 One response to this difficulty is to transpose the abstractionist proposal into a more metaphysical key (see Rosen &amp; Yablo 2020). The idea is that each Fregean number is, by its very nature, the number of some Fregean concept, just as each Fregean direction is, by its very nature, at least potentially the direction of some concrete line. In each case, the abstract object is essentially the value of an abstraction function for a certain class of arguments. This is not a claim about the meanings of linguistic expressions. It is a claim about the essences or natures of the objects themselves. (For the relevant notion of essence, see Fine 1994.) So for example, the Fregean number two (if there is such a thing) is, essentially, by its very nature, the number that belongs to a concept \(F\) if and only if there are exactly two \(F\text{s}\). More generally, for each Fregean abstract object \(x\), there is an abstraction function \(f\), such that \(x\) is essentially the value of \(f\) for every argument of a certain kind.