 It is sometimes said that definitions are mere recipes for abbreviations. Thus, Alfred North Whitehead and Bertrand Russell say of definitions—in particular, those used in Principia Mathematica—that they are “strictly speaking, typographical conveniences (1925, 11).” This viewpoint has plausibility only for regular homogeneous definitions—though it is not really tenable even here. (Whitehead and Russell’s own observations make it plain that their definitions are more than mere “typographical  conveniences.”[3])  The idea that definitions are mere abbreviations is not at all plausible for the second kind of definition, to which let us now turn.