272 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



same quantity. This aspect of quantity is not apparent but 

 may be made clear after a moment's consideration. Quan- 

 tity is usually supposed to be relative in the sense that it 

 always involves a relation of greater or less, i.e., an event 

 is called a quantity only if it is greater or less in some respect 

 than some other quantity. For example, a line is called 

 long because of the existence of another line which is short, 

 and a stone is called heavy because of the existence of another 

 stone which is light, and so on. From this point of view 

 no event could be called a quantity unless there existed at 

 least one other event to which it bore a certain relation. It 

 seems, however, that quantity is relative in a somewhat 

 more complicated sense than this. Quantity, in fact, never 

 arises unless there is something akin to the notion of an 

 intermediate or "between' 1 element, and this necessarily 

 involves at least three events. Suppose, for example, that 

 in a certain community every day were either hot, say 90°, 

 or cold, say 20°, and there were no days of intervening 

 temperature; it is not likely that in such a community the 

 notion of heat as a quantity would arise. Heat would be 

 considered as an absolute quality possessed by certain days 

 and lacking from certain other days; hot days would be 

 related to cold days as positive to negative, or the reverse. 

 Similarly, if all light was either very bright or very dim, 

 there would probably arise no conception of light intensity ; 

 and if all pleasures were of very great or very minute in- 

 tensity, there would probably arise no conception of quan- 

 tity of pleasure. Quantity arises only when there occur 

 three events similar in kind but so connected that the 

 relation of the first to the second is of essentially the same 

 kind as the relation of the second to the third, or, what 

 amounts to the same thing, when one event is between the 

 others and has a relation to one of them which is the con- 

 verse of its relation to the other. For example, so long as 

 propositions are considered to be either true or false, the 

 notion of degrees of truth cannot arise; but once the notion 

 of probability is introduced it is seen that the relation of a 



