 Systems are instantiations of structures. The systems that instantiate the structure that is described by a non-algebraic theory are isomorphic with each other, and thus, for the purposes of the theory, equally good. The systems I and II that were described in  section 4.1  can be seen as instantiations of the natural number structure. \(\{\{\{\varnothing \}\}\}\) and \(\{\varnothing , \{\varnothing \}, \{\varnothing , \{\varnothing \}\}\}\) are equally suitable for playing the role of the number three. But neither are the number three. For the number three is an open place in the natural number structure, and this open place does not have any internal structure. Systems typically contain structural properties over and above those that are relevant for the structures that they are taken to instantiate.