Non-Eliminative Structuralism, Fregean Abstraction, and Non-Rigid Structures

Linnebo and Pettigrew (Philos Q 64:267–283, 2014) have recently developed a
version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They recognize that this version of structuralism is vulnerable to
the well-known problem of non-rigid structures. This paper ofers a solution to the
problem for this version of structuralism. The solution involves expanding the languages used to describe mathematical structures. We then argue that this solution is
philosophically acceptable to those who endorse mathematical structuralism based
on Fregean abstraction principles.