ORDER, NUMRER, QUANTITY 273 



somewhat probable proposition to a false one is of the same 

 kind as the relation of a true proposition to one which is 

 somewhat probable, i.e., a probable proposition lies in be- 

 tween a false one and a true one. 



In view of the discussion of order these results may be 

 summarized by stating that it is essential to the notion of 

 quantities that they be orderable. Since this is still on the 

 empirical level one may define order in terms of the " be- 

 tween " relation. One may then say that quantity is a 

 property exhibited by any three-termed complex in which 

 there is a term such that (a) it has an asymmetrical relation 

 to each of the other two terms, and (b) its relation to one 

 of the terms is the converse of its relation to the other. 

 The relation "greater than," with its converse, "less than," 

 would satisfy this criterion, and enable one to order any 

 three such quantities. 



But if this were all that could be said about quantity, 

 there would be no means for distinguishing between quan- 

 tity and order. For example, a father, son, and grandson 

 could be ordered according to the relation "begets," yet 

 they would not be called quantities; events could be ar- 

 ranged in a causal chain by the relation "causes," but the 

 ordered events would not be considered quantities. What 

 is the unique feature which distinguishes a quantitative 

 series from a non-quantitative one? 



This differentiating feature is to be found in the ordering 

 relation. In a quantitative series the essential feature is 

 that the between relation should be interpretable as "greater 

 than" and "less than." This itself is an empirically given 

 relationship which is probably irreducible to anything psy- 

 chologically more primitive. Logically one sometimes de- 

 fines a greater quantity as a lesser quantity to which some- 

 thing has been added. But this does not seem to constitute 

 a psychological simplification, and it is, moreover, applicable 

 only to extensive quantities and not to intensive quantities. 

 Often a greater quantity cannot be obtained from a lesser 

 quantity by any sort of addition, especially in those cases 



