Abstract

The paper offers an overview of the motivation for structuralist ontology of mathematics and of the main structuralist position. It discusses the shortcomings ofeliminativist structuralism, and then presents the more promising options: ante rem structuralism, Platonic structuralism, and Parsons’ particular version of structuralism. Our discussion does not cover all of the issues that have relevance for the choice of the particular version of mathematical structuralism, but we do focus on the problem of indeterminacy and on the solution to it. So the positions of some versions of structuralism and the solutions to the problem of indeterminacy are briefly presented and compared, and a clear picture of structuralist ontologies is drawn.