SECT. 30.] Measurement of Belief. 155 



receive something, say a shilling, as the minimum receipt. 

 My receipts increase in proportion to the rarity of each 

 particular kind of set, and each kind is observed or inferred 

 to grow more rare in a certain definite but unlimited order. 

 By the wording of the problem, properly interpreted, I am 

 supposed never to stop. Clearly therefore, however large a 

 fee I pay for each of these sets, I shall be sure to make it up 

 in time. The mathematical expression of this is, that I 

 ought always to pay an infinite sum. To this the objection 

 is opposed, that no sensible man would think of advancing 

 even a large finite sum, say 50. Certainly he would not ; 

 but why ? Because neither he nor those who are to pay 

 him would be likely to live long enough for him to obtain 

 throws good enough to remunerate him for one-tenth of his 

 outlay ; to say nothing of his trouble and loss of time. We 

 must not suppose that the problem, as stated in the ideal 

 form, will coincide with the practical form in which it 

 presents itself in life. A carpenter might as well object to 

 Euclid s second postulate, because his plane came to a stop 

 in six feet on the plank on which he was at work. Many 

 persons have failed to perceive this, and have assumed that, 

 besides enabling us to draw numerical inferences about the 

 members of a series, the theory ought also to be called upon 

 to justify all the opinions which average respectable men 

 might be inclined to form about them, as well as the conduct 

 they might choose to pursue in consequence. It is obvious 

 that to enter upon such considerations as these is to diverge 

 from our proper ground. We are concerned, in these cases, 

 with the actions of men only, as given in statistics ; with the 

 emotions they experience in the performance of these actions 

 we have no direct concern whatever. The error is the same 

 as if any one were to confound, in political economy, value in 

 use with value in exchange, and object to measuring the 



