MEASUREMENTS 199 



performance of the Messiah. Similarly, when we say that 

 we would sooner hear a good sermon on Sunday, and a good 

 symphony on the day following, than either without the 

 other, we are pronouncing a perfectly sound and intel 

 ligible judgement. If, however, we say that we prefer both 

 at the same time, we are talking nonsense ; there would 

 then be no aggregate of pleasures, but a single disagreeable 

 feeling. There is nothing in the summation of pleasures 

 that remotely resembles the addition of one bucket of 

 water to another in the same tank ; but there is what may 

 be compared in some respects, but not all, with the addition 

 of a second bucket of water to soil which has already received 

 one. The difference in the second case is, that the cumula 

 tive effect may be measured, while with pleasures, though 

 equally real, it can only be estimated, and not measured. 

 The question of the summation of pleasures is usually 

 discussed with reference to the concept of an empirical 

 summum bonum as the end of action. Professor Green 

 argues : To say that ultimate good is a greatest possible 

 sum of pleasures, strictly taken, is to say that it is 

 an end which for ever recedes ; which is not only unattain 

 able but, from the nature of the case, can never be more 

 nearly approached ; and such an end clearly cannot serve 

 the purpose of a criterion, by enabling us to distinguish 

 actions which bring men nearer to it from those that do 

 not. Without such reference, (i. e. to a summum bonum), 

 is there any meaning in approval or disapproval at all ? 

 Surely there is. All appreciations, whether ethical or other, 

 start from a minimum, and not from a maximum. Like 

 number, they all proceed in a series which may be produced 

 to infinity. This is equally true whether our appreciation 

 has a mathematical counterpart or not. Three is more than 

 two when compared with one, but not when compared 

 with infinity ; a mile is longer than a furlong when com 

 pared with an inch, but not when compared with the 

 distances of infinite space. The mere fact that we are 

 unable to subtract degrees of pleasure from a hypothetical 

 1 Quoted by Mr. Rashdall, p. 359. 



