 Abstraction functions have two key features. First, for each abstraction function \(f\) there is an equivalence relation \(R\) such that it lies in the nature of \(f\) that \(f(x)\! =\! f(y)\) iff \(Rxy\). Intuitively, we are to think that \(R\) is metaphysically prior to \(f\), and that the abstraction function \(f\) is defined (in whole or in part) by this biconditional. Second, each abstraction function is a generating function: its values are essentially values of that function. Many functions are not generating functions. Paris is the capital of France, but it is not essentially a capital. The number of solar planets, by contrast, is essentially a number. The notion of an abstraction function may be defined in terms of these two features: