MEASUREMENT 121 



measure electrical resistance. And the discovery of 

 similar laws has made possible the development of other 

 branches of physics. 



But, it may be asked, has there ever been a failure to 

 discover the necessary laws ? The answer is that there 

 are certainly many properties which are not measurable 

 in the sense that we have been discussing ; there are more 

 properties, definitely recognized by science, that are not 

 so measurable than are so measurable. But, as will 

 appear presently, the very nature of these properties 

 makes it impossible that they should be measured in this 

 way. For the only properties to which this kind of 

 measurement seems conceivably applicable, are those 

 which fulfil the condition stated provisionally on p. in ; 

 they must be such that the combination of objects 

 possessing the property increases that property. For 

 this is the fundamental significance of the property 

 number ; it is something that is increased by addition ; 

 any property which does not agree with number in this 

 matter cannot be very closely related to number and 

 cannot possibly be measured by the scheme that has been 

 described. But it will be seen that fulfilment of this 

 condition only makes rule (2) true ; it is at least conceiv- 

 able that a property might obey rule (2) and not rules (i) 

 and (3). Does that ever happen, or can we always find 

 methods of addition and of judging equality such that, if 

 rule (2) is true, the laws are such that rules (i) and (3) 

 are also true ? In the vast majority of cases we can find 

 such methods and such laws ; and it is a very remarkable 

 fact that we can ; it is only one more instance of the way 

 in which nature kindly falls in with our ideas of what 

 ought to be. But I think there is one case in which the 

 necessary methods and laws have not yet been found and 

 are not likely to be found. It is a very difficult matter 

 concerning which even expert physicists might differ, 

 and so no discussion of it can be entered on here. But 



