  Reinach finds that so-called ordinal numbers are nothing but a shorthand way of referring to the (cardinal) number of terms a certain series contains up to some given term. In any given series, we have a first term, a last term, and any number of terms in between. Naturally, we may wish to denote the position of a term within an ordered series.  Yet this can quickly become very cumbersome. As Reinach notes, if we use letters to denote an ordered series of four terms—a, b, c, and d—then already “c” would be called “the term following the term following the opening term.” It is much easier simply to adopt a numerical convention according to which “c” is named in reflection of the fact that it is the term up to which the series contains three terms. Yet in no way does such designation constitute a new sort of number; in saying the series ‘contains three members up to this point’, we are still making use of the cardinal number three. Reinach writes that there is