 Benacerraf’s challenge can be mounted for the objects that non-algebraic theories appear to describe. But his challenge does not apply to algebraic theories. Algebraic theories are not interested in mathematical objects per se; they are interested in structural aspects of mathematical objects. This led Benacerraf to speculate whether the same could not be true also of non-algebraic theories. Perhaps the lesson to be drawn from Benacerraf’s identification problem is that even arithmetic does not describe specific mathematical objects, but instead only describes structural relations?