 Whitehead and Russell define a series in volume II of Principia Mathematica at *204.01 as the class Ser of all relations which is transitive, connected and irreflexive. A relation \(R\) is transitive when, if \(xRy\) and \(yRz\) then \(xRz\). It is connected when for any \(x\) and \(y\) for which it is defined, either \(xRy\) or \(yRx\). Finally, an irreflexive relation is one such that for all \(x\), it is not the case that \(xRx\). Any relation that has those properties forms a series of the things that it relates. Such relations are now called “linear orderings” or simply, “orderings”. Here the “logical construction” simply consists of an implicit definition of a certain property of relations. There is certainly no thought that series are merely invented “fictions”, and the symbol ‘Ser’ for them is “incomplete” only in that it can be explicitly defined as the intersection of other classes (a class of classes) and classes are themselves “incomplete”.