Permalink : http://hdl.handle.net/2115/35042

Structuralism considers structures to be principal. According to in re structuralism, a structure resides in particular systems exemplifying the former. I characterize a schema for any mathematical entity as a pattern framed by its definition including its axioms in mathematics, no matter how described by set theory or category theory. The aim of this paper is to present in re structuralism by schema and to argue for it. In re structuralism commits less abstract entities than ante rem structuralism. From the presented position we can regard all the structures (including variable sets) as schemas framed by definitions in mathematics. Such schemas can be comprehended through mathematicians' communication in metalanguage.