ORDER, NUMBER, QUANTITY 257 



dropping out something, so that what one ends with con- 

 tains less than what one started with; rather one retains 

 as a variable those features which were present as values. 

 The generalization of the concept of order may be exam- 

 ined from several points of view, all of which are essentially 

 equivalent. One is that of serial exlension. It seems obvious 

 that the relational-structure of an empirical series is not 

 changed by the discovery of an additional element; hence a 

 series does not become any less so by passing from a three- 

 termed series to an n-termed series. All that is required is 

 that the element designated as unique in the definition of 

 " betweenness v should no longer be considered as such; if 

 the series is ^-termed, where n is greater than 3, any ele- 

 ment except the first or the last may be the element which 

 was formerly spoken of as unique. Hence the attempt is 

 made to define the relation of betweenness in such a way 

 as to make it applicable generally to the series. An equiva- 

 lent result could be accomplished through an operation of 

 interpolation, i.e., by recognizing that an empirical series is 

 not changed by the discovery of a new element which would 

 presumably lie between two elements supposed to be adja- 

 cent; the notion of adjacency is not essential to the concept 

 of order. Through considerations of this kind many features 

 of the empirical series are seen to be essentially irrelevant 

 to the concept of order. It is seen that an order as such 

 involves no specific reference to the number of terms, except 

 that n must be at least 3 (or at least 2, if one wishes to in- 

 clude the directional features of nature under the concept 

 of order); this is to say that a series does not need a first 

 term nor does it need a last term in order to be a series. It is 

 also seen that an order as such involves no specific reference 

 to adjacency; this is to say that a series may have a term 

 between any two and still remain a series. 



order: scientific content 



The scientific concept of order, thus derived, is capable 

 of precise formulation. One of the most satisfactory of the 



