intention to place them in a circle, or did he merely mean to lay 

 them on the table, without intending any particular arrangement ? 

 In the latter case the circular disposition would be accidental. 

 " Common sense," however, suggests an irresistible conviction 

 that it was intentional. What is the account of this conviction ? 

 Is it enough to say that the mind is " impatient of causeless 

 phjenomena?" I think not; because the mind is surely quite 

 as impatient of an irregular or complex causeless phajnomenon, 

 as of a regular or simple one. It would be truer to say that the 

 mind refers a simple phfcnomenon to a simple cause (such as 

 design), and a complex pha^nomenon to a complex system of 

 causes (such as accident) j and this would perhaps be a sufficient 

 " common sense " explanation. Let us see how far it is in ac- 

 cordance with the mathematical theory. 



Let a be the « priori probability that the observed arrange- 

 ment would occur by accident. This is of course the same, 

 whether that an-angement be regular or not. Let d be the 

 a priori ])rol)ability that the ])(rson wlio placed the balls on the 

 table designed some arrangement ; and let r be the probability 

 that if he did, he would design some regular arrangement. 

 Finally, let p l)e the probability that if he designed a regular 



