In recent philosophy of mathematics a variety of writers have presented “structuralist” views and arguments. There are, however, a number of substantive differ- ences in what their proponents take “structuralism” to be. In this paper we make explicit these differences, as well as some underlying similarities and common roots. We thus identify systematically and in detail, several main variants of structuralism, including some not often recognized as such. As a result the relations between these variants, and between the respective problems they face, become manifest. Throughout our focus is on semantic and metaphysical issues, including what is or could be meant by “structure” in this connection.
Description:
In recent philosophy of mathematics a variety of writers have presented “structuralist” views and arguments. There are, however, a number of substantive differ- ences in what their proponents take “structuralism” to be. In this paper we make explicit these differences, as well as some underlying similarities and common roots. We thus identify systematically and in detail, several main variants of structuralism, including some not often recognized as such. As a result the relations between these variants, and between the respective problems they face, become manifest. Throughout our focus is on semantic and metaphysical issues, including what is or could be meant by “structure” in this connection.