274 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



where the greater does not seem to extend beyond the lesser 

 in any sense. For example, liquids may be arranged into a 

 quantitative specific gravity series on the basis of the rela- 

 tion "floats in," but this does not involve the notion that a 

 substance of high specific gravity extends beyond one of 

 low specific gravity. One simply decides that the relation 

 "floats in ,: determines a quantitative distinction. Essen- 

 tially the same technique is employed in arranging sub- 

 stances according to hardness on the basis of the relation 

 'scratches," and in the arrangement of masses according 

 to weight on the basis of the relation "displaces on a bal- 

 ance." The relation "greater than" can be defined only 

 as the abstract feature which each of these ordering relations 

 exhibits. 



It can be seen that at the empirical level the notion of 

 quantity is not dependent in any way either upon the notion 

 of number or upon the notion of measurement. Numbered 

 groups are, of course, quantities, since they may be arranged 

 in an order on the basis of the relation "greater than"; 

 they are, in fact, one of the most basic quantitative notions 

 since they afford the pattern for the understanding of the 

 less clear quantitative notions. But it does not seem essen- 

 tial to a quantity that it be measurable, and it does not 

 seem advisable to define the notion in this way. On the 

 empirical level quantity may be roughly defined as the 

 property exhibited by the elements of an event of at least 

 threefold complexity when these elements are similar in 

 some respect and capable of being ordered according to a 

 relation which may be interpreted as "greater than." 



QUANTITY : OPERATIONAL DERIVATION 



Empirical quantity is incorporated into scientific con- 

 ceptual schemes through the technique of measurement. 

 Scientific quantity, as will be seen presently, is identified 

 with measured value. Hence the operational transformation 

 of empirical quantity is such as can be accomplished through 

 the application of measurement. The detailed description 



