112 WHAT IS SCIENCE? 



potatoes has another definite property, namely the 

 number of potatoes in it, and the number is as much a 

 property of the object which we call a sack of potatoes 

 as its weight or its cost. This property can be (and 

 must be) " represented by a number " just as the weight 

 can be ; for instance, it might be represented by 200. 

 But this " 200 " is not itself a property of the sack ; 

 it is a mere mark on the paper for which would be sub- 

 stituted, if I was speaking instead of writing, a spoken 

 sound ; it is a name or symbol for the property. When 

 we say that measurement is the representation of 

 properties by " numbers," we mean that it is the repre- 

 sentation of properties, other than number, by the 

 symbols which are always used to represent number. 

 Moreover, there is a separate word for these symbols ; 

 they are called " numerals." We shall always use that 

 word in future and confine " number " to the meaning 

 of the property which is always represented by numerals. 



These considerations are not mere quibbling over 

 words ; they bring out clearly an important point, 

 namely, that the measurable properties of v an object 

 must resemble in some special way the property number, 

 since they can be fitly represented by the same symbols ; 

 they must have some quality common with number. 

 We must proceed to ask what this common quality is, 

 and the best way to begin is to examine the property 

 number rather more closely. 



The number of a sack of potatoes, or, as it is more 

 usually expressed, the number of potatoes contained 

 in it, is ascertained by the process of counting. Count- 

 ing is inseparably connected in our minds to-day with 

 numerals, but the process can be, and at an earlier stage 

 of civilization was, carried on without them. Without 

 any use of numerals I can determine whether the number 

 of one sack of potatoes is equal to that of another. For 

 this purpose I take a potato from one sack, mark it in 



